3.5: The Development of Commerce
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“The prime mover in the separation of household and business accounting, and hence in the development of the early capitalistic institutions, was the need for credit.”
NOTE ON SOURCE: This passage is from Wirtschaftsgeschicte , a collection of Weber’s lecture notes , first published after his death in 1923. The first English translation ( General Economic History ) was made in 1927, by Frank Knight, an American professor of political economy. It is known as the source of Weber’s institutionalist theory of capitalism. The selection below is direct from the Knight translation.
Introduction – Why this is important and what to look for
This selection is from Part III of the General Economic History, “Commerce and Exchange in the Pre-Capitalist Age.” It is a good example of Weber’s institutionalist approach. Unlike Durkheim, who evaluated the causes and consequences of existing social institutions, Weber seeks to explain historical and institutional change as the product of several small advances which, taken collectively, provide the possibility of new institutions (such as capitalism). This section has been shortened considerably to focus on these several small advances, with much of the specific historical detail omitted.
Chapter 14: Points of Departure in the Development of Commerce
In the beginnings commerce is an affair between ethnic groups; it does not take place between members of the same tribe or of the same community but is in the oldest social communities an external phenomenon, being directed only toward foreign tribes. It may, however, begin as a consequence of specialization in production between groups. In this case there is either tribal trade of producers or peddling trade in products of a foreign tribe. In any case the oldest commerce is an exchange relation between alien tribes.
The trade of a tribe in its own products may appear in various forms. It usually develops to begin with as an auxiliary occupation of peasants and persons engaged in house industry, and in general as a seasonal occupation.
Out of this stage grow peddling and huckstering as an independent occupation; tribal communities develop which soon engage in commerce exclusively.
Chapter 15. Technical Requisites for the Transportation of Goods
For the existence of commerce as an independent occupation, specific technological conditions are prerequisite. In the first place there must be regular and reasonably reliable transport opportunities. One must, to be sure, think of these in the most primitive possible terms through long ages. Not only in the Assyrian and Babylonian times were inflated goat skins use for the diagonal crossing of rivers, but even in the Mohammedan period, skin-bag boats long dominated the river traffic.
On land the trader had recourse far into the middle ages to primitive transport media. The first was his own back, on which he carried his goods down to the 13th century; then pack animals or a two-wheeled cart drawn by one or at the most two horses, the merchant being restricted to commercial routes as roads in our sense are not to be thought of. Only in the east and in the interior of Africa does caravan trade with slaves as porters appear to occur fairly early.
Traffic by sea had to make use of equally primitive means of transportation. In antiquity, and likewise in the early middle ages, the boat propelled by oars was the rule.
Chapter 16. Forms of Organization of Transportation and Commerce
The turnover of medieval commerce as measured by modern standards was extremely small. It was carried on by mere small dealers who worked with trifling quantities. The total trade between England and the Hanseatic League in the 14th century, at the time of its highest development, came to less than $4,000 dollars.
On account of the danger from pirates, a single ship was not in a position to determine independently its time of sailing. Ships formed themselves into caravans and were either conveyed by armed vessels or were themselves armed. The average duration of a voyage of a marine caravan in the Mediterranean varied from a half-year to a year. In Genoa only one caravan a year went east to Asia, in Venice two. The voyage in caravans resulted in an extremely slow turnover of the capital.
In the middle ages feudal lords were interested in the maintenance of commercial routes in order to make money. They cared for the roads by putting their peasants to work to maintain them and collected tolls on their use. There was no agreement among the lords establishing a rational layout of the roads; each located the road in a way to make sure of recouping its cost in duties and tolls.
In consequence, the volume of land trade in the middle ages was much smaller even than that of trade by sea.
The second great requirement of commerce was legal protection. The merchant was an alien (foreigner) and would not have the same legal opportunities as a member of the nation or tribe, and therefore required special legal arrangements.
A great step in progress happened was the organization of a large number of merchants in a hanse . This was ordinarily a guild of foreign merchants carrying on trade in a distant city, who organized for mutual protection. It goes without saying that the organization presupposed a permit from the ruler of the city.
Finally, it became necessary to establish fixed times for trading: the buyer and seller must be able to find one another. This requirement was met by fixed markets and gave rise to the market concessions. Markets were everywhere established for the foreign traders by concession from the princes – in Egypt, India, and European antiquity, and in the middle ages. The object of such a concession was on the one hand the provision for the needs of the authority granting the concession, and on the other, the promotion of fiscal aims: the prince wished to profit by the trade in the market.
Out of this original relation between the merchants visiting the market and the authority granting the concession, evolved still other institutions. The merchants needed large quarters for having their goods tested, weighed and stored.
A professional trading class of the towns developed in the following way. The resident merchant is to begin with an itinerant trader. He travels periodically in order to market products at a distance or to secure products from a distance and is a peddler who has acquired a fixed residence. The next stage is that in which he has the traveling done for him, either by an employee or servant or by a partner. The third stage is formed by the system of factories. [1] Finally, the resident trader becomes completely fixed in his location and deals with distant regions by correspondence only. This condition did not become possible until the late middle ages because there was not sufficient inter-territorial legal security.
The resident traders as a class had to contend against other groups. One series of such struggles were external, such as the struggle to maintain the monopoly of the urban market. The resident trader also contended with the merchants settled in the country, on the land. The second great object of contention in the merchant class was in regard to internal equality of opportunity. One of the members protected by the group must not have better chances than another, and this applied especially to retailing. This purpose was served by the prohibition of pre-sale or ‘forestalling’ and the right of sharing. The first of these rules prohibited dealers from selling goods before they had been brought into the town. On the other hand, if one merchant had bought more goods than another, the right sharing became operative; it specified that any member of the association could demand that a part of the goods in question be given up to him on payment of their actual cost.
Finally, the resident merchant class was in conflict with the consumer’s interests and was divided internally according as it was interested in the local market or in distant trade. The consumers wished as far as possible to buy at first hand from the foreign traders, while the interest of the great majority of the local merchants was opposed. So began the splitting off of a wholesale trading interest and an opposition of interest within the mercantile group, while the interests of the retailer and the consumer began to draw together.
Chapter 17. Forms of Commercial Enterprise
Rational commerce is the field in which quantitative reckoning first appeared, to become dominant finally over the whole extent of economic life. The necessity of exact calculation first arose wherever business was done by companies. In the beginning commerce was concerned with a turnover so slow and a profit so large that exact computation was not necessary. Goods were bought at a price that was fixed traditionally, and the trader could confine his efforts to getting as much as he could in sale. When trade was carried on by groups it was necessary to proceed to exact bookkeeping in order to render and accounting.
The technical means of computation were crude, down almost to the beginning of the modern period. Our system of characters, with values depending on their position, was an invention of the Hindus, from whom the Arabs took it over and was perhaps brought to Europe by the Jews. But not until the time of the crusades was it really known generally enough to serve as a method of computation; yet without this system, rational planning was impossible. All peoples who used a literal system of notation like that of antiquity and of the Chinese, had to have in addition some mechanical aid to computation. In antiquity and down to the late middle ages, the counting frame or abacus served this purpose. As the column system made its way into Europe it was at first viewed as a disreputable means of securing an immoral advantage in competition, since it worked in favor of the competitors of the virtuous merchant who disdained its use. Consequently, it was first sought to exclude it by prohibition. Down to the 15th and 16th century, the position system of notation struggled for official recognition.
It is true that there was bookkeeping in antiquity, in the banking business. The entries, however, were documentary in character; they were not designed as an instrument of control in connection with income. Genuine bookkeeping first arose in medieval Italy, and as late as the 16th century, a German clerk traveled to Venice to secure instruction in the art.
Bookkeeping grew up on the basis of the trading company. The family is everywhere the oldest unit supporting a continuous trading activity, in China and Babylonia, in India, and in the early middle ages. The son of a trading family was the confidential clerk and later the partner of the father. So, through generations one and the same family functioned as capitalists and lenders, as did the house of Igibi in Babylonia in the 6th century B.C.
The first form of group organization was occasional in character, the commenda . The continual participation in such ventures might gradually lead to a permanent enterprise. Permanent industrial enterprise developed with the spread of the commenda organization. Accountability penetrated into the family circle due to business connections outside of the family. Indeed, the prime mover in the separation of household and business accounting, and hence in the development of the early capitalistic institutions, was the need for credit. As long as dealing were in cash only, business remained a family affair. But as soon as transactions were suspended over a long interval, the question of guaranteeing credit intruded. To provide this guarantee, various means were used. The first was to make all members of a trading family liable for losses. This joint responsibility grew out of traditional criminal liability: in the case of high treason the house of the guilty person was razed and his family destroyed as suspect. Eventually, however, the most effective means for securing credit, and the method that outlived all others, was separation of the property of the trading company from the private wealth of its associates. This separation is found at the beginning of the 14th century in Florence. The step was unavoidable because more and more non-family members belonged to trading units. Out of the property of the firm evolved the concept of capital.
Chapter 21. Interests in the Pre-Capitalistic Period
In the beginnings interest is a phenomenon either of international or feudal law. Within a tribal village, or clan community, there is neither interest nor lending, since transfers of value in consideration for a payment are unknown. Where outside resources are used in economic life it is done under the form of neighborly help, such as house building.
The prohibition in the Torah against taking interest or usury against a brother rests partly on military and partly on religious grounds. The prohibition of interest taking from a brother is also characteristic of early Islam and Brahminism. Interest everywhere arises in the field of lending to foreigners outside the tribe or that of loans between classes. In this connection the contrast between creditor and debtor was originally always a contrast between a town-dwelling patriciate and rural peasants; it was so in China, India, and Rome, and so it is in the Old Testament as well.
The occasion for breaking through the prohibition against interest was provided by the loan of concrete property. In northern Europe the prohibition against usury was broken up by Protestantism, although not immediately.
Questions for Contemplation and Discussion
- Look up the standard dictionary meaning of “commerce.” What is the etymological root of this word? How does Weber’s explanation for its historical origin accord with this original meaning?
- This section can be read as a long list of requirements for trade, as we understand it, to be possible. Many of these prerequisites, such as roads, we take for granted now. Write down the complete list of items mentioned by Weber here. Do any surprise you? Can you think of any advances since the time of this writing (1923) that have helped advance commerce?
- Weber’s historical description of the rise of trade demonstrates that there has not been much “free” about this activity. What legal and political institutions supported the rise of commerce?
- Why would the consumer want to buy directly from foreign traders, rather than the local merchant? ( Chapter 16 ) Do you see similar struggles today? Which faction of the trading class is served by current economic policies?
- What is the position system of notation? Why was this at first prohibited? What was so revolutionary/threatening about this system? Note that Weber claims this as one of the primary perquisites for the development of capitalism in PESOC.
- This section ends with a short description of the traditional prohibitions against charging interest and a statement that these prohibitions were relaxed under Protestantism. For much more on why this was so, read PESOC. Consider the viability of currently existing capitalism had the prohibition never been lifted.
Concepts
Rational Commerce
Bookkeeping
Interest
-
Be careful here! Factories were originally places in which factors, representatives of the seller, were located. Only later did the term come to be associated with places of manufacturing. ↵


8.2: §58. Prefixes Denoting Place
Many Latin prefixes are derived from prepositions or adverbs that express spatial concepts. A similar principle can be seen at work in Germanic combinations like intake , outlet, undermine , and overthrow . If one can visualize the images that these prefixes convey, it is not necessary to memorize their meanings. The following schematic chart may provide some sense of the semantic picture. The shaded cube can be regarded as the representation of any space, affected by the various prefixes in the manner shown.
Just as super- and sub- can be viewed as a pair of semantic opposites, so can ad- (“to” or “toward”) be regarded as the opposite of a(b)- (“away,” “away from”). Ad- , which we won’t really be able to appreciate until we have some learned some verb vocabulary, has a bewildering tendency to assimilate with almost every consonant of the alphabet. It is present in the English words accept , affect , aggression , alleviate , announce , apprehend , acquire , arrogant , attract —and assimilate itself, which derives from ad- and similis (“liken toward”). Fortunately, ab- is much less prone to disguise, though it will appear sometimes in English as a- (a-verse) or abs- (abs-tract).
E- or ex- (“out,” “out of”), very common both in Latin and in English derivatives, is an easy prefix to recognize and remember. Eject is “throw out”; expel is “drive out.” In §42 we met egregious (L e-greg-ius ), “standing out from the flock.” In classical Latin, de- meant “down (from)”; the etymological meaning of descend is “climb down.” However, it could also suggest “off” or “away,” as in deter , “frighten off,” and devious (L de-vi-us ), “going off the road.”
Although they may perhaps overlap slightly in meaning, per- (“through”) and trans- (“across”) are quite straightforward. A perennial flower blooms “through the years,” whereas a transvestite “dresses across.” [1] If a substance is impervious (L im-per-vi-us ), it does not allow a way through. In addition to its spatial force, the prefix per- can also mean “thoroughly” ( perfervid , pellucid ); and occasionally it carries the strange meaning of “to the bad,” as in pervert , perjure , perfidy , perfidious , perish , and perdition .
The form circum- (“around”) may be the easiest of all Latin prefixes. Even a word as learned and polysyllabic as circumnavigate can be understood by young children, since the force of the prefix is so obvious. Still, we’ll find that circum- has produced some very interesting and unusual English derivatives. It is related to the Latin noun circus , and to the adverb circa , which appears in English dating formulas (c. 1950 or ca. 1950 = “around” 1950).
By now you have surely noticed the alarming fact that there are two separate Latin prefix spelled in- . Earlier we saw the negative form, which is actually less common in Latin than an identical morpheme with the very different English meaning of “in” or “into.” In conjunction with verb bases, in- will usually have this spatial force; thus infer and import both mean “bring in.” You must stay on guard to avoid being tricked by the two different meanings of in- . Sometimes English is downright mean, as in the case of flammable and inflammable , which are exact synonyms. If you want to say that something will not burn, you must call it non-flammable —though there is Christmas tinsel on sale in Victoria which describes itself, with admirable linguistic panache, as ininflammable .
-
The word
travesty
is derived from a form of entertainment in which men dressed as women. ↵


2.7: Skewness and the Mean, Median, and Mode
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Consider the following data set: 4; 5; 6; 6; 6; 7; 7; 7; 7; 7; 7; 8; 8; 8; 9; 10
This data set can be represented by following histogram. Each interval has width one, and each value is located in the middle of an interval.
The histogram displays a symmetrical distribution of data. A distribution is symmetrical if a vertical line can be drawn at some point in the histogram such that the shape to the left and the right of the vertical line are mirror images of each other. The mean, the median, and the mode are each seven for these data. In a perfectly symmetrical distribution, the mean and the median are the same. This example has one mode (unimodal), and the mode is the same as the mean and median. In a symmetrical distribution that has two modes (bimodal), the two modes would be different from the mean and median.
The histogram for the data: 4; 5; 6; 6; 6; 7; 7; 7; 7; 8 is not symmetrical. The right-hand side seems "chopped off" compared to the left side. A distribution of this type is called skewed to the left because it is pulled out to the left. We can formally measure the skewness of a distribution just as we can mathematically measure the center weight of the data or its general "speadness". The mathematical formula for skewness is:
\[a_{3}=\sum \frac{\left(x_{i}-\overline{x}\right)^{3}}{n s^{3}}.\nonumber\]
The greater the deviation from zero indicates a greater degree of skewness. If the skewness is negative then the distribution is skewed left as in Figure \(\PageIndex{2}\).
The mean is 6.3, the median is 6.5, and the mode is 7. Notice that the mean is less than the median, and they are both less than the mode. The mean and the median both reflect the skewing, but the mean reflects it more so.
The histogram for the data: 6; 7; 7; 7; 7; 8; 8; 8; 9; 10, is also not symmetrical, it is given in Figure \(\PageIndex{3}\). It is skewed to the right .
The mean is 7.7, the median is 7.5, and the mode is 7. Of the three statistics, the mean is the largest, while the mode is the smallest . Again, the mean reflects the skewing the most.
To summarize, generally if the distribution of data is skewed to the left, the mean is less than the median, which is often less than the mode. If the distribution of data is skewed to the right, the mode is often less than the median, which is less than the mean.
As with the mean, median and mode, and as we will see shortly, the variance, there are mathematical formulas that give us precise measures of these characteristics of the distribution of the data. Again looking at the formula for skewness we see that this is a relationship between the mean of the data and the individual observations cubed.
\[a_{3}=\sum \frac{\left(x_{i}-\overline{x}\right)^{3}}{n s^{3}}\nonumber\]
where \(s\) is the sample standard deviation of the data, \(x_{i}\), and \(\overline{x}\) is the arithmetic mean and \(n\) is the sample size.
Formally the arithmetic mean is known as the first moment of the distribution. The second moment we will see is the variance, and skewness is the third moment. The variance measures the squared differences of the data from the mean, and skewness measures the cubed differences of the data from the mean. While a variance can never be a negative number, the measure of skewness can and this is how we determine if the data are skewed right of left. The skewness for a normal distribution is zero, and any symmetric data should have skewness near zero. Negative values for the skewness indicate data that are skewed left and positive values for the skewness indicate data that are skewed right. By skewed left, we mean that the left tail is long relative to the right tail. Similarly, skewed right means that the right tail is long relative to the left tail. The skewness characterizes the degree of asymmetry of a distribution around its mean. While the mean and standard deviation are dimensional quantities (this is why we will take the square root of the variance ) that is, have the same units as the measured quantities \(x_{i}\), the skewness is conventionally defined in such a way as to make it nondimensional . It is a pure number that characterizes only the shape of the distribution. A positive value of skewness signifies a distribution with an asymmetric tail extending out towards more positive \(x\) and a negative value signifies a distribution whose tail extends out towards more negative \(x\). A zero measure of skewness will indicate a symmetrical distribution.
Skewness and symmetry become important when we discuss probability distributions in later chapters.


6.23: Public Speaking Resources- Open Source Textbooks, Assessment Tools, Webtools
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Here are some helpful resources I thought you might find helpful. I came across when researching this book.
National Communication Association Resources on Assessment
Assessing Motivation to Communication: Willingness to communicate and Personal Report of Communication Apprehension. National Communication Association
https://www.natcom.org/sites/default/files/pages/Assessment_Resources_Assessing_Motivation_to_Communicate_2ndEd.pdf
The Competent Speaker Speech Evaluation Form. National Communication Association https://www.natcom.org/sites/default/files/pages/Assessment_Resources_Competent_Speaker_Speech_Evaluation_Form_2ndEd.pdf
Advanced Public Speaking https://uark.pressbooks.pub/speaking/
Boundless Communications https://courses.lumenlearning.com/boundless-communications/
Communication in the Real World https://open.lib.umn.edu/communication
Communication in the Real World
https://lor.instructure.com/resources/34046bad87cf464c87e98bcfe97647e9?shared&fbclid=IwAR0dOtx4AqYQkYIj5_JKB8v3YjbUYJCSWUbIMgX3T8xSN2Dn1C8HlApjmfI
Exploring Public Speaking https://open.umn.edu/opentextbooks/textbooks/411
Exploring Public Speaking
https://alg.manifoldapp.org/projects/exploring-public-speaking
I included two links since each mentioned a different second author.
Introduction to Public Communication. http://textbooks.whatcom.edu/comm101/front-matter/title-page/
Presenting Your Research: Conferences, Symposiums, Poster Presentations, and Beyond. https://ebookcentral.proquest.com/lib/uark-ebooks/detail.action?docID=5613668
Principles of Public Speaking https://courses.lumenlearning.com/publicspeakingprinciples/
Public Speaking Basics, https://ebookcentral.proquest.com/lib/uark-ebooks/detail.action?docID=2010988.
Public Speaking Practice and Ethics https://2012books.lardbucket.org/boo...ics/index.html
The Public Speaking Project http://publicspeakingproject.org/
Inspire Your Audience.
https://westsidetoastmasters.com/resources/powerspeak/toc.html
Science of People https://www.scienceofpeople.com/public-speaking-tips/


3.1: Grain Size
Udden-Wentworth Grain Size Scale
The Udden-Wentworth grain size scale (or some derivative thereof) is the most common one used by geologists and forms the basis for subdividing clastic sedimentary rocks based on clast size. We tend to make the most basic subdivisions based on size because the maximum clast size is a function of the amount of energy in the system. We've used this classification scheme as the basis for Table 4.1.1, which combines grain size, phi units, and more detailed naming of clastic sediments and clastic sedimentary rocks.
Table \(\PageIndex{1}\): Grain size classification from Wentworth (1922) and phi scale from Krumbein (1934). Settling velocities from http://www.filtration-and-separation...g/settling.htm and entrainment (erosion) velocities from http://en.Wikipedia.org/wiki/File:We...Size-Chart.pdf ; both assume spherical particles of quartz.
Phi Units
In hydrogeology, we commonly describe sediment size in terms of phi units (Φ), where the conversion to real world units is:
Diameter (mm) = 1/2
n
where n = phi (Φ) value
They key thing to remember about this is that the bigger the phi value the smaller the diameter of the particle.
Sorting
Sorting is a measure of the uniformity of grain size in a specimen. A well sorted sample will have relatively uniform grain size whereas a poorly-sorted sample has a wide range of grain sizes. Geologists generally apply positive-sounding terms to uniform grain size because those samples have the most porosity and thus have the best potential for fluid flow and storage.You can estimate sorting visually (Figure 3.1.1) or measure it quantitatively using sieve analysis and plotting up the data on a cumulative distribution plot and histogram (Figure 3.1.2). Once plotted, you can use the equations and techniques in Figure 3.1.2 to determine mean (average), median (middle value when data is sorted smallest to largest), and mode (value that occurs most frequently) values for grain size, as well as calculate a numeric value for sorting and skewness (a measure of the symmetry of grain size distribution).
Table \(\PageIndex{1}\): Sorting and skewness terminology and values from Folk (1966).
Engineers and geologists live in opposite terminology worlds when it comes to grain size distribution. They use the term "grading" to describe the distribution of grain size. For them, compaction is what is important and a well-graded specimen has a wide range of grain sizes (can be densely compacted) and a poorly graded specimen has uniform grain size and does not compact as well.
Readings and Resources
- Folk, R. L., 1966, A review of grain‐size parameters. Sedimentology, v. 6, no. 2, p. 73-93.
- Krumbein, W. C. M., 1938, Size frequency distributions of sediments and the normal phi curve. Journal of Sedimentary Research, v. 8, no. 3, p. 84-90.
- Wentworth, C. K., 1922, A scale of grade and class terms for clastic sediments. The Journal of geology, v. 30, no. 5, p. 377-392


12.1: Introduction to Interpersonal Communication in the Workplace
Overview: Organizational Communication
Imagine an office full of robots. It would be almost silent, besides the buzzing of machines. There would be little to no errors and no sick days. There would be no wasted time on birthday celebrations in the lunchroom or checking in on coworkers’ weekend plans. The environment would be sterile, uninterrupted, and remote.  You call into this office for assistance. You are given pre-determined prompts to choose from, consistently frustrated because you are not receiving the help you need. Over the years, you notice the company continues to pump out the same, traditional products, with no upgrades, modifications, or accommodations to current technology. You realize that, though perhaps seemingly easier and more advantageous to daily flow, the lack of the human element also eliminates innovation, diversity, ingenuity, and personality. Fortunately, for those of us who are employed or looking for work, most industries still hire real people with personalities—and yes, flaws. Therefore, we will look at how humans interact in the workplace. We will examine the basics of interpersonal communication at work, organizational culture, types of workplace relationships, how power and emotions show up in the workplace and explore boundaries and professionalism. By the end of this chapter, we hope to give you tools that empower you to become more successful and effective communicators at work.
Organizational communication is studied extensively in the field of Communication Studies; some universities even offer it as an independent degree. As a field of study and practice, organizational communication usually pertains to internal communications within an organization, such as messaging regarding an organization’s mission or any kind of employee training. It can also include the various types of interpersonal communication that occurs between management and employees, as well as professional communication such as emails, announcements, and company documentation. Organizational communication can also include messaging that is more external-focused, such as public relations/public release documents, marketing materials, or branding. Interpersonal communication intersects with organizational communication in many ways. However, in this chapter, we will focus specifically on the types of relationships you will encounter in the workplace and the workplace dynamics you need to be aware of as you navigate those relationships. First, to get you acquainted with this chapter, in the next section we will talk about why it is to your advantage to understand the nuances of interpersonal communication as it relates to the workplace.
Reflection Questions
- What strengths does the human element bring to communication in the workplace?
- What weaknesses does the human element bring to the workplace?
- Can you connect any of the concepts shared in your previous chapters to an interpersonal relationship at work?


10.6: Integrating ODEs with Scipy
Except for educational purposes, it is almost always a bad idea to implement your own ODE solver; instead, you should use a pre-written solver.
10.6.1 The
scipy.integrate.odeint
Solver
In Scipy, the simplest ODE solver to use is the
scipy.integrate.odeint
function, which is in the
scipy.integrate
module. This is actually a wrapper around a low-level numerical library known as LSODE (the
L
ivermore
S
olver for
ODE
s"), which is part of a widely-used ODE solver library known as
ODEPACK
. The most important feature of this solver is that it is "adaptive": it can automatically figure out (i) which integration scheme to use (choosing between either a high-order Adams-Moulton method, or another implicit method known as the
Backward Differentiation Formula
which we haven't described), and (ii) the size of the discrete time steps, based on the behavior of the solutions as they are being worked out. In other words, the user only needs to specify the derivative function, the initial state, and the desired output times, without having to worry about the internal details of the solution method.
The function takes several inputs, of which the most important ones are:
-
func
, a function corresponding to the derivative function \(\vec{F}(\vec{y}, t)\). -
y0
, either a number or 1D array, corresponding to the initial state \(\vec{y}(t_0)\). -
t
, an array of times at which to output the ODE solution. The first element corresponding to the initial time \(t_{0}\). Note that these are the "output" times only—they do not specify the actual time steps which the solver uses for finding the solutions; those are automatically determined by the solver. -
(optional)
args
, a tuple of extra inputs to pass to the derivative functionfunc
. For example, ifargs=(2,3)
, thenfunc
should accept four inputs, and it will be passed 2 and 3 as the last two inputs.
The function then returns an array
y
, where
y[n]
contains the solution at time
t[n]
. Note that
y[0]
will be exactly the same as the input
y0
, the initial state which you specified.
Here is an example of using
odeint
to solve the damped harmonic oscillator problem \(m \ddot{x} = - \lambda \dot{x} - k x(t)\), using the previously-mentioned vectorization trick to cast it into a first-order ODE:
from scipy import * import matplotlib.pyplot as plt from scipy.integrate import odeint def ydot(y, t, m, lambd, k): x, v = y[0], y[1] return array([v, -(lambd/m) * v - k * x / m]) m, lambd, k = 1.0, 0.1, 1.0 # Oscillator parameters y0 = array([1.0, 5.0]) # Initial conditions [x, v] t = linspace(0.0, 50.0, 100) # Output times y = odeint(ydot, y0, t, args=(m, lambd, k)) ## Plot x versus t plt.plot(t, y[:,0], 'b-') plt.xlabel('t') plt.ylabel('x') plt.show()
There is an important limitation of
odeint
: it
does not handle complex ODEs
, and always assumes that \(\vec{y}\) and \(\vec{F}\) are real. However, this is not a problem in practice, because you can always convert a complex first-order ODE into a real one, by replacing the complex vectors \(\vec{y}\) and \(\vec{F}\) with double-length real vectors:
\[\vec{y}' \equiv \begin{bmatrix}\mathrm{Re}(\vec{y})\\ \mathrm{Im}(\vec{y})\end{bmatrix}, \;\; \vec{F}' \equiv \begin{bmatrix}\mathrm{Re}(\vec{F})\\ \mathrm{Im}(\vec{F})\end{bmatrix}.\]
10.6.2 The
scipy.integrate.ode
Solvers
Apart from
odeint
, Scipy provides a more general interface to a variety of ODE solvers, in the form of the
scipy.integrate.ode
class. This is a much more low-level interface; instead of calling a single function, you have to create an ODE "object", then use the methods of this object to specify the type of ODE solver to use, the initial conditions, etc.; then you have to repeatedly call the ODE object's
integrate
method, to integrate the solution up to each desired output time step.
The is an extremely aggravating inconsistency between the
odeint
function and this
ode
class: the expected order of inputs for the derivative functions are reversed! The
odeint
function assumes the derivative function has the form
F(y,t)
, but the
ode
class assumes it has the form
F(t,y)
. Watch out for this!
Here is an example of using
ode
class with the damped harmonic oscillator problem \(m \ddot{x} = - \lambda \dot{x} - k x(t)\), using a Runge-Kutta solver:
from scipy import * import matplotlib.pyplot as plt from scipy.integrate import ode ## Note the order of inputs (different from odeint)! def ydot(t, y, m, lambd, k): x, v = y[0], y[1] return array([v, -(lambd/m) * v - k * x / m]) m, lambd, k = 1.0, 0.1, 1.0 # Oscillator parameters y0 = array([1.0, 5.0]) # Initial conditions [x, v] t = linspace(0.0, 50.0, 100) # Output times ## Set up the ODE object r = ode(ydot) r.set_integrator('dopri5') # A Runge-Kutta solver r.set_initial_value(y0) r.set_f_params(m, lambd, k) ## Perform the integration. Note that the "integrate" method only integrates ## up to one single final time point, rather than an array of times. x = zeros(len(t)) x[0] = y0[0] for n in range(1,len(t)): r.integrate(t[n]) assert r.successful() x[n] = (r.y)[0] ## Plot x versus t plt.plot(t, x, 'b-') plt.xlabel('t') plt.ylabel('x') plt.show()
See the documentation for a more detailed list of options, including the list of ODE solvers that you can choose from.


7.4: Should I join a union or professional organization?
Introduction
Benefits of Joining a Union
Disadvantages of Joining a Union
Conclusion
- Answer
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By: Kayla Bise
Learning Objectives
Throughout time unions have worked to provide more for their employees. In 1857 the National Education Association; also known as the NEA; was formed by one hundred educators (NEA). The NEA became an advocate for children who were not learning to read and write. Over the course of one hundred and fifty years the NEA has become the largest teaching union (NEA). Currently there are over 3.2 million members across the United States (NEA). While the NEA is the largest teaching union the American Federation of Teachers is the second largest teaching union. The AFT was founded in 1916 to represent the economic, social and professional interests of classroom teachers (AFT). The American Federation of Teachers currently has 1.4 million members that belong to three thousand local affiliates nationwide and forty-three state affiliates (ATF). Virginia does not belong to the ATF as a state affiliate but there is a local affiliate in Fairfax County (ATF). Although teachers are not required to join the NEA or ATF many do to protect their selves in many aspects. These unions often provide employment security while protecting teacher’s rights with working conditions, teacher pay and benefits and other contract provisions. This raises the question to up and coming teachers as to whether they should join a teachers union.
Note
"Today unions represent 67 percent of the nation's 3 million active public elementary and secondary school teachers" Randall W. Eberts
There are many benefits of joining a teachers union. When a teacher joins a union they are granted many more benefits then teachers that do not join a union. The benefits that teachers are most concerned with are their pay and benefits, working conditions, employment security. A study found that teachers who are members of the union earned between five and twelve percent more than those who did not join a union (Eberts, 2007). These teachers also had more benefits and this may have increased the quality of education (Eberts, 2007). Teachers are often concerned about their working conditions such as class size, time for preparation and other activities away from students (Eberts, 2007). Studies found that that the student-teacher rations were seven to twelve percent lower for union teachers than for nonunion teachers (Eberts, 2007). The study also found that union teachers were allowed more time in class preparation and administrative duties (Eberts, 2007). Without the union teachers would not be allowed this planning time which is necessary for their classroom to run smoothly. While the unions protect a teachers pay and benefits and working conditions it also protects their employment security. Many teachers are granted tenure after teacher for a few years (Eberts, 2007). Tenure protects teachers from dismissal except for specific causes, which are not related to performance (Eberts, 2007). As you can see there are many benefits to joining the union that will protect you as a teacher.
While there are many benefits of joining a union there are also many disadvantages. Some teachers do not want to join the union because they are often very political and they may not agree with what the union stands for. Randall W. Eberts stated, “Teachers were not always anxious to be part of organized labor” (Eberts, 2007). While the unions often helped with the financial aspects of being a teacher they had many views and were often not agreed by the teachers (Eberts, 2007). There are also some districts that say that a teacher must be part of a union. Many people are forced to go along with the views of the largest unions like the NEA and AFT because there are no counter propaganda organizations (Moore, 1996). A disadvantage of joining the union is the cost. The average annual dues for the National Education Association is between four and six hundred dollars (Moore, 1996). This raises seven hundred and eighty five million dollars in revenue for the NEA (Moore, 1996). While the union may do a great job at protecting teachers pay, working conditions and their employment security it also protects bad teachers. An example of this is a high school teacher that was fired for producing and appearing in an x-rated video and asking students to be involved (Moore, 1996). The union defended this teacher claiming that he was working to augment his income (Moore, 1996). Teachers like this should not be protected under the union. These disadvantages may outweigh the benefits of joining a union.
There are many benefits and disadvantages of joining a teachers union. While some teachers want to protect their pay and benefits, working conditions, and employment security others view the unions as if it was forced upon them. Some may feel that unions are too political for them to join whither it is for a religious reason or ethical view of the NEA. Some may believe that joining the union is costly while others see that there are benefits in joining the unions that may increase their pay. As future teachers we will have to decide whither we will join the 3.2 million teachers across the United States in the NEA. One must weigh out their views of the unions and decide if joining will be an advantage or disadvantage for their career as a teacher.
Exercise \(\PageIndex{1}\)
1. Who is the largest Teaching Union in the United States
A. AFT
B. CBS
C. NEA
D. NNEA
2. How many members does the largest Teaching Union in the United States have?
 True or False: The average teacher's wages will increase if they join a union.
4. One reason many teachers do not join unions is:
A. They will have a pay increase
B. Religious and Political Views
C. To fight for better cafeteria food
D. There is not a teachers union
1. C
2. D
3. True
4. B
American Federation of Teachers. Retrieved Febrauary, 15, 2009 from http://www.aft.org Eberts, Randall W. (Spring, 2007)
Teachers Unions and Student Performance: Help or Hindrance? The Future of Children, Vol. 17. Retrieved February 15, 2009 from www.jstor.org/stable/4150025 Moore, Randy. (May, 1996) Teachers Unions.
The American Biology Teacher, Vol. 58. Rerieved February 15, 2009 from www. Jstor.org/stable/4450145 National Education Asscaition. Retrieved February 15, 2009 from http://www.nea.org


21.2.1: Chapter 1
Review Questions
1.
b.
10 grams of added sugars indicates this food has a significant amount of added sugar (20% of the recommended amount). Current dietary guidelines recommend limiting sugar consumption.
2.
b.
According to MyPlate, carbohydrates (fruits and vegetables) comprise the largest portion of the plate.
3.
c.
Although all the clients have nutritional concerns, a client recently diagnosed with a myocardial infarction (a “heart attack”) has an immediate need for diet instruction related to their new diagnosis.
4.
b.
WIC is designed to provide food assistance to low-income pregnant, breastfeeding, and non-breastfeeding postpartum women and infants and children up to age 5 who are at nutritional risk.
5.
b.
Diets and nutritional counseling should reflect scientific findings supported by research.
6.
a.
Clients who do not have a steady income may not be able to get food when needed. These clients should be screened for food insecurity.
7.
d.
Measuring the client’s WHR at a follow-up visit can provide objective data that reflects the client’s progress toward a nutrition-related goal.
8.
c.
Employment status is a nonmedical factor that influences health.
9.
a.
Educational materials should be developed so that readers with lower literacy levels can understand the content.
10.
d.
This response acknowledges the client’s feelings and initiates the process of educating the client on how to evaluate nutrition information on social media.


12.E: Thermodynamics (Exercises)
16.1: Spontaneity Exercises
Q16.1.1
What is a spontaneous reaction?
S16.1.1
A reaction has a natural tendency to occur and takes place without the continual input of energy from an external source.
Q16.1.2
What is a nonspontaneous reaction?
Q16.1.3
Indicate whether the following processes are spontaneous or nonspontaneous.
- Liquid water freezing at a temperature below its freezing point
- Liquid water freezing at a temperature above its freezing point
- The combustion of gasoline
- A ball thrown into the air
- A raindrop falling to the ground
- Iron rusting in a moist atmosphere
S16.1.2
spontaneous; nonspontaneous; spontaneous; nonspontaneous; spontaneous; spontaneous
Q16.1.4
A helium-filled balloon spontaneously deflates overnight as He atoms diffuse through the wall of the balloon. Describe the redistribution of matter and/or energy that accompanies this process.
Q16.1.5
Many plastic materials are organic polymers that contain carbon and hydrogen. The oxidation of these plastics in air to form carbon dioxide and water is a spontaneous process; however, plastic materials tend to persist in the environment. Explain.
S16.1.5
Although the oxidation of plastics is spontaneous, the rate of oxidation is very slow. Plastics are therefore kinetically stable and do not decompose appreciably even over relatively long periods of time.
16.2: Entropy Exercises
Q16.2.1
In the below Figure all possible distributions and microstates are shown for four different particles shared between two boxes. Determine the entropy change, Δ S , if the particles are initially evenly distributed between the two boxes, but upon redistribution all end up in Box (b).
Q16.2.2
In Figure all of the possible distributions and microstates are shown for four different particles shared between two boxes. Determine the entropy change, Δ S , for the system when it is converted from distribution to distribution (d).
S16.2.2
There are four initial microstates and four final microstates.
\[ΔS=k\ln\dfrac{W_\ce{f}}{W_\ce{i}}=\mathrm{1.38×10^{−23}\:J/K×\ln\dfrac{4}{4}=0}\]
Q16.2.4
Consider a system similar to the one below, except that it contains six particles instead of four. What is the probability of having all the particles in only one of the two boxes in the case? Compare this with the similar probability for the system of four particles that we have derived to be equal to \(\dfrac{1}{8}\). What does this comparison tell us about even larger systems?
S16.2.4
The probability for all the particles to be on one side is \(\dfrac{1}{32}\). This probability is noticeably lower than the \(\dfrac{1}{8}\) result for the four-particle system. The conclusion we can make is that the probability for all the particles to stay in only one part of the system will decrease rapidly as the number of particles increases, and, for instance, the probability for all molecules of gas to gather in only one side of a room at room temperature and pressure is negligible since the number of gas molecules in the room is very large.
Q16.2.5
Consider the system shown in Figure. What is the change in entropy for the process where the energy is initially associated only with particle A, but in the final state the energy is distributed between two different particles?
Q16.2.6
Consider the system shown in Figure . What is the change in entropy for the process where the energy is initially associated with particles A and B, and the energy is distributed between two particles in different boxes (one in A-B, the other in C-D)?
S16.2.6
There is only one initial state. For the final state, the energy can be contained in pairs A-C, A-D, B-C, or B-D. Thus, there are four final possible states.
\[ΔS=k\ln\left(\dfrac{W_\ce{f}}{W_\ce{i}}\right)=\mathrm{1.38×10^{−23}\:J/K×\ln\left(\dfrac{4}{1}\right)=1.91×10^{−23}\:J/K}\]
Q16.2.7
Arrange the following sets of systems in order of increasing entropy. Assume one mole of each substance and the same temperature for each member of a set.
- H 2 ( g ), HBrO 4 ( g ), HBr( g )
- H 2 O( l ), H 2 O( g ), H 2 O( s )
- He( g ), Cl 2 ( g ), P 4 ( g )
Q16.2.8
At room temperature, the entropy of the halogens increases from I 2 to Br 2 to Cl 2 . Explain.
S16.2.8
The masses of these molecules would suggest the opposite trend in their entropies. The observed trend is a result of the more significant variation of entropy with a physical state. At room temperature, I 2 is a solid, Br 2 is a liquid, and Cl 2 is a gas.
Q16.2.9
Consider two processes: sublimation of I 2 ( s ) and melting of I 2 ( s ) (Note: the latter process can occur at the same temperature but somewhat higher pressure).
\[\ce{I2}(s)⟶\ce{I2}(g)\]
\[\ce{I2}(s)⟶\ce{I2}(l)\]
Is Δ S positive or negative in these processes? In which of the processes will the magnitude of the entropy change be greater?
Q16.2.11
Indicate which substance in the given pairs has the higher entropy value. Explain your choices.
- C 2 H 5 OH( l ) or C 3 H 7 OH( l )
- C 2 H 5 OH( l ) or C 2 H 5 OH( g )
- 2Hor H( g )
S16.2.11
C 3 H 7 OH( l ) as it is a larger molecule (more complex and more massive), and so more microstates describing its motions are available at any given temperature. C 2 H 5 OH( g ) as it is in the gaseous state. 2H( g ), since entropy is an extensive property, and so two H atoms (or two moles of H atoms) possess twice as much entropy as one atom (or one mole of atoms).
Q16.2.11
Predict the sign of the entropy change for the following processes:
- An ice cube is warmed to near its melting point.
- Exhaled breath forms fog on a cold morning.
- Snow melts.
Q16.2.12
Predict the sign of the enthalpy change for the following processes. Give a reason for your prediction.
- \(\ce{Pb^2+}(aq)+\ce{S^2-}(aq)⟶\ce{PbS}(s)\)
- \(\ce{2Fe}(s)+\ce{3O2}(g)⟶\ce{Fe2O3}(s)\)
- \(\ce{2C6H14}(l)+\ce{19O2}(g)⟶\ce{14H2O}(g)+\ce{12CO2}(g)\)
S16.2.12
Negative. The relatively ordered solid precipitating decreases the number of mobile ions in solution. Negative. There is a net loss of three moles of gas from reactants to products. Positive. There is a net increase of seven moles of gas from reactants to products.
Q16.2.13
Write the balanced chemical equation for the combustion of methane, CH 4 ( g ), to give carbon dioxide and water vapor. Explain why it is difficult to predict whether Δ S is positive or negative for this chemical reaction.
Q16.2.14
Write the balanced chemical equation for the combustion of benzene, C 6 H 6 ( l ), to give carbon dioxide and water vapor. Would you expect Δ S to be positive or negative in this process?
S16.2.14
\[\ce{C6H6}(l)+7.5\ce{O2}(g)⟶\ce{3H2O}(g)+\ce{6CO2}(g)\]
There are 7.5 moles of gas initially, and 3 + 6 = 9 moles of gas in the end. Therefore, it is likely that the entropy increases as a result of this reaction, and Δ S is positive.
16.3: The Second and Third law
Q16.3.0
What is the difference between Δ S , Δ S °, and \(ΔS^\circ_{298}\) for a chemical change?
Q16.3.1
Calculate \(ΔS^\circ_{298}\) for the following changes.
- \(\ce{SnCl4}(l)⟶\ce{SnCl4}(g)\)
- \(\ce{CS2}(g)⟶\ce{CS2}(l)\)
- \(\ce{Cu}(s)⟶\ce{Cu}(g)\)
- \(\ce{H2O}(l)⟶\ce{H2O}(g)\)
- \(\ce{2H2}(g)+\ce{O2}(g)⟶\ce{2H2O}(l)\)
- \(\ce{2HCl}(g)+\ce{Pb}(s)⟶\ce{PbCl2}(s)+\ce{H2}(g)\)
- \(\ce{Zn}(s)+\ce{CuSO4}(s)⟶\ce{Cu}(s)+\ce{ZnSO4}(s)\)
S16.3.1
107 J/K; −86.4 J/K; 133.2 J/K; 118.8 J/K; −326.6 J/K; −171.9 J/K; (g) −7.2 J/K
Q16.3.2
Determine the entropy change for the combustion of liquid ethanol, C 2 H 5 OH, under standard state conditions to give gaseous carbon dioxide and liquid water.
Q16.3.3
Determine the entropy change for the combustion of gaseous propane, C 3 H 8 , under standard state conditions to give gaseous carbon dioxide and water.
S16.3.3
100.6 J/K
Q16.3.4
“Thermite” reactions have been used for welding metal parts such as railway rails and in metal refining. One such thermite reaction is:
\[\ce{Fe2O3}(s)+\ce{2Al}(s)⟶\ce{Al2O3}(s)+\ce{2Fe}(s)\]
Is the reaction spontaneous at room temperature under standard conditions? During the reaction, the surroundings absorb 851.8 kJ/mol of heat.
Q16.3.5
Using the relevant \(S^\circ_{298}\) values listed in Appendix G , calculate \(S^\circ_{298}\) for the following changes:
- \(\ce{N2}(g)+\ce{3H2}(g)⟶\ce{2NH3}(g)\)
- \(\ce{N2}(g)+\dfrac{5}{2}\ce{O2}(g)⟶\ce{N2O5}(g)\)
S16.3.5
−198.1 J/K; −348.9 J/K
Q16.3.6
From the following information, determine \(ΔS^\circ_{298}\) for the following:
- \(\ce{N}(g)+\ce{O}(g)⟶\ce{NO}(g) \hspace{20px} ΔS^\circ_{298}=\,?\)
- \(\ce{N2}(g)+\ce{O2}(g)⟶\ce{2NO}(g) \hspace{20px} ΔS^\circ_{298}=\mathrm{24.8\: J/K}\)
- \(\ce{N2}(g)⟶\ce{2N}(g) \hspace{20px} ΔS^\circ_{298}=\mathrm{115.0\: J/K}\)
- \(\ce{O2}(g)⟶\ce{2O}(g) \hspace{20px} ΔS^\circ_{298}=\mathrm{117.0\: J/K}\)
Q16.3.7
By calculating Δ S univ at each temperature, determine if the melting of 1 mole of NaCl( s ) is spontaneous at 500 °C and at 700 °C.
\[S^\circ_{\ce{NaCl}(s)}=\mathrm{72.11\:\dfrac{J}{mol⋅K}}\hspace{40px} S^\circ_{\ce{NaCl}(l)}=\mathrm{95.06\:\dfrac{J}{mol⋅K}}\hspace{40px ΔH^\circ_\ce{fusion}=\mathrm{27.95\: kJ/mol}\]
What assumptions are made about the thermodynamic information (entropy and enthalpy values) used to solve this problem?
S16.3.7
As Δ S univ < 0 at each of these temperatures, melting is not spontaneous at either of them. The given values for entropy and enthalpy are for NaCl at 298 K. It is assumed that these do not change significantly at the higher temperatures used in the problem.
Q16.3.8
Use the standard entropy data in Appendix G to determine the change in entropy for each of the reactions listed in [link] . All are run under standard state conditions and 25 °C.
Q16.3.8
2.86 J/K; 24.8 J/K; −113.2 J/K; −24.7 J/K; 15.5 J/K; 290.0 J/K
16.4: Free Energy
Q16.4.1
What is the difference between Δ G , Δ G °, and \(ΔG^\circ_{298}\) for a chemical change?
Q16.4.2
A reactions has \(ΔH^\circ_{298}\) = 100 kJ/mol and \(ΔS^\circ_{298}=\textrm{250 J/mol⋅K}\). Is the reaction spontaneous at room temperature? If not, under what temperature conditions will it become spontaneous?
S16.4.2
The reaction is nonspontaneous at room temperature. Above 400 K, Δ G will become negative, and the reaction will become spontaneous.
Q16.4.3
Explain what happens as a reaction starts with Δ G < 0 (negative) and reaches the point where Δ G = 0.
Use the standard free energy of formation data in Appendix G to determine the free energy change for each of the following reactions, which are run under standard state conditions and 25 °C. Identify each as either spontaneous or nonspontaneous at these conditions.
- \(\ce{MnO2}(s)⟶\ce{Mn}(s)+\ce{O2}(g)\)
- \(\ce{H2}(g)+\ce{Br2}(l)⟶\ce{2HBr}(g)\)
- \(\ce{Cu}(s)+\ce{S}(g)⟶\ce{CuS}(s)\)
- \(\ce{2LiOH}(s)+\ce{CO2}(g)⟶\ce{Li2CO3}(s)+\ce{H2O}(g)\)
- \(\ce{CH4}(g)+\ce{O2}(g)⟶\ce{C}(s,\,\ce{graphite})+\ce{2H2O}(g)\)
- \(\ce{CS2}(g)+\ce{3Cl2}(g)⟶\ce{CCl4}(g)+\ce{S2Cl2}(g)\)
S16.4.3
465.1 kJ nonspontaneous; −106.86 kJ spontaneous; −53.6 kJ spontaneous; −83.4 kJ spontaneous; −406.7 kJ spontaneous; −30.0 kJ spontaneous
Q16.4.4
Use the standard free energy data in Appendix G to determine the free energy change for each of the following reactions, which are run under standard state conditions and 25 °C. Identify each as either spontaneous or nonspontaneous at these conditions.
- \(\ce{C}(s,\, \ce{graphite})+\ce{O2}(g)⟶\ce{CO2}(g)\)
- \(\ce{O2}(g)+\ce{N2}(g)⟶\ce{2NO}(g)\)
- \(\ce{2Cu}(s)+\ce{S}(g)⟶\ce{Cu2S}(s)\)
- \(\ce{CaO}(s)+\ce{H2O}(l)⟶\ce{Ca(OH)2}(s)\)
- \(\ce{Fe2O3}(s)+\ce{3CO}(g)⟶\ce{2Fe}(s)+\ce{3CO2}(g)\)
- \(\ce{CaSO4⋅2H2O}(s)⟶\ce{CaSO4}(s)+\ce{2H2O}(g)\)
Given:
\[\ce{P4}(s)+\ce{5O2}(g)⟶\ce{P4O10}(s) \hspace{20px} ΔG^\circ_{298}=\mathrm{−2697.0\: kJ/mol}\]
\[\ce{2H2}(g)+\ce{O2}(g)⟶\ce{2H2O}(g) \hspace{20px} ΔG^\circ_{298}=\mathrm{−457.18\: kJ/mol}\]
\[\ce{6H2O}(g)+\ce{P4O10}(g)⟶\ce{4H3PO4}(l) \hspace{20px} ΔG^\circ_{298}=\mathrm{−428.66\: kJ/mol}\]
Q16.4.5
- Determine the standard free energy of formation, \(ΔG^\circ_\ce{f}\), for phosphoric acid.
- How does your calculated result compare to the value in Appendix G ? Explain.
S16.4.5
−1124.3 kJ/mol for the standard free energy change. The calculation agrees with the value in Appendix G because free energy is a state function (just like the enthalpy and entropy), so its change depends only on the initial and final states, not the path between them.
Q16.4.6
Is the formation of ozone (O 3 ( g )) from oxygen (O 2 ( g )) spontaneous at room temperature under standard state conditions?
Q16.4.7
Consider the decomposition of red mercury(II) oxide under standard state conditions.
\[\ce{2HgO}(s,\,\ce{red})⟶\ce{2Hg}(l)+\ce{O2}(g)\]
- Is the decomposition spontaneous under standard state conditions?
- Above what temperature does the reaction become spontaneous?
S16.4.7
The reaction is nonspontaneous; Above 566 °C the process is spontaneous.
Q16.4.8
Among other things, an ideal fuel for the control thrusters of a space vehicle should decompose in a spontaneous exothermic reaction when exposed to the appropriate catalyst. Evaluate the following substances under standard state conditions as suitable candidates for fuels.
- Ammonia: \(\ce{2NH3}(g)⟶\ce{N2}(g)+\ce{3H2}(g)\)
- Diborane: \(\ce{B2H6}(g)⟶\ce{2B}(g)+\ce{3H2}(g)\)
- Hydrazine: \(\ce{N2H4}(g)⟶\ce{N2}(g)+\ce{2H2}(g)\)
- Hydrogen peroxide: \(\ce{H2O2}(l)⟶\ce{H2O}(g)+\dfrac{1}{2}\ce{O2}(g)\)
Q16.4.9
Calculate Δ G ° for each of the following reactions from the equilibrium constant at the temperature given.
- \(\ce{N2}(g)+\ce{O2}(g)⟶\ce{2NO}(g) \hspace{20px} \mathrm{T=2000\:°C} \hspace{20px} K_p=4.1×10^{−4}\)
- \(\ce{H2}(g)+\ce{I2}(g)⟶\ce{2HI}(g) \hspace{20px} \mathrm{T=400\:°C} \hspace{20px} K_p=50.0\)
- \(\ce{CO2}(g)+\ce{H2}(g)⟶\ce{CO}(g)+\ce{H2O}(g) \hspace{20px} \mathrm{T=980\:°C} \hspace{20px} K_p=1.67\)
- \(\ce{CaCO3}(s)⟶\ce{CaO}(s)+\ce{CO2}(g) \hspace{20px} \mathrm{T=900\:°C} \hspace{20px} K_p=1.04\)
- \(\ce{HF}(aq)+\ce{H2O}(l)⟶\ce{H3O+}(aq)+\ce{F-}(aq) \hspace{20px} \mathrm{T=25\:°C} \hspace{20px} K_p=7.2×10^{−4}\)
- \(\ce{AgBr}(s)⟶\ce{Ag+}(aq)+\ce{Br-}(aq) \hspace{20px} \mathrm{T=25\:°C} \hspace{20px} K_p=3.3×10^{−13}\)
S16.4.9
1.5 × 10 2 kJ; −21.9 kJ; −5.34 kJ; −0.383 kJ; 18 kJ; 71 kJ
Q16.4.10
Calculate Δ G ° for each of the following reactions from the equilibrium constant at the temperature given.
- \(\ce{Cl2}(g)+\ce{Br2}(g)⟶\ce{2BrCl}(g) \hspace{20px} \mathrm{T=25\:°C} \hspace{20px} K_p=4.7×10^{−2}\)
- \(\ce{2SO2}(g)+\ce{O2}(g)⇌\ce{2SO3}(g) \hspace{20px} \mathrm{T=500\:°C} \hspace{20px} K_p=48.2\)
- \(\ce{H2O}(l)⇌\ce{H2O}(g) \hspace{20px} \mathrm{T=60\:°C} \hspace{20px} K_p=\mathrm{0.196\: atm}\)
- \(\ce{CoO}(s)+\ce{CO}(g)⇌\ce{Co}(s)+\ce{CO2}(g) \hspace{20px} \mathrm{T=550\:°C} \hspace{20px} K_p=4.90×10^2\)
- \(\ce{CH3NH2}(aq)+\ce{H2O}(l)⟶\ce{CH3NH3+}(aq)+\ce{OH-}(aq) \hspace{20px} \mathrm{T=25\:°C} \hspace{20px} K_p=4.4×10^{−4}\)
- \(\ce{PbI2}(s)⟶\ce{Pb^2+}(aq)+\ce{2I-}(aq) \hspace{20px} \mathrm{T=25\:°C} \hspace{20px} K_p=8.7×10^{−9}\)
Q16.4.11
Calculate the equilibrium constant at 25 °C for each of the following reactions from the value of Δ G ° given.
- \(\ce{O2}(g)+\ce{2F2}(g)⟶\ce{2OF2}(g) \hspace{20px} ΔG°=\mathrm{−9.2\: kJ}\)
- \(\ce{I2}(s)+\ce{Br2}(l)⟶\ce{2IBr}(g) \hspace{20px} ΔG°=\mathrm{7.3\: kJ}\)
- \(\ce{2LiOH}(s)+\ce{CO2}(g)⟶\ce{Li2CO3}(s)+\ce{H2O}(g) \hspace{20px} ΔG°=\mathrm{−79\: kJ}\)
- \(\ce{N2O3}(g)⟶\ce{NO}(g)+\ce{NO2}(g) \hspace{20px} ΔG°=\mathrm{−1.6\: kJ}\)
- \(\ce{SnCl4}(l)⟶\ce{SnCl4}(l) \hspace{20px} ΔG°=\mathrm{8.0\: kJ}\)
S16.4.11
K = 41; K = 0.053; K = 6.9 × 10 13 ; K = 1.9; K = 0.04
Q16.4.2
Calculate the equilibrium constant at 25 °C for each of the following reactions from the value of Δ G ° given.
- \(\ce{I2}(s)+\ce{Cl2}(g)⟶\ce{2ICl}(g) \hspace{20px} ΔG°=\mathrm{−10.88\: kJ}\)
- \(\ce{H2}(g)+\ce{I2}(s)⟶\ce{2HI}(g) \hspace{20px} ΔG°=\mathrm{3.4\: kJ}\)
- \(\ce{CS2}(g)+\ce{3Cl2}(g)⟶\ce{CCl4}(g)+\ce{S2Cl2}(g) \hspace{20px} ΔG°=\mathrm{−39\: kJ}\)
- \(\ce{2SO2}(g)+\ce{O2}(g)⟶\ce{2SO3}(g) \hspace{20px} ΔG°=\mathrm{−141.82\: kJ}\)
- \(\ce{CS2}(g)⟶\ce{CS2}(l) \hspace{20px} ΔG°=\mathrm{−1.88\: kJ}\)
Q16.4.13
Calculate the equilibrium constant at the temperature given.
- (a) \(\ce{O2}(g)+\ce{2F2}(g)⟶\ce{2F2O}(g) \hspace{20px} \mathrm{(T=100\:°C)}\)
- \(\ce{I2}(s)+\ce{Br2}(l)⟶\ce{2IBr}(g) \hspace{20px} \mathrm{(T=0.0\:°C)}\)
- \(\ce{2LiOH}(s)+\ce{CO2}(g)⟶\ce{Li2CO3}(s)+\ce{H2O}(g) \hspace{20px} \mathrm{(T=575\:°C)}\)
- \(\ce{N2O3}(g)⟶\ce{NO}(g)+\ce{NO2}(g) \hspace{20px} \mathrm{(T=−10.0\:°C)}\)
- \(\ce{SnCl4}(l)⟶\ce{SnCl4}(g) \hspace{20px} \mathrm{(T=200\:°C)}\)
S16.4.13
In each of the following, the value of Δ G is not given at the temperature of the reaction. Therefore, we must calculate Δ G ° from the values Δ H ° and Δ S ° and then calculate Δ G from the relation ΔG° = ΔH° − TΔS°.
- K = 1.29
- K = 2.51 × 10 −3
- K = 4.83 × 10 3
- K = 0.219
- K = 16.1
Q16.4.14
Calculate the equilibrium constant at the temperature given.
- (a) \(\ce{I2}(s)+\ce{Cl2}(g)⟶\ce{2ICl}(g) \hspace{20px} \mathrm{(T=100\:°C)}\)
- \(\ce{H2}(g)+\ce{I2}(s)⟶\ce{2HI}(g) \hspace{20px} \mathrm{(T=0.0\:°C)}\)
- \(\ce{CS2}(g)+\ce{3Cl2}(g)⟶\ce{CCl4}(g)+\ce{S2Cl2}(g) \hspace{20px} \mathrm{(T=125\:°C)}\)
- \(\ce{2SO2}(g)+\ce{O2}(g)⟶\ce{2SO3}(g) \hspace{20px} \mathrm{(T=675\:°C)}\)
- \(\ce{CS2}(g)⟶\ce{CS2}(l) \hspace{20px} \mathrm{(T=90\:°C)}\)
Q16.4.15
Consider the following reaction at 298 K:
\[\ce{N2O4}(g)⇌\ce{2NO2}(g) \hspace{20px} K_P=0.142\]
What is the standard free energy change at this temperature? Describe what happens to the initial system, where the reactants and products are in standard states, as it approaches equilibrium.
S16.4.16
The standard free energy change is \(ΔG^\circ_{298}=−RT\ln K=\mathrm{4.84\: kJ/mol}\). When reactants and products are in their standard states (1 bar or 1 atm), Q = 1. As the reaction proceeds toward equilibrium, the reaction shifts left (the amount of products drops while the amount of reactants increases): Q < 1, and \(ΔG_{298}\) becomes less positive as it approaches zero. At equilibrium, Q = K , and Δ G = 0.
Q16.4.17
Determine the normal boiling point (in kelvin) of dichloroethane, CH 2 Cl 2 . Find the actual boiling point using the Internet or some other source, and calculate the percent error in the temperature. Explain the differences, if any, between the two values.
Q16.4.18
Under what conditions is \(\ce{N2O3}(g)⟶\ce{NO}(g)+\ce{NO2}(g)\) spontaneous?
S16.4.18
The reaction will be spontaneous at temperatures greater than 287 K.
Q16.4.19
At room temperature, the equilibrium constant ( K w ) for the self-ionization of water is 1.00 × 10 −14 . Using this information, calculate the standard free energy change for the aqueous reaction of hydrogen ion with hydroxide ion to produce water. (Hint: The reaction is the reverse of the self-ionization reaction.)
Q16.4.20
Hydrogen sulfide is a pollutant found in natural gas. Following its removal, it is converted to sulfur by the reaction \(\ce{2H2S}(g)+\ce{SO2}(g)⇌\dfrac{3}{8}\ce{S8}(s,\,\ce{rhombic})+\ce{2H2O}(l)\). What is the equilibrium constant for this reaction? Is the reaction endothermic or exothermic?
S16.4.20
K = 5.35 × 10 15
The process is exothermic.
Q16.4.21
Consider the decomposition of CaCO 3 ( s ) into CaO( s ) and CO 2 ( g ). What is the equilibrium partial pressure of CO 2 at room temperature?
Q16.4.22
In the laboratory, hydrogen chloride (HCl( g )) and ammonia (NH 3 ( g )) often escape from bottles of their solutions and react to form the ammonium chloride (NH 4 Cl( s )), the white glaze often seen on glassware. Assuming that the number of moles of each gas that escapes into the room is the same, what is the maximum partial pressure of HCl and NH 3 in the laboratory at room temperature? (Hint: The partial pressures will be equal and are at their maximum value when at equilibrium.)
S16.4.22
1.0 × 10 −8 atm. This is the maximum pressure of the gases under the stated conditions.
Q16.4.23
Benzene can be prepared from acetylene. \(\ce{3C2H2}(g)⇌\ce{C6H6}(g)\). Determine the equilibrium constant at 25 °C and at 850 °C. Is the reaction spontaneous at either of these temperatures? Why is all acetylene not found as benzene?
Q16.4.24
Carbon dioxide decomposes into CO and O 2 at elevated temperatures. What is the equilibrium partial pressure of oxygen in a sample at 1000 °C for which the initial pressure of CO 2 was 1.15 atm?
\[x=\mathrm{1.29×10^{−5}\:atm}=P_{\ce{O2}}\]
Q16.4.25
Carbon tetrachloride, an important industrial solvent, is prepared by the chlorination of methane at 850 K.
\[\ce{CH4}(g)+\ce{4Cl2}(g)⟶\ce{CCl4}(g)+\ce{4HCl}(g)\]
What is the equilibrium constant for the reaction at 850 K? Would the reaction vessel need to be heated or cooled to keep the temperature of the reaction constant?
Q16.4.25B
Acetic acid, CH 3 CO 2 H, can form a dimer, (CH 3 CO 2 H) 2 , in the gas phase.
\[\ce{2CH3CO2H}(g)⟶\ce{(CH3CO2H)2}(g)\]
The dimer is held together by two hydrogen bonds with a total strength of 66.5 kJ per mole of dimer.
At 25 °C, the equilibrium constant for the dimerization is 1.3 × 10 3 (pressure in atm). What is Δ S ° for the reaction?
S16.4.25B
−0.16 kJ
Q16.4.26
Nitric acid, HNO 3 , can be prepared by the following sequence of reactions:
\[\ce{4NH3}(g)+\ce{5O2}(g)⟶\ce{4NO}(g)+\ce{6H2O}(g)\]
\[\ce{2NO}(g)+\ce{O2}(g)⟶\ce{2NO2}(g)\]
\[\ce{3NO2}(g)+\ce{H2O}(l)⟶\ce{2HNO3}(l)+\ce{NO}(g)\]
How much heat is evolved when 1 mol of NH 3 ( g ) is converted to HNO 3 ( l )? Assume standard states at 25 °C.
Q16.4.27A
Determine Δ G for the following reactions.
(a) Antimony pentachloride decomposes at 448 °C. The reaction is:
\[\ce{SbCl5}(g)⟶\ce{SbCl3}(g)+\ce{Cl2}(g)\]
An equilibrium mixture in a 5.00 L flask at 448 °C contains 3.85 g of SbCl 5 , 9.14 g of SbCl 3 , and 2.84 g of Cl 2 .
Chlorine molecules dissociate according to this reaction:
\[\ce{Cl2}(g)⟶\ce{2Cl}(g)\]
1.00% of Cl 2 molecules dissociate at 975 K and a pressure of 1.00 atm.
S16.4.27A
- (a) −22.1 kJ;
- 61.6 kJ/mol
Q16.4.27
Given that the \(ΔG^\circ_\ce{f}\) for Pb 2+ ( aq ) and Cl − ( aq ) is −24.3 kJ/mole and −131.2 kJ/mole respectively, determine the solubility product, K sp , for PbCl 2 ( s ).
Q16.4.28
Determine the standard free energy change, \(ΔG^\circ_\ce{f}\), for the formation of S 2− ( aq ) given that the \(ΔG^\circ_\ce{f}\) for Ag + ( aq ) and Ag 2 S( s ) are 77.1 k/mole and −39.5 kJ/mole respectively, and the solubility product for Ag 2 S( s ) is 8 × 10 −51 .
S16.4.28
90 kJ/mol
Q16.4.29
Determine the standard enthalpy change, entropy change, and free energy change for the conversion of diamond to graphite. Discuss the spontaneity of the conversion with respect to the enthalpy and entropy changes. Explain why diamond spontaneously changing into graphite is not observed.
Q16.4.30
The evaporation of one mole of water at 298 K has a standard free energy change of 8.58 kJ.
\[\ce{H2O}(l)⇌\ce{H2O}(g) \hspace{20px} ΔG^\circ_{298}=\mathrm{8.58\: kJ}\]
- (a) Is the evaporation of water under standard thermodynamic conditions spontaneous?
- Determine the equilibrium constant, K P , for this physical process.
- By calculating ∆ G , determine if the evaporation of water at 298 K is spontaneous when the partial pressure of water, \(P_{\ce{H2O}}\), is 0.011 atm.
- If the evaporation of water were always nonspontaneous at room temperature, wet laundry would never dry when placed outside. In order for laundry to dry, what must be the value of \(P_{\ce{H2O}}\) in the air?
S16.4.30
(a) Under standard thermodynamic conditions, the evaporation is nonspontaneous; K p = 0.031; The evaporation of water is spontaneous; \(P_{\ce{H2O}}\) must always be less than K p or less than 0.031 atm. 0.031 atm represents air saturated with water vapor at 25 °C, or 100% humidity.
Q16.4.31
In glycolysis, the reaction of glucose (Glu) to form glucose-6-phosphate (G6P) requires ATP to be present as described by the following equation:
\[\mathrm{Glu + ATP ⟶ G6P + ADP} \hspace{20px} ΔG^\circ_{298}=\mathrm{−17\: kJ}\]
In this process, ATP becomes ADP summarized by the following equation:
\[\mathrm{ATP⟶ADP} \hspace{20px} ΔG^\circ_{298}=\mathrm{−30\: kJ}\]
Determine the standard free energy change for the following reaction, and explain why ATP is necessary to drive this process:
\[\mathrm{Glu⟶G6P} \hspace{20px} ΔG^\circ_{298}=\:?\]
Q16.4.32
One of the important reactions in the biochemical pathway glycolysis is the reaction of glucose-6-phosphate (G6P) to form fructose-6-phosphate (F6P):
\[\mathrm{G6P⇌F6P} \hspace{20px} ΔG^\circ_{298}=\mathrm{1.7\: kJ}\]
- (a) Is the reaction spontaneous or nonspontaneous under standard thermodynamic conditions?
- Standard thermodynamic conditions imply the concentrations of G6P and F6P to be 1 M , however, in a typical cell, they are not even close to these values. Calculate Δ G when the concentrations of G6P and F6P are 120 μ M and 28 μ M respectively, and discuss the spontaneity of the forward reaction under these conditions. Assume the temperature is 37 °C.
S16.4.32
(a) Nonspontaneous as \(ΔG^\circ_{298}>0\); \(ΔG^\circ_{298}=−RT\ln K,\) \(ΔG = 1.7×10^3 + \left(8.314 × 335 × \ln\dfrac{28}{128}\right) = \mathrm{−2.5\: kJ}\). The forward reaction to produce F6P is spontaneous under these conditions.
Q16.4.33
Without doing a numerical calculation, determine which of the following will reduce the free energy change for the reaction, that is, make it less positive or more negative, when the temperature is increased. Explain.
- (a) \(\ce{N2}(g)+\ce{3H2}(g)⟶\ce{2NH3}(g)\)
- \(\ce{HCl}(g)+\ce{NH3}(g)⟶\ce{NH4Cl}(s)\)
- \(\ce{(NH4)2Cr2O7}(s)⟶\ce{Cr2O3}(s)+\ce{4H2O}(g)+\ce{N2}(g)\)
- \(\ce{2Fe}(s)+\ce{3O2}(g)⟶\ce{Fe2O3}(s)\)
When ammonium chloride is added to water and stirred, it dissolves spontaneously and the resulting solution feels cold. Without doing any calculations, deduce the signs of Δ G , Δ H , and Δ S for this process, and justify your choices.
S16.4.33
Δ G is negative as the process is spontaneous. Δ H is positive as with the solution becoming cold, the dissolving must be endothermic. Δ S must be positive as this drives the process, and it is expected for the dissolution of any soluble ionic compound.
Q16.4.34
An important source of copper is from the copper ore, chalcocite, a form of copper(I) sulfide. When heated, the Cu 2 S decomposes to form copper and sulfur described by the following equation:
\[\ce{Cu2S}(s)⟶\ce{Cu}(s)+\ce{S}(s)\]
- (a) Determine \(ΔG^\circ_{298}\) for the decomposition of Cu 2 S( s ).
- The reaction of sulfur with oxygen yields sulfur dioxide as the only product. Write an equation that describes this reaction, and determine \(ΔG^\circ_{298}\) for the process.
- The production of copper from chalcocite is performed by roasting the Cu 2 S in air to produce the Cu. By combining the equations from Parts (a) and (b), write the equation that describes the roasting of the chalcocite, and explain why coupling these reactions together makes for a more efficient process for the production of the copper.
Q16.4.35
What happens to \(ΔG^\circ_{298}\) (becomes more negative or more positive) for the following chemical reactions when the partial pressure of oxygen is increased?
- (a) \(\ce{S}(s)+\ce{O2}(g)⟶\ce{SO2}(g)\)
- \(\ce{2SO2}(g)+\ce{O2}(g)⟶\ce{SO3}(g)\)
- \(\ce{HgO}(s)⟶\ce{Hg}(l)+\ce{O2}(g)\)
S16.4.35
- (a) Increasing \(P_{\ce{O2}}\) will shift the equilibrium toward the products, which increases the value of K . \(ΔG^\circ_{298}\) therefore becomes more negative.
- Increasing \(P_{\ce{O2}}\) will shift the equilibrium toward the products, which increases the value of K . \(ΔG^\circ_{298}\) therefore becomes more negative.
- Increasing \(P_{\ce{O2}}\) will shift the equilibrium the reactants, which decreases the value of K . \(ΔG^\circ_{298}\) therefore becomes more positive.


Video introduction to the topics to be covered in this chapter: impulse, momentum, and their relationship; kinetics analysis of collisions and steady-flow devices.
Introduction to the impulse-momentum method of solving kinetic analysis problems. Includes discussion of impulse, momentum, and the conservation of momentum. Includes worked examples.
Analyzing one-dimensional particle collisions through momentum conservation; the types of collisions (elastic, semi-elastic, and inelastic) and the constraints they provide. Includes worked examples.
Analyzing two-dimensional particle collisions through momentum conservation for individual vector components. Types of collisions (elastic, semi-elastic, and inelastic) and the constraints they provide. Includes worked examples.


6.1: Anno Dom(Excerpt)
- 40718
Anno Dom: 1628.
…[T]her came over one Captaine Wolastone, (a man of pretie parts,) and with him 3. or 4. more of some eminencie, who brought with them a great many servants, with provissions & other implments for to begine a plantation; and pitched them selves in a place within the Massachusets, which they called, after their Captains Home [284] name, Mount-Wollaston. Amongst whom was one M r . Morton, who, it should seeme, had some small adventure (of his owne or other mens) amongst them; but had litle respecte [159] amongst them, and was sleghted by y e meanest servants. Haveing continued ther some time, and not finding things to answer their expectations, nor profite to arise as they looked for, Captaine Wollaston takes a great part of y e sarvants, and transports them to Virginia, wher he puts them of at good rates, selling their time to other men; and writs back to one M r . Rassdall, one of his cheefe partners, and accounted their marchant, to bring another parte of them to Verginia likewise, intending to put them of ther as he had done y e rest. And he, w th y e consente of y e said Rasdall, appoynted one Fitcher to be his Livetenante, and governe y e remaines of y e plantation, till he or Rasdall returned to take further order theraboute. But this Morton abovesaid, haveing more craft then honestie, (who had been a kind of petie-fogger, of Furnefells Inne,) in y e others absence, watches an oppertunitie, (commons being but hard amongst them,) and gott some strong drinck & other junkats, & made them a feast; and after they were merie, he begane to tell them, he would give them good counsell. You see (saith he) that many of your fellows are carried to Virginia; and if you stay till this Rasdall returne, you will also be carried away and sould for slaves with y e rest. Therfore I would Home [285] advise you to thruste out this Levetenant Fitcher; and I, having a parte in the plantation, will receive you as my partners and consociats; so may you be free from service, and we will converse, trad, plante, & live togeather as equalls, & supporte & protecte one another, or to like effecte. This counsell was easily received; so they tooke oppertunitie, and thrust Levetenante Fitcher out a dores, and would suffer him to come no more amongst them, but forct him to seeke bread to eate, and other releefe from his neigbours, till he could gett passages for England. After this they fell to great licenciousnes, and led a dissolute life, powering out them selves into all profanenes. And Morton became lord of misrule, and maintained (as it were) a schoole of Athisme. And after they had gott some good into their hands, and gott much by trading with y e Indeans, they spent it as vainly, in quaffing & drinking both wine & strong waters in great exsess, and, as some reported, 10 li . worth in a morning. They allso set up a May-pole, drinking and dancing aboute it many days togeather, inviting the Indean women, for their consorts, dancing and frisking togither, (like so many fairies, or furies rather,) and worse practises. As if they had anew revived & celebrated the feasts of y e Roman Goddes Flora, or y e beasly practieses of y e madd Bacchinalians. Morton likwise (to shew his poetrie) composed sundry rimes & verses, some tending to lasciviousnes, and Home [286] others to y e detraction & scandall of some persons, which he affixed to this idle or idoll May-polle. They chainged allso the name of their place, and in stead of calling it Mounte Wollaston, they call it Merie-mounte, [160] as if this joylity would have lasted ever. But this continued not long, for after Morton was sent for England, (as follows to be declared,) shortly after came over that worthy gentlman, M r . John Indecott, who brought over a patent under y e broad seall, for y e govermente of y e Massachusets, who visiting those parts caused y t May-polle to be cutt downe, and rebuked them for their profannes, and admonished them to looke ther should be better walking; so they now, or others, changed y e name of their place againe, and called it Mounte-Dagon.
Now to maintaine this riotous prodigallitie and profuse excess, Morton, thinking him selfe lawless, and hearing what gaine y e French & fisher-men made by trading of peeces, powder, & shotte to y e Indeans, he, as y e head of this consortship, begane y e practise of y e same in these parts; and first he taught them how to use them, to charge, & discharg, and what proportion of powder to give y e peece, according to y e sise or bignes of y e same; and what shotte to use for foule, and what for deare. And having thus instructed them, he imployed some of them to hunte & fowle for him, so as they became farr more active in that imploymente then any of y e English, by reason of ther Home [287] swiftnes of foote, & nimblnes of body, being also quick-sighted, and by continuall exercise well knowing y e hants of all sorts of game. So as when they saw y e execution that a peece would doe, and y e benefite that might come by y e same, they became madd, as it were, after them, and would not stick to give any prise they could attaine too for them; accounting their bowes & arrowes but bables in comparison of them.
And here I may take occasion to bewaile y e mischefe that this wicked man began in these parts, and which since base covetousnes prevailing in men that should know better, has now at length gott y e upper hand, and made this thing com̅one, notwithstanding any laws to y e contrary; so as y e Indeans are full of peeces all over, both fouling peeces, muskets, pistols, &c. They have also their moulds to make shotte, of all sorts, as muskett bulletts, pistoll bullets, swane & gose shote, & of smaler sorts; yea, some have seen them have their scruplats to make scrupins them selves, when they wante them, with sundery other implements, wherwith they are ordinarily better fited & furnished then y e English them selves. Yea, it is well knowne that they will have powder & shot, when the English want it, nor cannot gett it; and y t in a time of warr or danger, as experience hath manifested, that when lead hath been scarce, and men for their owne defence would gladly have given a groat a l which is dear enoughe, Home [288] yet hath it bene bought up & sent to other places, and sould to shuch as trade it with y e Indeans, at 12. pence y e li.; and it is like they give 3. or 4. s y e pound, for they will have it at any rate. And these things have been done in y e same times, when some of their neigbours & freinds are daly killed by y e Indeans, or are in deanger therof, and live but at y e Indeans mercie. [161] Yea, some (as they have aquainted them with all other things) have tould them how gunpowder is made, and all y e materialls in it, and that they are to be had in their owne land; and I am confidente, could they attaine to make saltpeter, they would teach them to make powder. O the horiblnes of this vilanie! how many both Dutch & English have been latly slaine by those Indeans, thus furnished; and no remedie provided, nay, y e evill more increased, and y e blood of their brethren sould for gaine, as is to be feared; and in what danger all these colonies are in is too well known. Oh! that princes & parlements would take some timly order to prevente this mischeefe, and at length to suppress it, by some exemplerie punishmente upon some of these gaine thirstie murderers, (for they deserve no better title,) before their collonies in these parts be over throwne by these barbarous savages, thus armed with their owne weapons, by these evill instruments, and traytors to their neigbors and cuntrie. But I have forgott my selfe, and have been to longe in this digression; but now to returne. This Morton having Home [289] thus taught them y e use of peeces, he sould them all he could spare; and he and his consorts detirmined to send for many out of England, and had by some of y e ships sente for above a score. The which being knowne, and his neigbours meeting y e Indeans in y e woods armed with guns in this sorte, it was a terrour unto them, who lived straglingly, and were of no strenght in any place. And other places (though more remote) saw this mischeefe would quietly spread over all, if not prevented. Besides, they saw they should keep no servants, for Morton would entertaine any, how vile soever, and all y e scume of y e countrie, or any discontents, would flock to him from all places, if this nest was not broken; and they should stand in more fear of their lives & goods (in short time) from this wicked & deboste crue, then from y e salvages them selves.
So sundrie of y e cheefe of y e stragling plantations, meeting togither, agreed by mutuall consente to sollissite those of Plimoth (who were then of more strength then them all) to joyne with them, to prevente y e further grouth of this mischeefe, and suppress Morton & his consortes before y ey grewe to further head and strength. Those that joyned in this acction (and after contributed to the charge of sending him for England) were from Pascataway, Namkeake, Winisimett, Weesagascusett, Natasco, and other places wher any English were seated. Those of Plimoth being thus sought too by their messengers & Home [290] letters, and waying both their reasons, and the com̅one danger, were willing to afford them their help; though them selves had least cause of fear or hurte. So, to be short, they first resolved joyntly to write to him, and in a freindly & neigborly way to admonish him to forbear these courses, & sent a messenger with their letters to bring his answer. But he was so highe as he scorned all advise, and asked who had to doe with him; he had and would trade peeces with y e Indeans in dispite of all, with many other scurillous termes full of disdaine. They sente to him a second time, and bad him be better advised, and more temperate in his termes, for y e countrie could not beare y e injure he did; it was against their comone saftie, and against y e king’s proclamation. He answerd in high terms as before, and that y e kings proclamation was no law; demanding what penaltie was upon it. It was answered, more then he could [162] bear, his majesties displeasure. But insolently he persisted, and said y e king was dead and his displeasure with him, & many y e like things; and threatened withall that if any came to molest him, let them looke to them selves, for he would prepare for them. Upon which they saw ther was no way but to take him by force; and having so farr proceeded, now to give over would make him farr more hautie & insolente. So they mutually resolved to proceed, and obtained of y e Gov r of Plimoth to send Home [291] Captaine Standish, & some other aide with him, to take Morton by force. The which accordingly was done; but they found him to stand stifly in his defence, having made fast his dors, armed his consorts, set diverse dishes of powder & bullets ready on y e table; and if they had not been over armed with drinke, more hurt might have been done. They som̅aned him to yeeld, but he kept his house, and they could gett nothing but scofes & scorns from him; but at length, fearing they would doe some violence to y e house, he and some of his crue came out, but not to yeeld, but to shoote; but they were so steeld with drinke as their peeces were to heavie for them; him selfe with a carbine (over charged & allmost halfe fild with powder & shote, as was after found) had thought to have shot Captaine Standish; but he stept to him, & put by his peece, & tooke him.  Morton they brought away to Plimoth, wher he was kepte, till a ship went from y e Ile of Shols for England, with which he was sente to y e Counsell of New-England; and letters writen to give them information of his course & cariage; and also one was sent at their com̅one charge to informe their Ho rs more perticulerly, & to prosecute against him. But he foold of y e messenger, after he was gone Home [292] from hence, and though he wente for England, yet nothing was done to him, not so much as rebukte, for ought was heard; but returned y e nexte year. Some of y e worst of y e company were disperst, and some of y e more modest kepte y e house till he should be heard from. But I have been too long aboute so un-worthy a person, and bad a cause…


2.3.3: "The Golden Speech"
(1601)
Mr Speaker,
We have heard your declaration and perceive your care of our estate. I do assure you there is no prince that loves his subjects better, or whose love can countervail our love. There is no jewel, be it of never so rich a price, which I set before this jewel: I mean your love. For I do esteem it more than any treasure or riches; for that we know how to prize, but love and thanks I count invaluable. And, though God hath raised me high, yet this I count the glory of my Crown, that I have reigned with your loves. This makes me that I do not so much rejoice that God hath made me to be a Queen, as to be a Queen over so thankful a people. Therefore I have cause to wish nothing more than to content the subject and that is a duty which I owe. Neither do I desire to live longer days than I may see your prosperity and that is my only desire. And as I am that person still yet, under God, hath delivered you and so I trust by the almighty power of God that I shall be his instrument to preserve you from every peril, dishonour, shame, tyranny and oppression, partly by means of your intended helps which we take very acceptably because it manifesteth the largeness of your good loves and loyalties unto your sovereign.
Of myself I must say this: I never was any greedy, scraping grasper, nor a strait fast-holding Prince, nor yet a waster. My heart was never set on any worldly goods. What you bestow on me, I will not hoard it up, but receive it to bestow on you again. Therefore render unto them I beseech you Mr Speaker, such thanks as you imagine my heart yieldeth, but my tongue cannot express. Mr Speaker, I would wish you and the rest to stand up for I shall yet trouble you with longer speech. Mr Speaker, you give me thanks but I doubt me I have greater cause to give you thanks, than you me, and I charge you to thank them of the Lower House from me. For had I not received a knowledge from you, I might have fallen into the lapse of an error, only for lack of true information.
Since I was Queen, yet did I never put my pen to any grant, but that upon pretext and semblance made unto me, it was both good and beneficial to the subject in general though a private profit to some of my ancient servants, who had deserved well at my hands. But the contrary being found by experience, I am exceedingly beholden to such subjects as would move the same at first. And I am not so simple to suppose but that there be some of the Lower House whom these grievances never touched. I think they spake out of zeal to their countries and not out of spleen or malevolent affection as being parties grieved. That my grants should be grievous to my people and oppressions to be privileged under colour of our patents, our kingly dignity shall not suffer it. Yea, when I heard it, I could give no rest unto my thoughts until I had reformed it. Shall they, think you, escape unpunished that have oppressed you, and have been respectless of their duty and regardless our honour? No, I assure you, Mr Speaker, were it not more for conscience’ sake than for any glory or increase of love that I desire, these errors, troubles, vexations and oppressions done by these varlets and lewd persons not worthy of the name of subjects should not escape without condign punishment. But I perceive they dealt with me like physicians who, ministering a drug, make it more acceptable by giving it a good aromatical savour, or when they give pills do gild them all over.
I have ever used to set the Last Judgement Day before mine eyes and so to rule as I shall be judged to answer before a higher judge, and now if my kingly bounties have been abused and my grants turned to the hurt of my people contrary to my will and meaning, and if any in authority under me have neglected or perverted what I have committed to them, I hope God will not lay their culps and offenses in my charge. I know the title of a King is a glorious title, but assure yourself that the shining glory of princely authority hath not so dazzled the eyes of our understanding, but that we well know and remember that we also are to yield an account of our actions before the great judge. To be a king and wear a crown is a thing more glorious to them that see it than it is pleasant to them that bear it. For myself I was never so much enticed with the glorious name of a King or royal authority of a Queen as delighted that God hath made me his instrument to maintain his truth and glory and to defend his kingdom as I said from peril, dishonour, tyranny and oppression. There will never Queen sit in my seat with more zeal to my country, care to my subjects and that will sooner with willingness venture her life for your good and safety than myself. For it is my desire to live nor reign no longer than my life and reign shall be for your good. And though you have had, and may have, many princes more mighty and wise sitting in this seat, yet you never had nor shall have, any that will be more careful and loving.
For I, oh Lord, what am I, whom practices and perils past should not fear? Or what can I do? That I should speak for any glory, God forbid.


Many people tend to overestimate their critical thinking skills. Here is just one example of documentation of this trend, from a business website, MindEdge , focused on helping students develop skills many employers say they want in college graduates:
“The second annual State of Critical Thinking survey from MindEdge asked respondents to complete a brief quiz requiring them to use digital literacy and critical thinking skills. “[…] In 2017, 44 percent of survey respondents received an ‘F’ on the critical thinking quiz. In 2018, 52 percent of respondents failed the quiz” (Ascione, 2020).
Many students taking a critical thinking course report a curve in their sense of confidence as thinkers. Like people in the MindEdge survey, they start out thinking they are pretty good thinkers. Then somewhere in the first third of the class, that sense of confidence takes a hit. The complexities of slow thinking can be hard to grasp at first. The homework and quizzes can feel confusing or tough. But as the term progresses, the techniques become more routine and less bewildering. Though slow thinking ALWAYS requires us to use a limited supply of our mental energy. This short excerpt from Kahneman’s work is a nice introduction.
Before you move further along there are some tenets to keep in mind. These will be covered in the next section.