9.7: Activity of an Uncharged Species
The activity \(a_i\) of uncharged species \(i\) (i.e., a substance) is defined by the relation \begin{gather} \s{ a_i \defn \exp\left(\frac{\mu_i-\mu_i\st}{RT}\right) } \tag{9.7.1} \cond{(uncharged species)} \end{gather} or \begin{gather} \s{ \mu_i = \mu_i\st + RT\ln a_i } \tag{9.7.2} \cond{(uncharged species)} \end{gather} where \(\mu_i\st\) is the standard chemical potential of the species. The activity of a species in a given phase is a dimensionless quantity whose value depends on the choice of the standard state and on the intensive properties of the phase: temperature, pressure, and composition.
Some chemists define the activity by \(\mu_i = \mu_i\rf + RT\ln a_i\). The activity defined this way is not the same as the activity used in this e-book unless the phase is at the standard pressure.
The quantity \(a_i\) is sometimes called the relative activity of \(i\), because it depends on the chemical potential relative to a standard chemical potential. An important application of the activity concept is the definition of equilibrium constants (Sec. 11.8.1).
For convenience in later applications, we specify that the value of \(a_i\) is the same in phases that have the same temperature, pressure, and composition but are at different elevations in a gravitational field, or are at different electric potentials. Section 9.8 10.1 will describe a modification of the defining equation \(\mu_i = \mu_i\st + RT\ln a_i\) for a system with phases of different elevations, and Sec. 10.1 will describe the modification needed for a charged species.
9.7.1 Standard states
The standard states of different kinds of mixture components have the same definitions as those for reference states (Table 9.3), with the additional stipulation in each case that the pressure is equal to the standard pressure \(p\st\).
When component \(i\) is in its standard state, its chemical potential is the standard chemical potential \(\mu\st_i\). It is important to note from Eq. 9.7.2 that when \(\mu_i\) equals \(\mu_i\st\), the logarithm of \(a_i\) is zero and the activity in the standard state is therefore unity.
The following equations in the form of Eq. 9.7.2 show the notation used in this e-book for the standard chemical potentials and activities of various kinds of uncharged mixture components: \begin{equation} \tx{Substance \(i\) in a gas mixture} \qquad \mu_i = \mu_i\st\gas + RT\ln a_i\gas \tag{9.7.3} \end{equation} \begin{equation} \tx{Substance \(i\) in a liquid or solid mixture} \qquad \mu_i = \mu_i\st + RT\ln a_i \tag{9.7.4} \end{equation} \begin{equation} \tx{Solvent A of a solution} \qquad \mu\A = \mu\A\st + RT\ln a\A \tag{9.7.5} \end{equation} \begin{equation} \tx{Solute B, mole fraction basis} \qquad \mu\B = \mu\xbB\st + RT\ln a\xbB \tag{9.7.6} \end{equation} \begin{equation} \tx{Solute B, concentration basis} \qquad \mu\B = \mu\cbB\st + RT\ln a\cbB \tag{9.7.7} \end{equation} \begin{equation} \tx{Solute B, molality basis} \qquad \mu\B = \mu\mbB\st + RT\ln a\mbB \tag{9.7.8} \end{equation}
9.7.2 Activities and composition
We need to be able to relate the activity of component \(i\) to the mixture composition. We can do this by finding the relation between the chemical potential of component \(i\) in its reference state and in its standard state, both at the same temperature. These two chemical potentials, \(\mu_i\rf\) and \(\mu_i\st\), are equal only if the mixture is at the standard pressure \(p\st\).
It will be useful to define the following dimensionless quantity: \begin{equation} \G_i \defn \exp\left(\frac{\mu_i\rf-\mu_i\st}{RT}\right) \tag{9.7.9} \end{equation} The symbol \(\G_i\) for this quantity was introduced by Pitzer and Brewer ( Thermodynamics , 2nd edition, McGraw-Hill, New York, 1961, p. 249). They called it the activity in a reference state . To see why, compare the definition of activity given by \(\mu_i = \mu_i\st + RT\ln a_i\) with a rearrangement of Eq. 9.7.9: \(\mu_i\rf = \mu_i\st + RT\ln\G_i\).
At a given temperature, the difference \(\mu_i\rf-\mu_i\st\) depends only on the pressure \(p\) of the mixture, and is zero when \(p\) is equal to \(p\st\). Thus \(\G_i\) is a function of \(p\) with a value of 1 when \(p\) is equal to \(p\st\). This e-book will call \(\G_i\) the pressure factor of species \(i\).
To understand how activity is related to composition, let us take as an example the activity \(a\mbB\) of solute B based on molality. From Eqs. 9.5.18 and 9.7.8, we have \begin{equation} \begin{split} \mu\B & = \mu\mbB\rf + RT\ln\left(\g\mbB\frac{m\B}{m\st}\right) \cr & = \mu\mbB\st + RT\ln a\mbB \end{split} \tag{9.7.10} \end{equation} The activity is then given by \begin{equation} \begin{split} \ln a\mbB & = \frac{\mu\mbB\rf-\mu\mbB\st}{RT} + \ln\left(\g\mbB\frac{m\B}{m\st}\right)\cr & = \ln\G\mbB + \ln\left(\g\mbB\frac{m\B}{m\st}\right) \end{split} \tag{9.7.11} \end{equation} \begin{equation} a\mbB = \G\mbB \g\mbB\frac{m\B}{m\st}\hspace{2.28cm} \tag{9.7.12} \end{equation} The activity of a constituent of a condensed-phase mixture is in general equal to the product of the pressure factor, the activity coefficient, and the composition variable divided by the standard composition.
We are now able to write explicit formulas for \(\G_i\) for each kind of mixture component. They are collected in Table 9.6.
Considering a constituent of a condensed-phase mixture, by how much is the pressure factor likely to differ from unity? If we use the values \(p\st=1\br\) and \(T=300\K\), and assume the molar volume of pure \(i\) is \(V_i^*=100\units{cm\(^3\) mol\(^{-1}\)}\) at all pressures, we find that \(\G_i\) is \(0.996\) in the limit of zero pressure, unity at \(1\br\), \(1.004\) at \(2\br\), \(1.04\) at \(10\br\), and \(1.49\) at \(100\br\). For a solution with \(V\B^{\infty}=100\units{cm\(^3\) mol\(^{-1}\)}\), we obtain the same values as these for \(\G\xbB\), \(\G\mbB\), and \(\G\cbB\). These values demonstrate that it is only at high pressures that the pressure factor differs appreciably from unity. For this reason, it is common to see expressions for activity in which this factor is omitted: \(a_i=\g_i x_i\), \(a\mbB=\g\mbB m\B/m\st\), and so on.
In principle, we can specify any convenient value for the standard pressure \(p\st\). For a chemist making measurements at high pressures, it would be convenient to specify a value of \(p\st\) within the range of the experimental pressures, for example \(p\st=1\units{kbar}\), in order that the value of each pressure factor be close to unity.


2 .
A laboring patient presents with a persistent occiput posterior position. How should a nurse explain the fetal causes of dystocia in this situation, and what nursing interventions might be beneficial in managing dystocia related to fetal factors?
3 .
A patient in active labor shows signs of slowed progress. How should a nurse explain the reasons for augmenting labor, and what nursing actions could be employed to facilitate the augmentation process?
4 .
A patient experiences variable decelerations in fetal heart rate patterns, and the health-care provider orders amnioinfusion. How would you explain the reasons for amnioinfusion, and what nursing actions should be implemented during and after the procedure?
5 .
A pregnant patient has a preexisting endocrine condition like diabetes. How should a nurse explain the pathophysiology of endocrine conditions that can place the birth at risk, and what nursing strategies might be employed to manage and optimize outcomes in such cases?
6 .
A pregnant patient has a preexisting musculoskeletal condition, such as scoliosis. How should a nurse explain the pathophysiology of musculoskeletal conditions that can place the birth at risk, and what nursing considerations should be taken into account for managing labor and delivery in such cases?
7 .
A laboring patient is experiencing prolonged second stage labor. How would you recognize the need for forceps assistance, and what obstetric indications would justify the use of forceps during birth? Additionally, what nursing considerations should be taken into account?
8 .
A laboring person is being prepared for an operative vaginal birth. What nursing care considerations should be discussed with the patient and the health-care team? How can a nurse provide support to the patient during this process?
9 .
A delivery is complicated by shoulder dystocia. What maneuvers can be employed to resolve shoulder dystocia, and how do you prioritize them? Discuss the potential complications of shoulder dystocia and how nursing actions contribute to minimizing risks.
10 .
Describe prolapsed cord, the nursing actions in response to prolapsed cord, and the potential complications associated with this obstetric emergency.
11 .
A patient is suspected of having uterine rupture. How can nursing actions contribute to the early detection and management of uterine rupture? Discuss the potential complications associated with uterine rupture and the role of the nurse in minimizing risks.


8.3: Plotting...
At the beginning, visually check the distribution of data. Make histogram:
Code \(\PageIndex{1}\) (R):
(To see more detailed histogram, increase the number of breaks .)
If for the histogram you want to split data in the specific way (for example, by 20 units, starting from 0 and ending in 100), type:
Code \(\PageIndex{2}\) (R):
Boxplots show outliers, maximum, minimum, quartile range and median for any measurement variable:
Code \(\PageIndex{3}\) (R):
... now for males and females separately, using formula interface:
Code \(\PageIndex{4}\) (R):
There are two commands which together help to check normality of the character:
Code \(\PageIndex{5}\) (R):
(These two separate commands work together to make a single plot, this is why we used semicolon. The more dots on the resulting plot are deviated from the line, the more non-normal is the data.)
Make scatterplot where all bugs represented with small circles. X axis will represent the length whereas Y axis—the weight:
Code \(\PageIndex{6}\) (R):
( type="p" is the default for plot() , therefore it is usually omitted.)
It is possible to change the size of dots varying the cex parameter. Compare
Code \(\PageIndex{7}\) (R):
with
Code \(\PageIndex{8}\) (R):
How to compare? The best way is to have more than one graphical window on the desktop. To start new window, type dev.new() .
It is also possible to change the type of plotting symbol. Figure \(\PageIndex{1}\) shows their numbers. If you want this table on the computer, you can run:
Code \(\PageIndex{9}\) (R):
To obtain similar graphic examples about types of lines, default colors, font faces and plot types, load the gmoon.r\(^{[1]}\) and run:
Code \(\PageIndex{10}\) (R):
Use symbol 2 (empty triangle):
Code \(\PageIndex{11}\) (R):
Use text codes (0/1) for the SEX instead of graphical symbol:
Code \(\PageIndex{12}\) (R):
(Here both commands make one plot together. The first one plots the empty field with axes, the second add there text symbols.)
The same plot is possible to make with the single command, but this works only for one-letter labels:
Code \(\PageIndex{13}\) (R):
If we want these numbers to have different colors, type:
Code \(\PageIndex{14}\) (R):
(Again, both commands make one plot. We added +1 because otherwise female signs would be of 0 color, which is “invisible”.)
Different symbols for males and females:
Code \(\PageIndex{15}\) (R):
The more complicated variant—use symbols from Hershey fonts\(^{[2]}\) which are internal in R (Figure \(\PageIndex{2}\)):
Code \(\PageIndex{16}\) (R):
(Note also how expression() was employed to make advanced axes labels. Inside expression() , different parts are joined with star * . To know more, run ?plotmath .)
 Saving into the external file, never forget to type dev.off() !
If you do not want any of axis and main labels, insert options main="", xlab="", ylab="" into your plot() command.
There is also a better way to save plots because it does not duplicate to screen and therefore works better in R scripts:
Code \(\PageIndex{20}\) (R):
(Please note here that R issues no warning if the file with the same name is already exist on the disk, it simply erases it and saves the new one. Be careful!)
References
1. With command source("ashipunov.info/r/gmoon.r").
2. To know which symbols are available, run demo(Hershey).


16.1: Introduction
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Learning Outcomes
After reading this chapter, you should be able to answer these questions:
- How do finance and the financial manager affect a firm’s overall strategy?
- What types of short-term and long-term expenditures does a firm make?
- What are the main sources and costs of unsecured and secured short-term financing?
- What are the key differences between debt and equity, and what are the major types and features of long-term debt?
- When and how do firms issue equity, and what are the costs?
- How do securities markets help firms raise funding, and what securities trade in the capital markets?
- Where can investors buy and sell securities, and how are securities markets regulated?
- What are the current developments in financial management and the securities markets?
EXPLORING BUSINESS CAREERS
Vicki Saunders, Venture Capitalist & Entrepreneur
Many women dream of starting their own business. But this involves a large investment of time, dedication, creativity—and money. Even the best ideas fall flat without strong financial backing and fiscal management. Most start-ups don’t have a chief financial officer, let alone an unlimited amount of cash to fund their owners’ dreams.
According to a recent report, there are more than 11 million woman-owned businesses in the United States that employ close to 9 million people and generate more than $1.6 trillion in revenues. And revenues have increased for these businesses more than 35% over the last decade compared to 27% among all U.S. companies. Despite these impressive statistics, less than 4 percent of venture capital funding goes to this group of entrepreneurs. That’s where Vicki Saunders and SheEO, her venture capital start-up, come into the picture.
Saunders, who describes herself as a serial entrepreneur, previously cofounded and ran four different business ventures. She believes that the funding universe for women entrepreneurs needs to be fixed and offers her plan via SheEO, a platform to enlist women “activators” to invest money to create a pool of capital distributed to select woman-owned businesses in the form of 0% interest loans that are paid back within five years. The activators are more than just investors, however. Saunders envisions these women as being a crucial part of the businesses in which they invest, by providing operational support, resources for suppliers and other vendors, and a solid networking opportunity for everything from legal support to cultivating new customers. In a recent campaign called Radical Generosity, $1,000 was raised from each of 500 women, and that pool of $500,000 was split among five woman-led businesses.
In year three of the funding venture in 2017, SheEO funded 15 companies and invested $1.5 million. SheEO has funded entrepreneurs working on a variety of businesses, including artificial intelligence, hardware for people with disabilities, food, and education. While SheEO currently operates in four regions, Canada, Los Angeles, San Francisco, and Colorado, Saunders’s goals for funding woman-led businesses are lofty. By 2020, Saunders hopes to have a million investors and a billion dollars to fund 10,000 entrepreneurs. But her ultimate goal is to change the culture around how investors support businesses—all businesses. According to Saunders, activating women on behalf of other women will change the world.
Sources: Company website, “About Us,” https://sheeo.world , accessed November 5, 2017; Emma Hinchliffe, “SheEO Has a Plan to Build a $1 Billion Fund for Female Founders,” Mashable, http://mashable.com , October 24, 2017; Catherine McIntyre, “How Vicki Saunders Plans to Get a Million Women Involved in Venture Capital,” Canadian Business, http://www.canadianbusiness.com , accessed October 24, 2017; Kimberly Weisul, “Venture Capital Is Broken. These Women Are Trying to Fix It,” Inc., https://www.inc.com , accessed October 24, 2017; Geri Stengel, “Women Become Financiers to Disrupt the Funding Landscape for Entrepreneurs,” Forbes, https://www.forbes.com , October 18, 2017; Kathleen Chaykowski, “Meet the Top Women Investors in VC in 2017,” Forbes, https://www.forbes.com , April 18, 2017; Jill Richmond, “Everything May Be Broken But This CEO’s Glasses Are a Rose Hue,” Forbes, https://www.forbes.com , December 16, 2016.
In today’s fast-paced global economy, managing a firm’s finances is more complex than ever. For financial managers, a thorough command of traditional finance activities—financial planning, investing money, and raising funds—is only part of the job. Financial managers are more than number crunchers. As part of the top management team, chief financial officers (CFOs) need a broad understanding of their firm’s business and industry, as well as leadership ability and creativity. They must never lose sight of the primary goal of the financial manager: to maximize the value of the firm to its owners.
Financial management—spending and raising a firm’s money—is both a science and an art. The science part is analyzing numbers and flows of cash through the firm. The art is answering questions such as these: Is the firm using its financial resources in the best way? Aside from costs, why choose a particular form of financing? How risky is each option? Another important concern for both business managers and investors is understanding the basics of securities markets and the securities traded on them, which affect both corporate plans and investor pocketbooks. About 52 percent of adult Americans now own stocks, compared to just 25 percent in 1981. 1
This chapter focuses on the financial management of a firm and the securities markets in which firms raise funds. We’ll start with an overview of the role of finance and of the financial manager in the firm’s overall business strategy. Discussions of short- and long-term uses of funds and investment decisions follow. Next, we’ll examine key sources of short- and long-term financing. Then we’ll review the function, operation, and regulation of securities markets. Finally, we’ll look at key trends affecting financial management and securities markets.


5.1: Oxidation of Alcohols
Oxidation of alcohols to carbonyl compounds is a pivotal process in organic chemistry. In particular, the oxidations that use readily available molecular oxygen, especially ambient air, as the stoichiometric oxidant are the most preferable. During the recent years, asymmetric version of the process has been developed using molecular catalysis, which can be divided into kinetic resolution of secondary alcohols and desymmetrization of meso - or prochiral diols (Scheme \(\PageIndex{1}\)).
5.1.1 Palladium Catalyst
The palladium catalyzed aerobic oxidation of alcohols to carbonyl compounds has received much attention in recent years and the catalytic cycle for this process is presented in Scheme \(\PageIndex{2}\). The cycle consists two separate processes: the oxidation of alcohols and the regeneration of the catalyst. In the oxidation of alcohols palladium alkoxide is generated after the coordination of the alcohol, and then β -hydride elimination occurs to afford the carbonyl compounds. The resultant palladium hydride reacts with molecular oxygen to generate palladium hydroperoxo complex and the subsequent ligand exchange reproduce the catalyst.
A series of experiments by three research groups have carried out using palladium complex bearing naturally occurring diamine, (-)-sparteine, to catalyzes the oxidation of aliphatic, benzylic and allylic alcohols with moderate to good k rel values (Scheme \(\PageIndex{3}\)).
However, the isolated palladium-sparteine complex shows no catalytic activity and the reaction is effective employing additional (-)-sparteine (Scheme \(\PageIndex{4}\)). This result suggest that the additional (-)-sparteine serves as base to abstract a proton to a palladium bound alcohol in the alkoxide formation process.
Subsequently, the combination of palladium complexes bearing chiral and achiral N-heterocyclic carbene lignads with (-)-sparteine has been used for the kinetic resolution of secondary alcohols with high selectivity (Scheme \(\PageIndex{5}\)).
The reaction is found to be accelerated in the presence of Cs 2 CO 3 under ambient air (Scheme \(\PageIndex{6}\)). The procedure is found to be useful for the synthesis of several pharmaceutically important substances including Prozac®, Singlair®, and Merck's h-NK1 receptor antagonist.
5.1.2 Ruthenium Catalyst
Chiral Ru-salen complex 3 having nitrosyl ligand has been found to be effective catalyst for the oxidative kinetic resolution of secondary alcohols under ambient air as oxidant under visible light (Scheme \(\PageIndex{7}\)). The irradiation of the visible light promotes dissociation of the nitrosyl ligand and generates a catalytically active ruthenium species. Kinetic resolution of aryl, alkynyl and alkyl alcohols has been observed with k rel up to 30.
Scheme \(\PageIndex{7}\)
The chiral ruthenium based complex 4 is also effective for the oxidative desymmetrization of 1,4- meso -diols (Scheme \(\PageIndex{8}\)).
Scheme \(\PageIndex{9}\) shows the proposed mechanism for the Ru-catalyzed aerobic oxidation of alcohols which is similar to the galactose oxidase system.
5 . 1.3 Vanadium Catalyst
Vanadium complexes having chiral tridentate Schiff base ligand 5 derived from optically active amino alcohol and benzaldehyde derivative catalyze efficiently the kinetic resolution of α -hydroxy carbonyl compounds (Scheme \(\PageIndex{10}\)). The reactions of α -hydroxy esters can be accomplished with k rel ranging from 6 to 50. Subsequently, the chiral tridentate Schiff base ligand 6 derived from optically active α -amino acids and aldehydes have also been found to be effective for the vanadium catalyzed aerobic kinetic solution of hydroxy compounds (Scheme \(\PageIndex{11}\)). For example, the reaction of α -hydroxyphosphonic acids can be accomplished with excellent selectivity ( k rel 99). The observed experimental results suggest that these oxidation reactions don't involve radical process.
5.1.4 Iridium Catalyst
Few studies are focused on the use of chiral iridium complexes for the oxidative kinetic resolution of racemic secondary alcohols. Chiral iridium complex 6 has been shown to catalyze the oxidation benzylic alcohols with high k rel under air. Using these reaction conditions, the oxidation of 1-indanol is reported with enantioselectivity of up to 99% and 50 yield.
Iridium chloride complex 7 has been used for the oxidation of racemic secondary alcohols with k rel as high as 48.8 (Scheme \(\PageIndex{13}\)). The Rh analogue 8 exhibits high catalytic activity in the presence of base, while the related Ru complex 9 gives diminished result.


6.7: PROTEST AND SHOCK
Art also connects to our lives as a means of expressing protest, as can be seen in the work of Jaune Quick-to-See Smith (b. 1940, USA), a Native American who often sarcastically comments on the history of the treatment of her people by Americans in general and by the United States government in particular. The impetus for these two works was the 1992 celebration of the 500th anniversary of Columbus’s discovery of the “New World.” ( Trade (Gifts for Trading Land with White People) , Juane Quick-to-See Smith: www.chrysler.org/ajax/load-artwork/26; Pa- per Dolls for a Post Columbian World with Ensembles Contributed by US Government , Juane Quick-to-See Smith: sam.nmartmuseum.org/view/obje...ple$0040636/5/ primaryMakerAlpha-asc?t:state:flow=41dede4d-4192-4c2a-86e4-cd9d50f583c2) Her commentary includes the commercialization and stereotyping of her people, and their relegation to reservations, with forced cultural changes, as well as such harmful effects as the introduction of the deadly smallpox disease among people with no previous exposure to it. Her drawings and paint- ings are often very simple and straightforward in method and style but show masterful techniques that she developed through sophisticated artistic training.
Certainly, the category of shock could be applied to the works by Smith we have just seen, and shock has been used increasingly in contemporary art to bolster political statements of protest or just commentary on our expectations and frames of reference. Ron Mueck (b. 1958, Australia) has made a point of repeatedly challenging the viewer with questions about life and relationships in his hyperrealist sculpture. ( Mask II , Ron Mueck: http://www.visualarts.qld.gov.au/mueck/ images/MUECKron_MaskII_EXHI010912_RGB.jpg) He often creates works of the human form that are exceptionally out of scale, unexpectedly undressed, or placed in unusual postures, there- by creating many surprises among gallery goers, especially those who approach these uncanny works at a close distance.


12.3: Goodness-of-Fit Test
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In this type of hypothesis test, you determine whether the data "fit" a particular distribution or not. For example, you may suspect your unknown data fit a binomial distribution. You use a chi-square test (meaning the distribution for the hypothesis test is chi-square) to determine if there is a fit or not. The null and the alternative hypotheses for this test may be written in sentences or may be stated as equations or inequalities.
The test statistic for a goodness-of-fit test is:
\[\sum_k \frac{(O - E)^{2}}{E}\]
where:
- \(O =\) observed values (data)
- \(E =\) expected values (from theory)
- \(k =\) the number of different data cells or categories
The observed values are the data values and the expected values are the values you would expect to get if the null hypothesis were true. There are \(n\) terms of the form \(\frac{(O - E)^{2}}{E}\).
The number of degrees of freedom is \(df = (\text{number of categories} - 1)\).
The goodness-of-fit test is almost always right-tailed. If the observed values and the corresponding expected values are not close to each other, then the test statistic can get very large and will be way out in the right tail of the chi-square curve.
The expected value for each cell needs to be at least five in order for you to use this test.
Example 11.3.1
Absenteeism of college students from math classes is a major concern to math instructors because missing class appears to increase the drop rate. Suppose that a study was done to determine if the actual student absenteeism rate follows faculty perception. The faculty expected that a group of 100 students would miss class according to the table below.
| Number of absences per term | Expected number of students |
|---|---|
| 0–2 | 50 |
| 3–5 | 30 |
| 6–8 | 12 |
| 9–11 | 6 |
| 12+ | 2 |
A random survey across all mathematics courses was then done to determine the actual number (observed) of absences in a course. The chart in the table below displays the results of that survey.
| Number of absences per term | Actual number of students |
|---|---|
| 0–2 | 35 |
| 3–5 | 40 |
| 6–8 | 20 |
| 9–11 | 1 |
| 12+ | 4 |
Determine the null and alternative hypotheses needed to conduct a goodness-of-fit test.
- \(H_{0}\) : Student absenteeism fits faculty perception.
- \(H_{a}\) : Student absenteeism does not fit faculty perception.
Exercise <IP_ADDRESS>
a. Can you use the information as it appears in the charts to conduct the goodness-of-fit test?
Answer
a. No. Notice that the expected number of absences for the "12+" entry is less than five (it is two). Combine that group with the "9–11" group to create new tables where the number of students for each entry are at least five. The new results are in the table below.
| Number of absences per term | Expected number of students |
|---|---|
| 0–2 | 50 |
| 3–5 | 30 |
| 6–8 | 12 |
| 9+ | 8 |
| Number of absences per term | Actual number of students |
|---|---|
| 0–2 | 35 |
| 3–5 | 40 |
| 6–8 | 20 |
| 9+ | 5 |
Exercise <IP_ADDRESS>
b. What is the number of degrees of freedom (\(df\))?
Answer
b. There are four "cells" or categories in each of the new tables.
\(df = \text{number of cells} - 1 = 4 - 1 = 3\)
Exercise 11.3.1
A factory manager needs to understand how many products are defective versus how many are produced. The number of expected defects is listed in the table below.
| Number produced | Number defective |
|---|---|
| 0–100 | 5 |
| 101–200 | 6 |
| 201–300 | 7 |
| 301–400 | 8 |
| 401–500 | 10 |
A random sample was taken to determine the actual number of defects. The table below shows the results of the survey.
| Number produced | Number defective |
|---|---|
| 0–100 | 5 |
| 101–200 | 7 |
| 201–300 | 8 |
| 301–400 | 9 |
| 401–500 | 11 |
State the null and alternative hypotheses needed to conduct a goodness-of-fit test, and state the degrees of freedom.
Answer
\(H_{0}\):The number of defects fits expectations.
\(H_{a}\):The number of defects does not fit expectations.
\(df = 4\)
Example 11.3.2
Employers want to know which days of the week employees are absent in a five-day work week. Most employers would like to believe that employees are absent equally during the week. Suppose a random sample of 60 managers were asked on which day of the week they had the highest number of employee absences. The results were distributed as in the table below. For the population of employees, do the days for the highest number of absences occur with equal frequencies during a five-day work week? Test at a 5% significance level.
| Monday | Tuesday | Wednesday | Thursday | Friday | |
|---|---|---|---|---|---|
| Number of Absences | 15 | 12 | 9 | 9 | 15 |
Answer
The null and alternative hypotheses are:
- \(H_{0}\): The absent days occur with equal frequencies, that is, they fit a uniform distribution.
- \(H_{a}\): The absent days occur with unequal frequencies, that is, they do not fit a uniform distribution.
If the absent days occur with equal frequencies, then, out of 60 absent days (the total in the sample: \(15 + 12 + 9 + 9 + 15 = 60\)), there would be 12 absences on Monday, 12 on Tuesday, 12 on Wednesday, 12 on Thursday, and 12 on Friday. These numbers are the expected (\(E\)) values. The values in the table are the observed (\(O\)) values or data.
This time, calculate the \(\chi^{2}\) test statistic by hand. Make a chart with the following headings and fill in the columns:
- Expected (\(E\)) values \((12, 12, 12, 12, 12)\)
- Observed (\(O\)) values \((15, 12, 9, 9, 15)\)
- \((O – E)\)
- \((O – E)^{2}\)
- \(\frac{(O - E)^{2}}{E}\)
Now add (sum) the last column. The sum is three. This is the \(\chi^{2}\) test statistic.
To find the p -value, calculate \(P(\chi^{2} > 3)\). This test is right-tailed. (Use a computer or calculator to find the p -value. You should get \(p\text{-value} = 0.5578\).)
The \(dfs\) are the \(\text{number of cells} - 1 = 5 - 1 = 4\)
There are many online calculators that calculate a probability given \(\chi^{2}\) and the degrees of freedom. Rounded to four decimal places, the value is 0.5578, which is the \(p\text{-value}\).
Next, complete a graph like the following one with the proper labeling and shading. (You should shade the right tail.)
Figure 11.3.1.The decision is not to reject the null hypothesis.
Conclusion: At a 5% level of significance, from the sample data, there is not sufficient evidence to conclude that the absent days do not occur with equal frequencies.
The LibreTexts Goodness of Fit calculator can be used. You just enter in the observed data, separated by commas. Then enter in the expected values, separated by commas. Hit Calculate and the \(\chi^{2}\) test statistic and p-Value are calculated.
\(\chi^{2}\) Goodness of fit Calculator
Type in the values from the observed and expected sets separated by commas, for example, 2,4,5,8,11,2. Then hit Calculate and the test statistic, \(\chi^{2}\), and the p-value, p, will be shown.
Observed:
Expected:
| \(\chi^{2}\): | p |
Exercise 11.3.2
Teachers want to know which night each week their students are doing most of their homework. Most teachers think that students do homework equally throughout the week. Suppose a random sample of 49 students were asked on which night of the week they did the most homework. The results were distributed as in the table below.
| Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | |
|---|---|---|---|---|---|---|---|
| Number of Students | 11 | 8 | 10 | 7 | 10 | 5 | 5 |
From the population of students, do the nights for the highest number of students doing the majority of their homework occur with equal frequencies during a week? What type of hypothesis test should you use?
Answer
\(df = 6\)
\(p\text{-value} = 0.6093\)
We decline to reject the null hypothesis. There is not enough evidence to support that students do not do the majority of their homework equally throughout the week.
Example 11.3.3
One study indicates that the number of televisions that American families have is distributed (this is the given distribution for the American population) as in the table below.
| Number of Televisions | Percent |
|---|---|
| 0 | 10 |
| 1 | 16 |
| 2 | 55 |
| 3 | 11 |
| 4+ | 8 |
The table contains expected (\(E\)) percents.
A random sample of 600 families in the far western United States resulted in the data in the table below.
| Number of Televisions | Frequency |
|---|---|
| Total = 600 | |
| 0 | 66 |
| 1 | 119 |
| 2 | 340 |
| 3 | 60 |
| 4+ | 15 |
The table contains observed (\(O\)) frequency values.
Exercise <IP_ADDRESS>
At the 1% significance level, does it appear that the distribution "number of televisions" of far western United States families is different from the distribution for the American population as a whole?
Answer
This problem asks you to test whether the far western United States families distribution fits the distribution of the American families. This test is always right-tailed.
The first table contains expected percentages. To get expected ( E ) frequencies, multiply the percentage by 600. The expected frequencies are shown in the table below.
| Number of Televisions | Percent | Expected Frequency |
|---|---|---|
| 0 | 10 | (0.10)(600) = 60 |
| 1 | 16 | (0.16)(600) = 96 |
| 2 | 55 | (0.55)(600) = 330 |
| 3 | 11 | (0.11)(600) = 66 |
| over 3 | 8 | (0.08)(600) = 48 |
Therefore, the expected frequencies are 60, 96, 330, 66, and 48. In the TI calculators, you can let the calculator do the math. For example, instead of 60, enter \(0.10*600\).
\(H_{0}\): The "number of televisions" distribution of far western United States families is the same as the "number of televisions" distribution of the American population.
\(H_{a}\): The "number of televisions" distribution of far western United States families is different from the "number of televisions" distribution of the American population.
Distribution for the test: \(\chi^{2}_{4}\) where \(df = (\text{the number of cells}) - 1 = 5 - 1 = 4\).
Note <IP_ADDRESS>
\(df \neq 600 - 1\)
Calculate the test statistic: \(\chi^{2} = 29.65\)
Graph:
Figure 11.3.2.Probability statement: \(p\text{-value} = P(\chi^{2} > 29.65) = 0.000006\)
Compare α and the p -value:
\(\alpha = 0.01\)
\(p\text{-value} = 0.000006\)
So, \(\alpha > p\text{-value}\).Make a decision: Since \(\alpha > p\text{-value}\), reject \(H_{0}\).
This means you reject the belief that the distribution for the far western states is the same as that of the American population as a whole.
Conclusion: At the 1% significance level, from the data, there is sufficient evidence to conclude that the "number of televisions" distribution for the far western United States is different from the "number of televisions" distribution for the American population as a whole.
The LibreTexts Goodness of Fit calculator can be used as follows. Enter in the observed percents, separated by commas. Then enter in the expected frequencies, separated by commas. Hit Calculate. \(\chi^{2} = 29.65\) and the p-Value is \(p = 0.000006\).
Exercise 11.3.3
The expected percentage of the number of pets students have in their homes is distributed (this is the given distribution for the student population of the United States) as in t he table below.
| Number of Pets | Percent |
|---|---|
| 0 | 18 |
| 1 | 25 |
| 2 | 30 |
| 3 | 18 |
| 4+ | 9 |
A random sample of 1,000 students from the Eastern United States resulted in the data in the table below.
| Number of Pets | Frequency |
|---|---|
| 0 | 210 |
| 1 | 240 |
| 2 | 320 |
| 3 | 140 |
| 4+ | 90 |
At the 1% significance level, does it appear that the distribution “number of pets” of students in the Eastern United States is different from the distribution for the United States student population as a whole? What is the \(p\text{-value}\)?
Answer
\(p\text{-value} = 0.0036\)
We reject the null hypothesis that the distributions are the same. There is sufficient evidence to conclude that the distribution “number of pets” of students in the Eastern United States is different from the distribution for the United States student population as a whole.
Example 11.3.4
Suppose you flip two coins 100 times. The results are 20 HH , 27 HT , 30 TH , and 23 TT . Are the coins fair? Test at a 5% significance level.
Answer
This problem can be set up as a goodness-of-fit problem. The sample space for flipping two fair coins is \({HH, HT, TH, TT}\). Out of 100 flips, you would expect 25 HH , 25 HT , 25 TH , and 25 TT . This is the expected distribution. The question, "Are the coins fair?" is the same as saying, "Does the distribution of the coins (\(20 HH, 27 HT, 30 TH, 23 TT\)) fit the expected distribution?"
Random Variable: Let \(X =\) the number of heads in one flip of the two coins. \(X\) takes on the values 0, 1, 2. (There are 0, 1, or 2 heads in the flip of two coins.) Therefore, the number of cells is three . Since \(X =\) the number of heads, the observed frequencies are 20 (for two heads), 57 (for one head), and 23 (for zero heads or both tails). The expected frequencies are 25 (for two heads), 50 (for one head), and 25 (for zero heads or both tails). This test is right-tailed.
\(H_{0}\): The coins are fair.
\(H_{a}\): The coins are not fair.
Distribution for the test: \(\chi^{2}_{2}\) where \(df = 3 - 1 = 2\).
Calculate the test statistic: \(\chi^{2} = 2.14\)
Graph:
Figure 11.3.3.Probability statement: \(p\text{-value} = P(\chi^{2} > 2.14) = 0.3430\)
Compare α and the p -value:
\(\alpha = 0.05\)
\(p\text{-value} = 0.3430\)
\(\alpha < p\text{-value}\).Make a decision: Since \(\alpha < p\text{-value}\), do not reject \(H_{0}\).
Conclusion: There is insufficient evidence to conclude that the coins are not fair.
The LibreTexts Goodness of Fit calculator can be used as follows. Enter in the observed frequencies, separated by commas. Then enter in the expected frequencies (all 25), separated by commas. Hit Calculate. \(\chi^{2} = 2.14\) and the p-Value is \(p = 0.3430\).
Exercise 11.3.4
Students in a social studies class hypothesize that the literacy rates across the world for every region are 82%. The table below shows the actual literacy rates across the world broken down by region. What are the test statistic and the degrees of freedom?
| MDG Region | Adult Literacy Rate (%) |
|---|---|
| Developed Regions | 99.0 |
| Commonwealth of Independent States | 99.5 |
| Northern Africa | 67.3 |
| Sub-Saharan Africa | 62.5 |
| Latin America and the Caribbean | 91.0 |
| Eastern Asia | 93.8 |
| Southern Asia | 61.9 |
| South-Eastern Asia | 91.9 |
| Western Asia | 84.5 |
| Oceania | 66.4 |
Answer
\(df = 9\)
\(\chi^{2} \text{test statistic} = 26.38\)
Figure 11.3.4.The LibreTexts Goodness of Fit calculator can be used as follows. Enter in the observed frequencies, separated by commas. Then enter in the expected frequencies, separated by commas. Hit Calculate. \(\chi^{2} = 26.38\) and the p-Value is \(p = 0.0018\).
References
- Data from the U.S. Census Bureau
- Data from the College Board. Available online at http://www.collegeboard.com .
- Data from the U.S. Census Bureau, Current Population Reports.
- Ma, Y., E.R. Bertone, E.J. Stanek III, G.W. Reed, J.R. Hebert, N.L. Cohen, P.A. Merriam, I.S. Ockene, “Association between Eating Patterns and Obesity in a Free-living US Adult Population.” American Journal of Epidemiology volume 158, no. 1, pages 85-92.
- Ogden, Cynthia L., Margaret D. Carroll, Brian K. Kit, Katherine M. Flegal, “Prevalence of Obesity in the United States, 2009–2010.” NCHS Data Brief no. 82, January 2012. Available online at http://www.cdc.gov/nchs/data/databriefs/db82.pdf (accessed May 24, 2013).
- Stevens, Barbara J., “Multi-family and Commercial Solid Waste and Recycling Survey.” Arlington Count, VA. Available online at http://www.arlingtonva.us/department.../file84429.pdf (accessed May 24,2013).
Chapter Review
To assess whether a data set fits a specific distribution, you can apply the goodness-of-fit hypothesis test that uses the chi-square distribution. The null hypothesis for this test states that the data come from the assumed distribution. The test compares observed values against the values you would expect to have if your data followed the assumed distribution. The test is almost always right-tailed. Each observation or cell category must have an expected value of at least five.
Formula Review
\(\sum_k \frac{(O - E)^{2}}{E}\) goodness-of-fit test statistic where:
\(O\): observed values
\(E\): expected value
\(k\): number of different data cells or categories
\(df = k - 1\) degrees of freedom
Determine the appropriate test to be used in the next three exercises.
Exercise 11.3.5
An archeologist is calculating the distribution of the frequency of the number of artifacts she finds in a dig site. Based on previous digs, the archeologist creates an expected distribution broken down by grid sections in the dig site. Once the site has been fully excavated, she compares the actual number of artifacts found in each grid section to see if her expectation was accurate.
Exercise 11.3.6
An economist is deriving a model to predict outcomes on the stock market. He creates a list of expected points on the stock market index for the next two weeks. At the close of each day’s trading, he records the actual points on the index. He wants to see how well his model matched what actually happened.
Answer
a goodness-of-fit test
Exercise 11.3.7
A personal trainer is putting together a weight-lifting program for her clients. For a 90-day program, she expects each client to lift a specific maximum weight each week. As she goes along, she records the actual maximum weights her clients lifted. She wants to know how well her expectations met with what was observed.
Use the following information to answer the next five exercises: A teacher predicts that the distribution of grades on the final exam will be and they are recorded in the table below.
| Grade | Proportion |
|---|---|
| A | 0.25 |
| B | 0.30 |
| C | 0.35 |
| D | 0.10 |
The actual distribution for a class of 20 is in the table below.
| Grade | Frequency |
|---|---|
| A | 7 |
| B | 7 |
| C | 5 |
| D | 1 |
Exercise 11.3.8
\(df =\) ______
Answer
3
Exercise 11.3.9
State the null and alternative hypotheses.
Exercise 11.3.10
\(\chi^{2} \text{test statistic} =\) ______
Answer
2.04
Exercise 11.3.11
\(p\text{-value} =\) ______
Exercise 11.3.12
At the 5% significance level, what can you conclude?
Answer
We decline to reject the null hypothesis. There is not enough evidence to suggest that the observed test scores are significantly different from the expected test scores.
Use the following information to answer the next nine exercises: The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as in the table below.
| Ethnicity | Number of Cases |
|---|---|
| White | 2,229 |
| Hispanic | 1,157 |
| Black/African-American | 457 |
| Asian, Pacific Islander | 232 |
| Total = 4,075 |
The percentage of each ethnic group in Santa Clara County is as in the table below.
| Ethnicity | Percentage of total county population | Number expected (round to two decimal places) |
|---|---|---|
| White | 42.9% | 1748.18 |
| Hispanic | 26.7% | |
| Black/African-American | 2.6% | |
| Asian, Pacific Islander | 27.8% | |
| Total = 100% |
Exercise 11.3.13
If the ethnicities of AIDS victims followed the ethnicities of the total county population, fill in the expected number of cases per ethnic group.
Perform a goodness-of-fit test to determine whether the occurrence of AIDS cases follows the ethnicities of the general population of Santa Clara County.
Exercise 11.3.14
\(H_{0}\): _______
Answer
\(H_{0}\): the distribution of AIDS cases follows the ethnicities of the general population of Santa Clara County.
Exercise 11.3.15
\(H_{a}\): _______
Exercise 11.3.16
Is this a right-tailed, left-tailed, or two-tailed test?
Answer
right-tailed
Exercise 11.3.17
degrees of freedom = _______
Exercise 11.3.18
\(\chi^{2} \text{test statistic}\) = _______
Answer
88,621
Exercise 11.3.19
\(p\text{-value} =\) _______
Exercise 11.3.20
Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade in the region corresponding to the \(p\text{-value}\).
Figure 11.3.5.Let \(\alpha = 0.05\)
Decision: ________________
Reason for the Decision: ________________
Conclusion (write out in complete sentences): ________________
Answer
Graph: Check student’s solution.
Decision: Reject the null hypothesis.
Reason for the Decision: \(p\text{-value} < \alpha\)
Conclusion (write out in complete sentences): The make-up of AIDS cases does not fit the ethnicities of the general population of Santa Clara County.
Exercise 11.3.21
Does it appear that the pattern of AIDS cases in Santa Clara County corresponds to the distribution of ethnic groups in this county? Why or why not?


26.0: Prelude to Seed Plants
The lush palms on tropical shorelines do not depend on water for the dispersal of their pollen, fertilization, or the survival of the zygote—unlike mosses, liverworts, and ferns of the terrain. Seed plants, such as palms, have broken free from the need to rely on water for their reproductive needs. They play an integral role in all aspects of life on the planet, shaping the physical terrain, influencing the climate, and maintaining life as we know it. For millennia, human societies have depended on seed plants for nutrition and medicinal compounds: and more recently, for industrial by-products, such as timber and paper, dyes, and textiles. Palms provide materials including rattans, oils, and dates. Wheat is grown to feed both human and animal populations. The fruit of the cotton boll flower is harvested as a boll, with its fibers transformed into clothing or pulp for paper. The showy opium poppy is valued both as an ornamental flower and as a source of potent opiate compounds.


20.6: Chapter 6 (Cognitive Impairments)
Answer Key to Chapter 6 Learning Activities
Scenario A
1. In the immediate postoperative period, it is important to assess for signs of infection, electrolyte imbalances, confusion related to new medications, and hypoxia.
2. Table 1
| Dementia | Delirium | Depression | |
|---|---|---|---|
| Onset | Vague, insidious onset; symptoms progress slowly | Sudden onset over hours and days with fluctuations | Onset often rapid with identifiable trigger or life event such as bereavement |
| Symptoms | Symptoms may go unnoticed for years. May attempt to hide cognitive problems or may be unaware of them. Often disoriented to time, place, and person. Impaired short-term memory and information processing. Confusion is often worse in the evening (sundowning) | Often disoriented to time, place, and person. Impaired short-term memory loss and information processing. Confusion is often worse in the evening | Obvious at early stages and often worse in the morning. Can include subjective complaints of memory loss |
| Consciousness | Normal | Impaired attention/alertness | Normal |
| Mental State | Possibly labile mood. Consistently decreased cognitive performance | Emotional lability with anxiety, fear, depression, aggression. Variable cognitive performance | Distressed/unhappy. Variable cognitive performance |
| Delusions/ Hallucinations | Common | Common | Rare |
| Psychomotor Disturbance | Psychomotor disturbance in later stages | Psychomotor disturbance present – hyperactive, purposeless, or apathetic | Slowed psychomotor status in severe depression |
Based upon the patient’s sudden exacerbation of symptoms, she would most likely be exhibiting signs of delirium related to her recent surgery.
3. Interventions include the following:
- Control the environment. Make sure that the room is quiet and well-lit, have clocks or calendars in view, and encourage family members to visit.
- Administer prescribed medications, including those that control aggression or agitation and pain relievers if there is pain.
- Ensure the patient has their glasses, hearing aids, or other assistive devices for communication in place. Lack of assistive sensory devices can worsen delirium.
- Avoid sedatives. Sedatives can worsen delirium.
- Assign the same staff for patient care when possible.
Scenario B
1. Symptoms of moderate Alzheimer’s disease include the following:
- Require assistance with reminders to eat, wash, and use the restroom.
- Lack of recognition of family and friends.
- Behavioral symptoms such as wandering, getting lost, hallucinations, delusions, and repetitive behavior may occur.
- Patients living at home may engage in risky behavior, such as leaving the house in clothing inappropriate for weather conditions or leaving on the stove burners.
2. Additional assessments would include assessing for signs of physical discomfort, changes in the environment that may be contributing to the increased anxiety or confusion, and communication pattern.
3. Strategies for therapeutic response:
- Back off and ask permission before performing care tasks. Use calm, positive statements, slow down, add lighting, and provide reassurance. Offer guided choices between two options when possible. Focus on pleasant events and try to limit stimulation.
- Use effective language. When speaking, try phrases such as, “May I help you? Do you have time to help me? You’re safe here. Everything is under control. I apologize. I’m sorry that you are upset. I know it’s hard. I will stay with you until you feel better.”
- Listen to the person’s frustration. Find out what may be causing the agitation, and try to understand.
- Check yourself. Do not raise your voice, show alarm or offense, or corner, crowd, restrain, criticize, ignore, or argue with the person. Take care not to make sudden movements out of the person’s view.
4. Medications may include the following:
- Donepezil (Aricept), approved to treat all stages of Alzheimer’s disease
- Galantamine (Razadyne), approved for mild-to-moderate stages
- Rivastigmine (Exelon), approved for mild-to-moderate stages
- Memantine (Namenda) and a combination of memantine and donepezil (Namzaric) are by approved the FDA for treatment of moderate to severe Alzheimer’s.
Answers to interactive elements are given within the interactive element.


16.2: The Impact of Nutrition on Renal Wellness Across the Lifespan
By the end of this section, you should be able to:
- 16.1.1 Describe the impact of nutrition on the renal and urologic systems during pregnancy.
- 16.1.2 Describe the impact of nutrition on the renal and urologic systems during infancy.
- 16.1.3 Describe the impact of nutrition on the renal and urologic systems during childhood.
- 16.1.4 Describe the impact of nutrition on the renal and urologic systems during adolescence.
- 16.1.5 Describe the impact of nutrition on the renal and urologic systems during adulthood.
- 16.1.6 Describe the impact of nutrition on the renal and urologic systems during later adulthood.
Pregnancy
Nutrition plays a role in the development and function of every system in the body, including the renal system. This role starts with the in utero development of a person and continues throughout their life. Nutrition combined with lifestyle decisions can interact with normal and pathologic processes in the renal system, sometimes resulting in system failure.
Poor nutrition during pregnancy can lead to fetal abnormalities that can cause kidney disease in the future (National Kidney Foundation, 2022). Additionally, individuals with renal disease experience more problems during pregnancy and must manage their nutritional intake differently. This section will cover these nutritional considerations and their impact on the renal system during pregnancy.
The Healthy Pregnant Client
Pregnancy is accompanied by expected urinary and renal changes. Increased blood volume and cardiac output result in increased glomerular filtration rate (GFR) and renal blood flow, which in turn causes increased excretion and reduced blood levels of bicarbonate, urea, creatinine, and urate (Willacy, 2022). In increased GFR, the renal tubules are unable to meet the increased fluid demands, resulting in mild glycosuria and proteinuria; fluid retention increases, reducing plasma osmolality. The smooth muscle of the renal pelvis, ureters, and bladder relaxes and dilates, causing the kidneys to increase in length; the ureters to lengthen, curve, and increase in residual urine volume; and the bladder to increase its capacity. The uterus may also put pressure on the bladder and ureters as it increases in size.
Good nutrition during pregnancy can prevent problems and support overall renal health for the pregnant client and fetus. To achieve these aims, the client should:
- Increase caloric intake by 340 calories per day starting with the second trimester and 452 calories per day starting with the third trimester (for a singleton pregnancy).
- Take a prenatal vitamin that includes iron or take a separate iron supplement in addition to a prenatal vitamin to prevent iron-deficiency anemia.
- Avoid caffeine or limit it to less than 200 mg/day (Gleason, et al, 2022).
- Increase fluid intake, especially water.
(source: American College of Obstetricians and Gynecologists, 2023; Holcombe, 2022)
Because of the normal physiologic changes expected, specific renal issues that most commonly arise during pregnancy include urinary tract infection s (UTIs), pyelonephritis, and nephrolithiasis ( kidney stones ). Changes make urine less acidic, and it contains more hormones and sugars, increasing risk for bacterial growth (Sissons, 2019). Signs and symptoms of UTI include dysuria, frequency of urination, hematuria (American College of Obstetricians and Gynecologists, 2023b), abdominal cramps, and dyspareunia (pain during sexual intercourse).
If a UTI spreads from the lower urinary tract into the kidneys and develops into a more serious infection, pyelonephritis , signs and symptoms may then also include fever of 38.0°C (100.4°F) or higher; flank pain; costovertebral angle tenderness (American College of Obstetricians and Gynecologists, 2023b); chills; nausea; vomiting; and back, side, or groin pain. Significant fetal and maternal morbidity and mortality have been associated directly with pyelonephritis (Wing & Johnston, 2017). For instance, it has been linked to preterm delivery , in which case all of the newborn’s systems will be underdeveloped; disseminated intravascular coagulation (DIC), which can lead to hemorrhage and death of both mother and fetus; and maternal sepsis and respiratory distress, which can lead to renal failure and maternal and fetal death (Wing & Johnston, 2017).
Prevention of UTIs, and subsequently pyelonephritis, is based on urinary hygiene and nutritional recommendations. The nurse should instruct the client to drink 64–96 oz of water daily (American College of Obstetricians and Gynecologists, 2020). Drinking 8–10 oz of unsweetened cranberry juice or taking cranberry supplements daily may also help decrease the risk of UTI. Pregnant clients should also keep caffeine intake to 200 mg or less daily (Holcombe, 2022) and eat an overall healthy diet that includes proper nutritional and caloric intake (Sissons, 2019).
Nephrolithiasis usually occurs in the second or third trimester, when there is greater pressure on the renal organs from the growing uterus, and within the first year of giving birth (Furst, 2021; Urology Care Foundation, 2023). The pressure and narrowing of the passages for urine flow can concentrate urine and thus increase the risk for stone formation. Another factor that increases the risk for kidney stones is an elevated vitamin D level, which increases calcium levels in the urine (Orlando Health, 2023). Signs and symptoms the pregnant client may experience include nausea; vomiting; urgency and frequency of urination; hematuria (blood in the urine); and pain in the back, flank, or upper abdomen. The nurse should provide the following nutritional recommendations for nephrolithiasis during pregnancy:
- Get adequate daily amounts of vitamin B 6 and magnesium (Weinberg, 2023).
- Avoid excessive vitamin C (Peerapen & Thongboonkerd, 2023).
- Limit sodium intake to less than 2.3 g/day (UT Southwestern Medical Center, 2023).
- Drink ten 10 oz glasses of water or other fluids daily (Urology Care Foundation, 2023).
- For calcium oxalate stones, maintain calcium intake at 1000–2000 mg/day and limit intake of oxalate-rich foods (Peerapen & Thongboonkerd, 2023; UT Southwestern Medical Center, 2023).
- For uric acid stones, limit animal proteins and eat more plant proteins (Peerapen & Thongboonkerd, 2023).
A recent study has shown that healthy individuals who developed hypertension during pregnancy had twice the risk of developing kidney disease within the first several years after the birth of their baby. Risks were even higher in those who had hypertension before pregnancy and had worsening of their condition during the pregnancy (Malek et al., 2022; Williamson, 2022). Nutritional recommendations for hypertension include limiting sodium intake to less than 2 g/day, getting 4700 mg of potassium daily, limiting meats and saturated fats, eating 4–5 servings each of fruits and vegetables, and following all other recommendations included in the Dietary Approaches to Stop Hypertension (DASH) diet.
Research evidence reveals a racial disparity exists showing that Black women were much more highly affected than White women: Black women who had hypertension before and during pregnancy were three times more likely to develop kidney disease (Malek et al., 2022).
The Pregnant Client with Preexisting Renal Disease
Pregnant clients with preexisting renal conditions will be more severely impacted by mild anemia , due to dilution of the blood from fluid retention; an increased GFR, putting more work on the glomeruli; decreased serum sodium, potassium, urea, creatinine, calcium, and albumin; mild glycosuria and proteinuria; reduced plasma osmolality; increased urine retention in the system, which increases infection risks; decreased urine acidity; and increased pressure in the system due to the growing uterus. Preexisting maternal renal conditions that can be affected by pregnancy include polycystic kidney disease (PKD); post–renal transplant status; and chronic kidney disease (CKD) , a progressive disease of the kidneys that eventually ends in kidney failure.
Individuals with CKD are at much greater risk for experiencing adverse pregnancy outcomes, which can include preeclampsia; acceleration in the loss of kidney function, thereby speeding the process of CKD to end-stage renal disease (ESRD) or complete renal failure; fetal intrauterine growth restriction (IUGR); preterm delivery; the infant being of low birthweight or/and small for gestational age (SGA); the need for the infant to receive care in the neonatal intensive care unit (NICU); and maternal or fetal demise (Siligato et al., 2020; Wiles et al., 2019, 2020).
Kidney function declines as much in the 9 months of pregnancy as it does for a client living 1.7–4.9 years with kidney disease. Therefore, pregnancy could lead the client with CKD to complete kidney failure and need for a transplant or dialysis , purification of blood through means other than the kidneys, which can be extremely dangerous for the mother and fetus (Wiles et al., 2020).
Clients with CKD who have problems with chronic anemia, hypertension, proteinuria, or fluid and electrolyte imbalance before pregnancy will have continuation, and likely worsening, of these problems during pregnancy. Nutritional modifications for these clients involve a delicate balance between the needs of the growing fetus and the requirements of CKD. It has been found, however, that plant-based diets that are moderately restricted in protein decrease risks for preterm delivery and SGA status resulting from IUGR (Attini et al., 2022).
The Fetus
Certain nutritional components have been found to be critical for renal development in utero, and the pregnant person’s nutrition before and during pregnancy, as well as during early lactation, has been shown to have a substantial impact on this system. Clients with severe iron deficiency anemia during pregnancy have been shown to have elevated risks for preterm birth, placental abruption, and fetal malformation, which can include malformations of the fetal renal system (Shi et al., 2022). Pregnant clients with various disease processes may need specific dietary restrictions, but low-protein, low-carbohydrate, low-calorie, and low-sodium diets, as well as diets deficient in the micronutrients folic acid, iron, zinc, and vitamin A, have all been shown to have potential long-term adverse effects on the development of the renal system in the fetus (Nusken et al., 2020). High-fat, high-sodium, and high-fructose diets have also been shown to be detrimental to renal system development. Depending on the exact timing of the deficiency or the amount of exposure during development, adverse effects could include an altered number of nephrons, blood pressure dysregulation, mitochondrial dysfunction, altered sodium handling, endothelial dysfunction, inflammation, and oxidative stress of the kidney.
Studies have shown that increases in fetal growth and infant birth weight may be achieved by enhancing maternal nutrition during pregnancy (Columbia University Irving Medical Center, n.d.). Inadequate maternal nutrition during pregnancy is also a significant modifiable determinant for the development of chronic diseases in the child (Lee et al., 2021). Nutritional intake that is not sufficiently supplied with key nutrients such as iodine, iron, folate, calcium, and zinc can cause severe health problems in the mother (UNICEF, n.d.) that will directly affect fetal development and the individual’s lifelong health. The nurse should instruct a pregnant client to take in 30 mg of iron, 220 mg of iodine, 600 mcg of folate, 1000 mg of calcium, and 0.6 mg of zinc daily.
Infancy
Infants must receive proper nutrition for growth and development because all organs are impacted by malnutrition. Well-balanced nutrition should provide enough calories for energy expenditure. Healthy, full-term infants require around 100 kcal/kg/day (Patel & Rouster, 2022), whereas preterm infants require around 130 kcal/kg/day (Medical Home Portal, n.d).
Other nutritional recommendations to consider in an infant’s diet concern micronutrients , including iron, zinc, copper, chromium, manganese, and selenium (Patel & Rouster, 2022). Infants 7–12 months old should get 11 mg of iron (Gavin, 2021), 3 mg of zinc (Stanford Medicine Children’s Health, n.d.), 220 mcg of copper (National Institutes of Health, 2022a), 5.5 mcg of chromium (Duda, 2022), 0.6 mg of manganese (National Institutes of Health, 2021), and 20 mcg of selenium daily (Lubeck, 2023). Infants can quickly become dehydrated , so proper fluid intake is extremely important.
The preceding recommendations are for infants born without renal system defects. Those born with renal issues may need nutritional alterations and fluid restrictions based on their level of kidney function. These restricted diets may be in the form of a specially balanced formula that includes 2–4 mEq of sodium per 100 mL of formula and a restriction of 1–3 mmol/kg/day of potassium (Nelms, 2018). Depending on the specific needs, restrictions may also be in place for calcium, phosphorus, protein, calories, and fluids.
Oligohydramnios , a very low to almost absent amount of amniotic fluid, is a severe condition that must be managed before birth and can be related to impaired or absent kidney function in the fetus (Keilman & Shanks, 2022).  Immediate treatment for oligohydramnios is imperative because the fetus’s lungs need this fluid to develop properly.
Read the following clinical scenario and then answer the questions that follow. This case study will evolve throughout the chapter.
Jennifer Davis had a difficult pregnancy. Prior to conceiving, she lived with type 2 diabetes, hypertension, chronic moderate anemia, and stage 2 CKD. During the pregnancy, despite being very adherent, her kidney disease advanced. She closely followed her nutritional restrictions for low sodium, low sugar, low carbohydrate, low fat, and low protein, and as she progressed closer to kidney failure, she had to restrict fluids as well. Even though she followed these dietary modifications, after delivery she was diagnosed with ESRD and was scheduled to have a catheter placed to start hemodialysis (mechanical waste filtration).
Because of her health issues, she experienced preeclampsia that developed into eclampsia (seizures), requiring an emergency cesarean birth of her infant at 32 weeks’ gestation. Her infant demonstrated effects from Jennifer’s health issues as well. Due to Jennifer’s chronic anemia, nutritional restrictions, and preterm delivery, the infant was of very low birth weight and small for gestational age (SGA) due to intrauterine growth restrictions. She required 8 weeks of care in the NICU after birth.
Kayla Davis is now 1 week old. She weighs 1 kg (2.2 lb) and is 33 cm (13 in.) long.
-
Water
-
Proteins
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Fats
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Carbohydrate
Childhood
The U.S. Department of Agriculture (USDA) updated nutritional requirements in 2020, including recommendations for infants and toddlers for the first time. It is recommended that children have no added sugar in their diet until age 2 years (USDA, 2020). They should eat a large selection of fruits, vegetables, and grains, preferably with at least half of the grains being whole grains, and their proteins should come from lean meat sources or plant-based proteins (McCarthy, 2021), with low-fat dairy products added after age 2 years. They should not receive the same portion sizes as adults.
In children with altered kidney function, it may be difficult to ensure that they get enough calories and protein to grow within the confines of their restrictive nutritional needs. To protect renal health in children who do not have altered kidney function, sodium should be limited to less than 2 g/day because amounts greater than this can lead to fluid retention and hypertension. Sugar intake should be limited to less than 25 g/day (American Heart Association, n.d.) because it can lead to obesity, hypertension, and kidney hyperfiltration. Children should be encouraged to eat fruits and vegetables because, in addition to their other benefits, the fiber will help prevent constipation (Deshpande, n.d.) and keep cholesterol in check. Fruits also contain citrate, which helps prevent stone formation (Deshpande, n.d.). Adequate water intake of 34–61 oz/day (1–1.8 L) can prevent urinary infections, constipation, dehydration, and kidney stones and assist in weight control (Deshpande, n.d.).
Common conditions that can develop even if children are not born with renal problems are UTIs, enuresis (bladder incontinence after the age of 3 years), and nephrolithiasis. Nutritional recommendations can help maintain optimal renal health.
Nephrolithiasis has become more common than it once was in children and adolescents (American Academy of Pediatrics, 2021) due to diets higher in processed foods, low vegetable intake, and lower physical activity levels. Risk factors for developing kidney stones in children and adolescents include family history of nephrolithiasis; a diet high in salt, meat, and processed foods; a diet low in fruits and vegetables; dehydration with low urine output; inherited conditions such as cystinuria (a rare condition in which kidney stones form from an amino acid called cysteine ) and hyperoxaluria (excessive oxalate in the urine); some medications, including furosemide and topiramate; blocked urine flow; bowel diseases; kidney infection; prolonged sedentary periods, especially bed rest; weight loss surgery (American Academy of Pediatrics, 2021); and urinary tract infection s (UTIs).
Enuresis may be diurnal (occurring in the daytime), nocturnal (occurring in the nighttime), primary (occurring in someone who has never had total bladder control), or secondary (occurring in someone who previously could control their bladder) (Johns Hopkins Medicine, n.d.). Enuresis has many psychological and physical causes. Renal causes include bladder pressure from constipation, overactive bladder (OAB), small bladder, structural problems in the urinary tract, inability to feel when the bladder is full (such as during sleep), UTI, and failure to urinate enough. Many of these causes would need to be addressed with the child’s primary care provider. However, teaching the child different hygiene habits can be helpful, and OAB can be helped by following special nutritional considerations, discussed later in this chapter.
Children urinate more often than adults because they tend to drink more fluids in relation to their size, have smaller bladders, and have less control over their urinary muscles, which results in feeling the need to “go” more often. UTIs can be very common in this age group; therefore, young children need to be educated on proper urinary hygiene (American Academy of Pediatrics, 2015). Females are more susceptible to UTIs than males because they have shorter urethras, so bacteria can more readily enter the urinary tract (American Academy of Pediatrics, 2015). General signs and symptoms of a UTI include vomiting, high temperature, lethargy, irritability, poor feeding, poor weight gain, and jaundice (NHS Inform, 2023). More specific signs and symptoms include pain or burning with urination; frequency or urgency of urination; deliberate holding of urine; change in toileting habits (such as enuresis); pain in the side, back, or abdomen; bloody or cloudy urine; and foul-smelling urine.
Some nutritional measures can help prevent UTIs. Children should drink plenty of water to avoid constipation and to maintain the kidneys’ function in eliminating waste products. Cranberry or blueberry juice can help create a more acidic urinary environment that will discourage bacterial growth (American Academy of Pediatrics, 2015). Colas and caffeinated beverages should be discouraged because these irritate the bladder and cause diuresis.
Certain foods are beneficial in preventing UTIs as well. Yogurts with live and active cultures and other fermented products are recommended because they contain bacteria that help balance the body’s systems and can thereby decrease the risk for UTIs (Norton Children’s, 2020; Urology Specialists, 2015). Foods high in vitamin C, including oranges, lemons, strawberries, grapefruits, tomatoes, broccoli, and spinach, are beneficial to maintain a balanced urine acidity level (Figure 16.2). Foods containing proanthocyanidins , including cranberries, raspberries, and blueberries, are a good addition because these substances help prevent Escherichia coli infection, the number one bacterial cause of common UTIs (Norton Children’s, 2020; Urology Specialists, 2015). High-fiber foods such as whole grains, apples, bananas, and legumes are important to prevent constipation, which can block urine excretion from the body and in turn cause urine stasis, which encourages bacterial growth (Norton Children’s, 2020). Sugar intake should be limited because it provides a fuel source and breeding ground for bacteria to thrive (Urology Specialists, 2015).
Read the following clinical scenario and then answer the questions that follow. This case study is a follow-up to Case Study Part A.
Kayla was diagnosed with hydronephrosis (swollen kidney due to urine accumulation) related to uteropelvic junction obstruction (blockage). This resolved on its own after 2 weeks of life. She was transferred from the NICU to the regular pediatric floor for care at 8 weeks of age and was discharged home the following week. Her prematurity and intrauterine growth restriction have resulted in ongoing effects on her development. She was diagnosed with type 1 diabetes because her pancreas is nonfunctioning, and one of her kidneys is nonfunctioning. The kidney is small and undeveloped. The other kidney is functioning despite the hydronephrosis.
Unfortunately, by age 6, Kayla has developed CKD and is in stage 3 when diagnosed.
3
Which nutritional restrictions will pose the most problems for her growth and development at this stage?
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Protein and calories
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Fluid and potassium
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Phosphorus and calcium
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Magnesium and sodium
4
Because this client already has serious issues with their kidneys, the nurse educates the client’s parents on nutritional measures to prevent further kidney issues that can exacerbate their other conditions. Which option would necessitate the need for further education?
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Broccoli
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Whole grain bread
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Cranberries
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Ramen noodles
Adolescence
During adolescence, puberty, hormonal changes, and growth spurts occur. The body goes through many changes that require healthy and supportive nutrition to ensure proper growth and maturity. Food should include high levels of calcium, vitamin D, and iron for bone and muscle development (Castle, 2022). Iron for males and females aged 9–13 should be around 8 mg/day. Males aged 14–18 should receive 11 mg/day, whereas females in this age group should receive 15 mg/day. The calcium recommendation for adolescents is 1300 mg/day, and the vitamin D recommendation is 600 International Units daily. Caloric intake should range from 1800–3200 calories daily for males and from 1600–2400 calories daily for females, depending on activity level (USDA, 2020).
Adolescents should follow the same nutritional guidelines as other age groups for urinary health. UTIs and nephrolithiasis are the more common kidney-related issues in this age group. The same nutritional restrictions and recommendations discussed elsewhere in this chapter for these conditions apply for adolescents as well.
UTIs have different causes in this group, necessitating additional educational points to discuss with the adolescent. All of the earlier hygiene recommendations are still important, but an additional cause of UTIs in adolescents (as well as in adults) is sexually transmitted infections (STIs) . Chlamydia, gonorrhea, and trichomoniasis all can infect the urethra and advance into the urinary system. Females also have increased risk for developing cross infections from bacterial vaginosis (BV) and yeast infections .
Nutritional recommendations to help avoid BV and yeast infections include staying hydrated with plenty of water and avoiding sugary, caffeinated, and carbonated beverages to help maintain a healthy pH balance. Probiotic and prebiotic foods also help maintain the pH balance in the vagina and prevent yeast or bacterial overgrowth. Foods that contain probiotic s include yogurt with live cultures, sauerkraut, kimchi, pickles, miso, tempeh, and kombucha (Sass, 2022). Prebiotic s can be found in chicory root, leeks, garlic, asparagus, and onions.
Foods with a low glycemic index may also help prevent BV by helping maintain the pH balance ; such foods include whole grains, including oatmeal and barley; quinoa; yogurt; milk; nuts; legumes; beans; grapefruit; oranges; and carrots (Sass, 2022). High-fiber foods support healthy bacterial growth and help prevent BV. Vitamin D has been found to be important in overall vaginal health and pH balance). Foods that contain vitamin D include trout, cooked salmon, sardines, eggs, cheddar cheese, and fortified milk (Sass, 2022). Another important addition to the diet is apples, at least one daily, as these have been shown to improve vaginal lubrication (Sass, 2022; Tommaso et al., 2014). Foods to restrict include white bread, high-sugar foods, white rice, honey, processed grains, and highly processed foods (Sass, 2022).
Read the following clinical scenario and then answer the questions that follow. This case study is a follow-up from Case Study Parts A and B.
Kayla and her mother have been managing her condition well, and her stage 3 CKD has remained stable. She is now 13 years old and has come into the clinic for a regular check-up. The nurse is planning to provide Kayla with education on continued management of her CKD.
5
What would the nurse include when teaching a client Kayla’s age how to best promote renal health and slow the progression of CKD?
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Recommendation to increase fiber intake
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STI prevention
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Recommendation to increase fluids
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Recommendation to decrease exercise
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How many calories would be in the acceptable daily allowance range for Kayla?
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2,000 calories daily
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1,500 calories daily
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2,600 calories daily
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3,000 calories daily
Adulthood
Adults will not require as much from their nutritional intake for growth, although certain hormonal changes still occur in adulthood. Individuals in this age group face more health risks that can impact the kidneys and their functioning, including hypertension, diabetes types 1 and 2, CKD, PKD, benign prostatic hyperplasia (BPH), nephrolithiasis, cardiovascular disease, and hyperlipidemia. Foods should be nutrient dense; low in sugars, sodium, and saturated fats; high in fiber and calcium; and include vitamin D (USDA, 2020, p. 101). Nutritional recommendations specific for renal health mentioned previously in the chapter apply to this age group as well. Nephrolithiasis, UTIs, BPH, and CKD are more common in this age group due to the comorbidities that often develop.
Read the following clinical scenario and then answer the questions that follow. This case study is a follow-up from Case Study Parts A, B, and C.
At age 18, Kayla becomes pregnant. Her GFR is 49 mL/min/1.73 m 2 , and she has hypertension, type 1 diabetes, and chronic anemia. Despite the known risks to her and the fetus, she wants to go through with the pregnancy. She is currently not restricting fluids, but she is restricting protein, potassium, phosphorus, sodium, sugar, and carbohydrates. She is following all heart-healthy recommendations.
7
The nurse is educating Kayla about the potential problems in a pregnancy involving her unique health conditions. What would the nurse include in this education?
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Postterm delivery
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Spina bifida
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Multifetal pregnancy
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Fetal intrauterine growth restriction
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When Kayla is being monitored during her pregnancy, which lab value would be concerning and require immediate treatment?
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GFR 56 mL/min/1.73 m 2
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GFR 15 mL/min/1.73 m 2
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GFR 87 mL/min/1.73 m 2
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GFR 92 mL/min/1.73 m 2
Kayla decides to continue with the pregnancy despite the risks. During her second trimester, the fetus is markedly small due to intrauterine growth restriction, and Kayla has advanced to stage 4 CKD and is approaching the need for dialysis. Because of Kayla’s rapid decline and the struggle to keep her potassium levels normal, her health care provider orders a catheter to be placed for the impending need for dialysis and plans to deliver the baby as early as safely possible. Unfortunately, 2 days before she is scheduled to have the catheter placed, Kayla goes into cardiac arrest due to a dysrhythmia from hyperkalemia. She is unable to be revived, and her fetus is too premature to survive.
Later Adulthood
For adults aged 60 years and older, the risk for chronic disease is highest. Such conditions include cardiovascular disease, type 2 diabetes, obesity, hypertension, hyperlipidemia, CKD, congestive heart failure, cancers, and BPH. Renal function also naturally declines in this age group, with defined GFR being less than 60 mL/min/1.73 m 2 (National Kidney Foundation, 2023). Therefore, preserving kidney function is very important, and medication dosages may need to be adjusted to ensure safety.
Nutritional intake should include nutrient-dense foods and be rich in whole grains, fruits, vegetables, and dairy, as well as protein to prevent muscle loss. Older individuals should also increase their intake of vitamin B 12 because the ability to absorb this vitamin declines as people age (USDA, 2020, p. 128). Foods high in B 12 include beef liver, clams, cooked salmon, tuna, eggs, fortified breakfast cereal, spinach, and kidney beans (National Institutes of Health, 2022b). Adults in this age group must also be sure to drink enough fluids, especially water, because the sensation of thirst declines with age, increasing the risk for dehydration and UTIs (U.S. Department of Agriculture, 2020, p. 129).


4.10: Homology of σ and π orbitals in MO diagrams
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The ozone molecule (and related 18e molecules that contain three non-H atoms, such as NO 2 - and the allyl anion [CH 2 -CH-CH 2 ] - ) is an example of 3-center 4-electron π-bonding. Our MO treatment of ozone is entirely analogous to the 4-electron H 3 - anion. We map that solution onto this one as follows:
The nonbonding π-orbital has a node at the central O atom. This means that the non-bonding electron pair in the π-system is shared by the two terminal O atoms, i.e., that the formal charge is shared by those atoms. This is consistent with the octet resonance structure of ozone.
This trick of mapping the solution for a set of s-orbitals onto a π-bonding problem is a simple example of a broader principle called the isolobal analogy . This idea, developed extensively by Roald Hoffmann at Cornell University, has been used to understand bonding and reactivity in organometallic compounds. [5] In the isolobal analogy, symmetry principles (as illustrated above in the analogy between H 3 - and ozone) are used to construct MO diagrams of complex molecules containing d-frontier orbitals from simpler molecular fragments.
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Professor Roald Hoffmann's ideas about orbital symmetry have helped explain the bonding and reactivity of organic and organometallic molecules, and also the structures and properties of extended solids. |
The triiodide ion.
An analogous (and seemingly more complicated) case of 3-center 4-electron bonding is
I
3
-
. Each I atom has 4 valence orbitals (5s, 5p
x
, 5p
y
, 5p
z
), making a total of 12 frontier orbitals, and the I
3
-
anion has 22 electrons.
We can simplify the problem by recalling two periodic trends:
- The s-p orbital splitting is large, relative to the bond energy, after the second row of the periodic table. Thus, the 5s orbital is low in energy and too contracted to make bonds with its neighbors.
- π-overlap of 5p orbitals is very weak, so the 5p x and 5p y orbitals will also be non-bonding.
This leaves only the three 5p z orbitals to make bonding/nonbonding/antibonding combinations. Again, the problem is entirely analogous to ozone or H 3 - .
Counting orbitals we obtain 9 lone pairs from the nonbonding 5s, 5p x , and 5p y orbitals, as well as one bond and one lone pair from the 5p z orbital combinations above. The total of 10 nonbonding pairs and one bond accounts for the 22 electrons in the ion. The non-bonding 5p z pair is localized on the terminal I atoms, giving each a -1/2 formal charge. This MO description is entirely consistent with the octet no-bond resonance picture of I 3 - that we developed in Chapter 1.


26.1: Introduction
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- Steven Farmer & Dietmar Kennepohl
- University of Illinois Springfield
Objectives
After completing this section, you should be able to
- give examples of the various biological roles played by proteins.
- identify amino acids as being the building blocks from which all proteins are made.
- show, in a general way, how the joining together of a number of amino acids through the formation of peptide bonds results in the formation of proteins.
Key Terms
Make certain that you can define, and use in context, the key terms below.
- amino acid
- enzyme
- peptide bond
- protein
Study Notes
The “peptide bond” or “peptide linkage” that is formed between the amino group of one amino acid and the carboxyl group of a second amino acid is identical to the C$\ce{-}$N bond present in amides (see Section 21.7). We shall review the nature of such bonds in Section 26.4.
Proteins are polymers of amino acids , linked by amide groups known as peptide bond s. An amino acid can be thought of as having two components: a 'backbone', or 'main chain', composed of an ammonium group, an 'alpha-carbon', and a carboxylate, and a variable 'side chain' (in green below) bonded to the alpha-carbon.
There are twenty different side chains in naturally occurring amino acids , and it is the identity of the side chain that determines the identity of the amino acid: for example, if the side chain is a -CH 3 group, the amino acid is alanine, and if the side chain is a -CH 2 OH group, the amino acid is serine. Many amino acid side chains contain a functional group (the side chain of serine, for example, contains a primary alcohol), while others, like alanine, lack a functional group, and contain only a simple alkane.
The two 'hooks' on an amino acid monomer are the amine and carboxylate groups. Proteins (polymers of ~50 amino acids or more) and peptides (shorter polymers) are formed when the amino group of one amino acid monomer reacts with the carboxylate carbon of another amino acid to form an amide linkage, which in protein terminology is a peptide bond . Which amino acids are linked, and in what order - the protein sequence - is what distinguishes one protein from another, and is coded for by an organism's DNA. Protein sequences are written in the amino terminal (N-terminal) to carboxylate terminal (C-terminal) direction, with either three-letter or single-letter abbreviations for the amino acids (see amino acid table ). Below is a four amino acid peptide with the sequence "cysteine - histidine - glutamate - methionine". Using the single-letter code, the sequence is abbreviated CHEM.
When an amino acid is incorporated into a protein it loses a molecule of water and what remains is called a residue of the original amino acid. Thus we might refer to the 'glutamate residue' at position 3 of the CHEM peptide above.
Once a protein polymer is constructed, it in many cases folds up very specifically into a three-dimensional structure, which often includes one or more 'binding pockets' in which other molecules can be bound. It is this shape of this folded structure, and the precise arrangement of the functional groups within the structure (especially in the area of the binding pocket) that determines the function of the protein.
Enzymes are proteins which catalyze biochemical reactions. One or more reacting molecules - often called substrates - become bound in the active site pocket of an enzyme, where the actual reaction takes place. Receptors are proteins that bind specifically to one or more molecules - referred to as ligands - to initiate a biochemical process. For example, we saw in the introduction to this chapter that the TrpVI receptor in mammalian tissues binds capsaicin (from hot chili peppers) in its binding pocket and initiates a heat/pain signal which is sent to the brain.
Shown below is an image of the glycolytic enzyme fructose-1,6-bisphosphate aldolase (in grey), with the substrate molecule bound inside the active site pocket.
(x-ray crystallographic data are from Protein Science 1999 , 8, 291 ; pdb code 4ALD. Image produced with JMol First Glance )


11.4: Phase Changes
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Learning Objectives
- Determine the heat associated with a phase change.
Matter can exist in one of several different states, including a gas, liquid, or solid state. The amount of energy in molecules of matter determines the state of matter .
- A gas is a state of matter in which atoms or molecules have enough energy to move freely. The molecules come into contact with one another only when they randomly collide.
- A liquid is a state of matter in which atoms or molecules are constantly in contact but have enough energy to keep changing positions relative to one another.
- A solid is a state of matter in which atoms or molecules do not have enough energy to move. They are constantly in contact and in fixed positions relative to one another.
The following are the changes of state:
| Solid → Liquid | Melting or fusion |
|---|---|
| Liquid → Gas | Vaporization |
| Liquid → Solid | Freezing |
| Gas → Liquid | Condensation |
| Solid → Gas | Sublimation |
- If heat is added to a substance, such as in melting, vaporization, and sublimation, the process is endothermic . In this instance, heat is increasing the speed of the molecules causing them move faster (examples: solid to liquid; liquid to gas; solid to gas).
- If heat is removed from a substance, such as in freezing and condensation, then the process is exothermic . In this instance, heat is decreasing the speed of the molecules causing them move slower (examples: liquid to solid; gas to liquid). These changes release heat to the surroundings.
- The amount of heat needed to change a sample from solid to liquid would be the same to reverse from liquid to solid. The only difference is the direction of heat transfer.
Example \(\PageIndex{1}\)
Label each of the following processes as endothermic or exothermic.
- water boiling
- ice forming on a pond
Solution
- endothermic - you must put a pan of water on the stove and give it heat in order to get water to boil. Because you are adding heat/energy, the reaction is endothermic.
- exothermic - think of ice forming in your freezer instead. You put water into the freezer, which takes heat out of the water, to get it to freeze. Because heat is being pulled out of the water, it is exothermic. Heat is leaving.
Exercise \(\PageIndex{1}\)
Label each of the following processes as endothermic or exothermic.
- water vapor condensing
- gold melting
- Answer
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a. exothermic
b. endothermic
A phase change is a physical process in which a substance goes from one phase to another. Usually the change occurs when adding or removing heat at a particular temperature, known as the melting point or the boiling point of the substance. The melting point is the temperature at which the substance goes from a solid to a liquid (or from a liquid to a solid). The boiling point is the temperature at which a substance goes from a liquid to a gas (or from a gas to a liquid). The nature of the phase change depends on the direction of the heat transfer. Heat going into a substance changes it from a solid to a liquid or a liquid to a gas. Removing heat from a substance changes a gas to a liquid or a liquid to a solid.
Two key points are worth emphasizing. First, at a substance’s melting point or boiling point, two phases can exist simultaneously. Take water (H 2 O) as an example. On the Celsius scale, H 2 O has a melting point of 0°C and a boiling point of 100°C. At 0°C, both the solid and liquid phases of H 2 O can coexist. However, if heat is added, some of the solid H 2 O will melt and turn into liquid H 2 O. If heat is removed, the opposite happens: some of the liquid H 2 O turns into solid H 2 O. A similar process can occur at 100°C: adding heat increases the amount of gaseous H 2 O, while removing heat increases the amount of liquid H 2 O (Figure \(\PageIndex{1}\)).
Water is a good substance to use as an example because many people are already familiar with it. Other substances have melting points and boiling points as well.
Second, as shown in Figure \(\PageIndex{1}\), the temperature of a substance does not change as the substance goes from one phase to another . In other words, phase changes are isothermal (isothermal means “constant temperature”). Again, consider H 2 O as an example. Solid water (ice) can exist at 0°C. If heat is added to ice at 0°C, some of the solid changes phase to make liquid, which is also at 0°C. Remember, the solid and liquid phases of H 2 O can coexist at 0°C. Only after all of the solid has melted into liquid does the addition of heat change the temperature of the substance.
For each phase change of a substance, there is a characteristic quantity of heat needed to perform the phase change per gram (or per mole) of material. The heat of fusion (Δ H fus ) is the amount of heat per gram (or per mole) required for a phase change that occurs at the melting point. The heat of vaporization (Δ H vap ) is the amount of heat per gram (or per mole) required for a phase change that occurs at the boiling point. If you know the total number of grams or moles of material, you can use the Δ H fus or the Δ H vap to determine the total heat being transferred for melting or solidification using these expressions:
\[\text{heat} = n \times ΔH_{fus} \label{Eq1a} \]
wher e \(n\) is th e number of moles and \(ΔH_{fus}\) is expressed in energy/mole or
\[\text{heat} = m \times ΔH_{fus} \label{Eq1b} \]
where \(m\) is the mass in grams and \(ΔH_{fus}\) is expressed in energy/gram.
For the boiling or condensation, use these expressions:
\[\text{heat} = n \times ΔH_{vap} \label{Eq2a} \]
wher e \(n\) is the number of moles) and \(ΔH_{vap}\) is expressed in energy/mole or
\[\text{heat} = m \times ΔH_{vap} \label{Eq2b} \]
wh ere \(m\) i s the mass in grams and \(ΔH_{vap}\) is expressed in energy/gram.
Remember that a phase change depends on the direction of the heat transfer. If heat transfers in, solids become liquids, and liquids become solids at the melting and boiling points, respectively. If heat transfers out, liquids solidify, and gases condense into liquids. At these points, there are no changes in temperature as reflected in the above equations.
Example \(\PageIndex{2}\)
How much heat is necessary to melt 55.8 g of ice (solid H 2 O) at 0°C? The heat of fusion of H 2 O is 79.9 cal/g.
Solution
We can use the relationship between heat and the heat of fusion (Equation \(\PageIndex{1}\)) to determine how many cal of heat are needed to melt this ice:
\[ \begin{align*} \ce{heat} &= \ce{m \times ΔH_{fus}} \\[4pt] \mathrm{heat} &= \mathrm{(55.8\: \cancel{g})\left(\dfrac{79.9\: cal}{\cancel{g}}\right)=4,460\: cal} \end{align*} \nonumber \]
Exercise \(\PageIndex{2}\)
How much heat is necessary to vaporize 685 g of H 2 O at 100°C? The heat of vaporization of H 2 O is 540 cal/g.
- Answer
-
\[ \begin{align*} \ce{heat} &= \ce{m \times ΔH_{vap}} \\[4pt] \mathrm{heat} &= \mathrm{(685\: \cancel{g})\left(\dfrac{540\: cal}{\cancel{g}}\right)=370,000\: cal} \end{align*} \nonumber \]
Table \(\PageIndex{1}\) lists the heats of fusion and vaporization for some common substances. Note the units on these quantities; when you use these values in problem solving, make sure that the other variables in your calculation are expressed in units consistent with the units in the specific heats or the heats of fusion and vaporization.
| Substance | ΔH fus (cal/g) | ΔH vap (cal/g) |
|---|---|---|
| aluminum (Al) | 94.0 | 2,602 |
| gold (Au) | 15.3 | 409 |
| iron (Fe) | 63.2 | 1,504 |
| water (H 2 O) | 79.9 | 540 |
| sodium chloride (NaCl) | 123.5 | 691 |
| ethanol (C 2 H 5 OH) | 45.2 | 200.3 |
| benzene (C 6 H 6 ) | 30.4 | 94.1 |
Sublimation
There is also a phase change where a solid goes directly to a gas:
\[\text{solid} \rightarrow \text{gas} \label{Eq3} \]
This phase change is called sublimation . Each substance has a characteristic heat of sublimation associated with this process. For example, the heat of sublimation (Δ H sub ) of H 2 O is 620 cal/g.
We encounter sublimation in several ways. You may already be familiar with dry ice, which is simply solid carbon dioxide (CO 2 ). At −78.5°C (−109°F), solid carbon dioxide sublimes, changing directly from the solid phase to the gas phase:
\[\mathrm{CO_2(s) \xrightarrow{-78.5^\circ C} CO_2(g)} \label{Eq4} \]
Solid carbon dioxide is called dry ice because it does not pass through the liquid phase. Instead, it does directly to the gas phase. (Carbon dioxide can exist as liquid but only under high pressure.) Dry ice has many practical uses, including the long-term preservation of medical samples.
Even at temperatures below 0°C, solid H 2 O will slowly sublime. For example, a thin layer of snow or frost on the ground may slowly disappear as the solid H 2 O sublimes, even though the outside temperature may be below the freezing point of water. Similarly, ice cubes in a freezer may get smaller over time. Although frozen, the solid water slowly sublimes, redepositing on the colder cooling elements of the freezer, which necessitates periodic defrosting (frost-free freezers minimize this redeposition). Lowering the temperature in a freezer will reduce the need to defrost as often.
Under similar circumstances, water will also sublime from frozen foods (e.g., meats or vegetables), giving them an unattractive, mottled appearance called freezer burn. It is not really a “burn,” and the food has not necessarily gone bad, although it looks unappetizing. Freezer burn can be minimized by lowering a freezer’s temperature and by wrapping foods tightly so water does not have any space to sublime into.
Key Takeaway
- There is an energy change associated with any phase change.


12.3: Conservation of an angular momentum
A special situation is the case where the external angular impulse \(\overrightarrow{\boldsymbol{H}}_{\text {ang }, P}\) is zero. We substitute this condition in Equation 12.4 and obtain that angular momentum does not change in this situation:
If the total angular impulse generated by external moments on a system with respect to a fixed reference point \(P\) is zero \(\left(\overrightarrow{\boldsymbol{H}}_{\mathrm{ang}, P}=\overrightarrow{\mathbf{0}}\right)\), then the total angular momentum of the system is conserved, and does not change in time.
\[\sum_{i} \overrightarrow{\boldsymbol{L}}_{i / P}\left(t_{1}\right)=\sum_{i} \overrightarrow{\boldsymbol{L}}_{i / P}\left(t_{2}\right) \tag{12.7} \label{12.7}\]
Whether or not conservation of angular momentum occurs can depend on the choice of the reference point \(P\). For example when a single external force \(\overrightarrow{\boldsymbol{F}}_{i}\) acts at a fixed point of action \(i\) on a system, the reference point \(P\) can be chosen at point \(i\), or at any other point on the line of action of force \(\overrightarrow{\boldsymbol{F}}_{i}\), to ensure that \(\overrightarrow{\boldsymbol{H}}_{\text {ang }, P}=\overrightarrow{\mathbf{0}}\) and the law of conservation of angular momentum holds.
An important case for conservation of angular momentum are systems on which there are no external moments and forces acting because in those systems the law of conservation of angular momentum holds for any choice of reference point \(P\).
It is important to note that when analysing systems, the boundaries of the system can be chosen arbitrarily. By expanding the system boundaries to include all objects that generate forces, all forces will become internal forces,
and conservation of (angular) momentum for this expanded system will hold. In the extreme case, the momentum and angular momentum of our whole universe are expected to be constant, since there are no external forces and moments acting on it, such that the law of conservation of momentum and angular momentum hold.