11.2: Energy and Its Units
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Learning Objectives
- To define energy and he a t.
- To relate calories to nutrition and exercise.
Energy is the ability to do work. You can understand what this means by thinking about yourself when you feel “energetic.” You feel ready to go—to jump up and get something done. When you have a lot of energy, you can perform a lot of work. By contrast, if you do not feel energetic, you have very little desire to do much of anything. This description is not only applicable to you but also to all physical and chemical processes. The quantity of work that can be done is related to the quantity of energy available to do it.
Energy can be transferred from one object to another if the objects have different temperatures. The transfer of energy due to temperature differences is called heat. For example, if you hold an ice cube in your hand, the ice cube slowly melts as energy in the form of heat is transferred from your hand to the ice. As your hand loses energy, it starts to feel cold.
Because of their interrelationships, energy, work, and heat have the same units. The SI unit of energy, work, and heat is the joule (J). A joule is a tiny amount of energy. For example, it takes about 4 J to warm 1 mL of H 2 O by 1°C. Many processes occur with energy changes in thousands of joules, so the kilojoule (kJ) is also common. Another unit of energy, used widely in the health professions and everyday life, is the calorie (cal). The calorie was initially defined as the amount of energy needed to warm 1 g of H 2 O by 1°C, but in modern times, the calorie is related directly to the joule, as follows:
\[1\; cal = 4.184\; J \nonumber \]
We can use this relationship to convert quantities of energy, work, or heat from one unit to another.
Although the joule is the proper SI unit for energy, we will use the calorie or the kilocalorie (or Calorie) in this chapter because they are widely used by health professional
Example \(\PageIndex{1}\)
The energy content of a single serving of bread is 70.0 Cal. What is the energy content in calories? In joules?
Solution
This is a simple conversion-factor problem. Using the relationship 1 Cal = 1,000 cal, we can answer the first question with a one-step conversion:
\(\mathrm{70.0 \: Cal\times\dfrac{1,000\: cal}{1\: Cal}= 70,000\: cal}\)
Then we convert calories into joules
\(\mathrm{70,000 \: cal \times \dfrac{4.184\: J}{1\: cal}=293,000\: J}\)
and then kilojoules
\(\mathrm{293,000\: J\times\dfrac{1\: kJ}{1,000\: J}=293\: kJ}\)
The energy content of bread comes mostly from carbohydrates.
Exercise \(\PageIndex{1}\)
The energy content of one cup of honey is 1,030 Cal. What is its energy content in calories and joules?
- Answer
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1,030,000 (1.03 x 10 6 ) cal; 4,309,520 (4.31 x 10 6 ) J
The calorie is used in nutrition to express the energy content of foods. However, because a calorie is a rather small quantity, nutritional energies are usually expressed in kilocalories (kcal) , also called Calories (capitalized; Cal) . For example, a candy bar may provide 120 Cal (nutritional calories) of energy, which is equal to 120,000 cal. Figure \(\PageIndex{1}\) shows an example.
The caloric content of foods is determined by analyzing the food for protein, carbohydrate, fat, water, and “minerals” and then calculating the caloric content using the average values for each component that produces energy ( 9 Cal/g for fats, 4 Cal/g for carbohydrates and proteins, and 0 Cal/g for water and minerals ). An example of this approach is shown in Table \(\PageIndex{1}\) for a slice of roast beef.
| Composition | Calories |
|---|---|
| 97.5 g of water | × 0 Cal/g = 0 |
| 58.7 g of protein | × 4 Cal/g = 235 |
| 69.3 g of fat | × 9 Cal/g = 624 |
| 0 g of carbohydrates | × 4 Cal/g = 0 |
| 1.5 g of minerals | × 0 Cal/g = 0 |
| Total mass: 227.0 g | Total calories: about 900 Cal |
The compositions and caloric contents of some common foods are given in \(\PageIndex{2}\).
| Food (quantity) | Approximate Composition (%) | Food Value (Cal/g) | Calories | |||
|---|---|---|---|---|---|---|
| Water | Carbohydrate | Protein | Fat | |||
| beer (12 oz) | 92 | 3.6 | 0.3 | 0 | 0.4 | 150 |
| coffee (6 oz) | 100 | ~0 | ~0 | ~0 | ~0 | ~0 |
| milk (1 cup) | 88 | 4.5 | 3.3 | 3.3 | 0.6 | 150 |
| egg (1 large) | 75 | 2 | 12 | 12 | 1.6 | 80 |
| butter (1 tbsp) | 16 | ~0 | ~0 | 79 | 7.1 | 100 |
| apple (8 oz) | 84 | 15 | ~0 | 0.5 | 0.6 | 125 |
| bread, white (2 slices) | 37 | 48 | 8 | 4 | 2.6 | 130 |
| brownie (40 g) | 10 | 55 | 5 | 30 | 4.8 | 190 |
| hamburger (4 oz) | 54 | 0 | 24 | 21 | 2.9 | 326 |
| fried chicken (1 drumstick) | 53 | 8.3 | 22 | 15 | 2.7 | 195 |
| carrots (1 cup) | 87 | 10 | 1.3 | ~0 | 0.4 | 70 |
Because the Calorie represents such a large amount of energy, a few of them go a long way. An average 73 kg (160 lb) person needs about 67 Cal/h (1600 Cal/day) to fuel the basic biochemical processes that keep that person alive. This energy is required to maintain body temperature, keep the heart beating, power the muscles used for breathing, carry out chemical reactions in cells, and send the nerve impulses that control those automatic functions. Physical activity increases the amount of energy required but not by as much as many of us hope. A moderately active individual requires about 2500−3000 Cal/day; athletes or others engaged in strenuous activity can burn 4000 Cal/day. Any excess caloric intake is stored by the body for future use, usually in the form of fat, which is the most compact way to store energy. When more energy is needed than the diet supplies, stored fuels are mobilized and oxidized. We usually exhaust the supply of stored carbohydrates before turning to fats, which accounts in part for the popularity of low-carbohydrate diets.
To Your Health: Energy Expenditures
Most health professionals agree that exercise is a valuable component of a healthy lifestyle. Exercise not only strengthens the body and develops muscle tone but also expends energy. After obtaining energy from the foods we eat, we need to expend that energy somehow, or our bodies will store it in unhealthy ways (e.g., fat). Like the energy content in food, the energy expenditures of exercise are also reported in kilocalories, usually kilocalories per hour of exercise. These expenditures vary widely, from about 440 kcal/h for walking at a speed of 4 mph to 1,870 kcal/h for mountain biking at 20 mph. Table \(\PageIndex{3}\) lists the energy expenditure for a variety of exercises.
| Exercise | Energy Expended (kcal/h) |
|---|---|
| aerobics, low-level | 325 |
| basketball | 940 |
| bike riding, 20 mph | 830 |
| golfing, with cart | 220 |
| golfing, carrying clubs | 425 |
| jogging, 7.5 mph | 950 |
| racquetball | 740 |
| skiing, downhill | 520 |
| soccer | 680 |
| walking upstairs | 1,200 |
| yoga | 280 |
Because some forms of exercise use more energy than others, anyone considering a specific exercise regimen should consult with his or her physician first.
Summary
Energy is the ability to do work. Heat is the transfer of energy due to temperature differences. Energy and heat are expressed in units of joules.


8.7C: Betaproteobacteria
- Evaluate the importance of Betaproteobacteria
Betaproteobacteria is a class of Proteobacteria that are all Gram-negative. The Betaproteobacteria consist of several groups of aerobic or facultative bacteria that are often highly versatile in their degradation capacities, but also contain chemolithotrophic genera (e.g., the ammonia-oxidising genus Nitrosomonas ) and some phototrophs (members of the genera Rhodocyclus and Rubrivivax ).
Nitrosomonas is a genus comprising rod shaped chemoautotrophic bacteria. This rare bacteria oxidizes ammonia into nitrite as a metabolic process. Nitrosomonas are useful in treatment of industrial and sewage waste and in the process of bioremediation. They play an important role in the nitrogen cycle by increasing the availability of nitrogen to plants while limiting carbon dioxide fixation.
Betaproteobacteria play a role in nitrogen fixation in various types of plants, oxidizing ammonium to produce nitrite- an important chemical for plant function. Many of them are found in environmental samples, such as waste water or soil. Pathogenic species within this class are the Neisseriaceae (gonorrhea and meningitis) and species of the genus Burkholderia .
Burkholderia is a genus of proteobacteria probably best known for its pathogenic members: Burkholderia mallei , responsible for glanders, a disease that occurs mostly in horses and related animals; Burkholderia pseudomallei , causative agent of melioidosis ; and Burkholderia cepacia , an important pathogen of pulmonary infections in people with cystic fibrosis (CF). The Burkholderia (previously part of Pseudomonas ) genus name refers to a group of virtually ubiquitous gram-negative, motile, obligately aerobic rod-shaped bacteria including both animal/human (see above) and plant pathogens as well as some environmentally important species.
The currently accepted taxonomy is based on the List of Prokaryotic names with Standing in Nomenclature (LPSN) and National Center for Biotechnology Information (NCBI) and the phylogeny is based on 16S rRNA-based LTP release 106 by ‘The All-Species Living Tree’ Project.
Key Points
- The Betaproteobacteria consist of several groups of aerobic or facultative bacteria that are often highly versatile in their degradation capacities.
- The Betaproteobacteria contain chemolithotrophic genera (e.g., the ammonia-oxidising genus Nitrosomonas) and some phototrophs (members of the genera Rhodocyclus and Rubrivivax).
- Betaproteobacteria play a role in nitrogen fixation in various types of plants, oxidizing ammonium to produce nitrite- an important chemical for plant function.
Key Terms
- Betaproteobacteria : Betaproteobacteria is a class of Proteobacteria. Betaproteobacteria are, like all Proteobacteria, Gram-negative.
- glanders : An infectious disease of horses, mules and donkeys caused by the bacterium Burkholderia, one species of which may be transmitted to humans.
- melioidosis : An infectious disease caused by a Gram-negative bacterium, Burkholderia pseudomallei, found in soil and water. It is endemic in Southeast Asia and northern Australia. Symptoms may include pain in chest, bones, or joints; cough; skin infections, lung nodules and pneumonia.


1.7: Electric Field Lines
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Learning Objectives
By the end of this section, you will be able to:
- Explain the purpose of an electric field diagram
- Describe the relationship between a vector diagram and a field line diagram
- Explain the rules for creating a field diagram and why these rules make physical sense
- Sketch the field of an arbitrary source charge
Now that we have some experience calculating electric fields, let’s try to gain some insight into the geometry of electric fields. As mentioned earlier, our model is that the charge on an object (the source charge) alters space in the region around it in such a way that when another charged object (the test charge) is placed in that region of space, that test charge experiences an electric force. The concept of electric field line s , and of electric field line diagrams, enables us to visualize the way in which the space is altered, allowing us to visualize the field. The purpose of this section is to enable you to create sketches of this geometry, so we will list the specific steps and rules involved in creating an accurate and useful sketch of an electric field.
It is important to remember that electric fields are three-dimensional. Although in this book we include some pseudo-three-dimensional images, several of the diagrams that you’ll see (both here, and in subsequent chapters) will be two-dimensional projections, or cross-sections. Always keep in mind that in fact, you’re looking at a three-dimensional phenomenon.
Our starting point is the physical fact that the electric field of the source charge causes a test charge in that field to experience a force. By definition, electric field vectors point in the same direction as the electric force that a (hypothetical) positive test charge would experience, if placed in the field (Figure \(\PageIndex{1}\)).
We’ve plotted many field vectors in the figure, which are distributed uniformly around the source charge. Since the electric field is a vector, the arrows that we draw correspond at every point in space to both the magnitude and the direction of the field at that point. As always, the length of the arrow that we draw corresponds to the magnitude of the field vector at that point. For a point source charge, the length decreases by the square of the distance from the source charge. In addition, the direction of the field vector is radially away from the source charge, because the direction of the electric field is defined by the direction of the force that a positive test charge would experience in that field. (Again, keep in mind that the actual field is three-dimensional; there are also field lines pointing out of and into the page.)
This diagram is correct, but it becomes less useful as the source charge distribution becomes more complicated. For example, consider the vector field diagram of a dipole (Figure \(\PageIndex{2}\)).
There is a more useful way to present the same information. Rather than drawing a large number of increasingly smaller vector arrows, we instead connect all of them together, forming continuous lines and curves, as shown in Figure \(\PageIndex{3}\).
Although it may not be obvious at first glance, these field diagrams convey the same information about the electric field as do the vector diagrams. First, the direction of the field at every point is simply the direction of the field vector at that same point. In other words, at any point in space, the field vector at each point is tangent to the field line at that same point. The arrowhead placed on a field line indicates its direction.
As for the magnitude of the field, that is indicated by the field line density —that is, the number of field lines per unit area passing through a small cross-sectional area perpendicular to the electric field. This field line density is drawn to be proportional to the magnitude of the field at that cross-section. As a result, if the field lines are close together (that is, the field line density is greater), this indicates that the magnitude of the field is large at that point. If the field lines are far apart at the cross-section, this indicates the magnitude of the field is small. Figure \(\PageIndex{4}\) shows the idea.
In Figure \(\PageIndex{4}\), the same number of field lines passes through both surfaces \(S\) and \(S'\), but the surface \(S\) is larger than surface \(S'\). Therefore, the density of field lines (number of lines per unit area) is larger at the location of \(S'\), indicating that the electric field is stronger at the location of \(S'\) than at \(S\). The rules for creating an electric field diagram are as follows.
Problem-Solving Strategy: Drawing Electric Field Lines
- Electric field lines either originate on positive charges or come in from infinity, and either terminate on negative charges or extend out to infinity.
- The number of field lines originating or terminating at a charge is proportional to the magnitude of that charge. A charge of 2\(q\) will have twice as many lines as a charge of \(q\).
- At every point in space, the field vector at that point is tangent to the field line at that same point.
- The field line density at any point in space is proportional to (and therefore is representative of) the magnitude of the field at that point in space.
- Field lines can never cross. Since a field line represents the direction of the field at a given point, if two field lines crossed at some point, that would imply that the electric field was pointing in two different directions at a single point. This in turn would suggest that the (net) force on a test charge placed at that point would point in two different directions. Since this is obviously impossible, it follows that field lines must never cross.
Always keep in mind that field lines serve only as a convenient way to visualize the electric field; they are not physical entities. Although the direction and relative intensity of the electric field can be deduced from a set of field lines, the lines can also be misleading. For example, the field lines drawn to represent the electric field in a region must, by necessity, be discrete. However, the actual electric field in that region exists at every point in space.
Field lines for three groups of discrete charges are shown in Figure \(\PageIndex{5}\). Since the charges in parts (a) and (b) have the same magnitude, the same number of field lines are shown starting from or terminating on each charge. In (c), however, we draw three times as many field lines leaving the \(+3q\) charge as entering the \(-q\). The field lines that do not terminate at \(-q\) emanate outward from the charge configuration, to infinity.
The ability to construct an accurate electric field diagram is an important, useful skill; it makes it much easier to estimate, predict, and therefore calculate the electric field of a source charge. The best way to develop this skill is with software that allows you to place source charges and then will draw the net field upon request. We strongly urge you to search the Internet for a program. Once you’ve found one you like, run several simulations to get the essential ideas of field diagram construction. Then practice drawing field diagrams, and checking your predictions with the computer-drawn diagrams.
PhET: Charges and Fields
Arrange positive and negative charges in space and view the resulting electric field and electrostatic potential. Plot equipotential lines and discover their relationship to the electric field. Create models of dipoles, capacitors, and more!


6.2: The Irrationality of √2
In this section we will prove one of the oldest and most important theorems in mathematics: \(\sqrt{2}\) is irrational (see Theorem 6.19). First, we need to know what this means.
Definition 6.18. Let \(r\in\mathbb{R}\) .
- We say that \(r\) is rational if \(r=\frac{m}{n}\) , where \(m,n\in\mathbb{Z}\) and \(n\neq 0\) .
- In contrast, we say that \(r\) is irrational if it is not rational.
The Pythagoreans were an ancient secret society that followed their spiritual leader: Pythagoras of Samos (c. 570–495 BCE). The Pythagoreans believed that the way to spiritual fulfillment and to an understanding of the universe was through the study of mathematics. They believed that all of mathematics, music, and astronomy could be described via whole numbers and their ratios. In modern mathematical terms they believed that all numbers are rational. Attributed to Pythagoras is the saying, “Beatitude is the knowledge of the perfection of the numbers of the soul.” And their motto was “All is number.”
Thus they were stunned when one of their own—Hippasus of Metapontum (c. 5th century BCE)—discovered that the side and the diagonal of a square are incommensurable. That is, the ratio of the length of the diagonal to the length of the side is irrational. Indeed, if the side of the square has length \(a\) , then the diagonal will have length \(a\sqrt{2}\) ; the ratio is \(\sqrt{2}\) (see Figure 6.1).
In Section 5.1, we took for granted that \(\sqrt{2}\) was irrational. We now prove this fact. Consider using a proof by contradiction. Suppose that there exist \(m,n\in\mathbb{Z}\) such that \(n\ne 0\) and \(\sqrt{2}=\frac{m}{n}\) . Are there an odd or even number of factors of 2 on each side of this equation? Does your conclusion violate the Fundamental Theorem of Arithmetic (Theorem 6.17)?
Theorem 6.19. The real number \(\sqrt{2}\) is irrational.
As one might expect, the Pythagoreans were unhappy with this discovery. Legend says that Hippasus was expelled from the Pythagoreans and was perhaps drowned at sea. Ironically, this result, which angered the Pythagoreans so much, is probably their greatest contribution to mathematics: the discovery of irrational numbers.
See if you can generalize the technique in the proof of Theorem 6.19 to prove the next two theorems.
Theorem 6.20. Let \(p\) be a prime number. Then \(\sqrt{p}\) is irrational.
Theorem 6.21. Let \(p\) and \(q\) be distinct primes. Then \(\sqrt{pq}\) is irrational.
Problem 6.22. State a generalization of Theorem 6.21 and briefly describe how its proof would go. Be as general as possible.
It is important to point out that not every positive irrational number is equal to the square root of some natural number. For example, \(\pi\) is irrational, but is not equal to the square root of a natural number.


11.5: Neutralization of Fatty Acids and Hydrolysis of Triglycerides
- Describe how carboxylic acids react with basic compounds.
- Identify the products of an acidic or basic hydrolysis of an ester.
- Understand the interactions of soap and detergent with hard water.
Neutralization Reaction of a Carboxylic Acid with NaOH
Carboxylic acids react with aqueous solutions of sodium hydroxide (NaOH) to form salts and water in a double replacement reaction. This reaction is an acid-base reaction known as neutralization reaction.
CH 3 COOH + NaOH(aq) → CH 3 COO − Na + (aq) + H 2 O
The salt is the conjugate base of the carboxylic acid is called the carboxylate ion (CH 3 COO − Na + ).
Carboxylate ions (RCOO − Na + ) are more soluble in water than carboxylic acids (RCOOH).
Neutralization Reaction of a Fatty Acid with NaOH
Fatty acids are long chain carboxylic acids. They are insoluble in water and hence hydrophobic. When treated with NaOH, fatty acids are converted into carboxylate ion salts (ionic compounds) containing Na + and amphipathic fatty acid anion.
Figure \(\PageIndex{1}\): Oleic acid (hydrophobic), when reacted with aq NaOH, it is converted to an ionic compound sodium oleate (amphipathic)
Like all fatty acids, oleic acid is hydrophobic. In figure 11.5.1 oleic acid is converted into sodium oleate. Sodium oleate is soap. In aqueous solutions, soaps will spontaneously form micelles , a spherical structure that allows the hydrophobic tails to avoid contact with water and simultaneously form cluster in the center via London dispersion forces. The hydrophilic heads make up the outer surface and dissolves in water.
Figure \(\PageIndex{2}\): Micelle
Dirt and grime usually adhere to skin and clothing by combining with body oils, cooking fats, and lubricating greases. These substances are nonpolar and so they are not miscible in water. Washing with water alone will not remove them. These nonpolar oils and grease along with dirt will be trapped in the hydrophobic interior of the micelle of soap, while the micelle is easily rinsed away with water.
Hydrolysis of Esters
Hydrolysis is “splitting with water.” Hydrolysis is the most important reaction of esters. The hydrolysis of esters is catalyzed by either an acid or a base. During acid catalysed hydrolysis the ester is heated with water containing a small amount of a strong-acid catalyst such as sulfuric acid. The sulfuric acid is a source of the hydrogen ion (H + ), the catalyst in the reaction.
Acidic hydrolysis of an ester gives a carboxylic acid and an alcohol. Note that the -OH of the carboxylic acid and the H of the alcohol comes from water (shown in purple).
When a base (such as sodium hydroxide [NaOH] or potassium hydroxide [KOH]) is used to hydrolyze an ester, the products are a carboxylate salt and an alcohol.
As a specific example, ethyl acetate and NaOH react to form sodium acetate and ethanol:
Because soaps are prepared by the alkaline hydrolysis of fats and oils, alkaline hydrolysis of esters is called saponification (Latin sapon , meaning “soap,” and facere , meaning “to make”). In a saponification reaction, the base is a reactant and a catalyst.
Saponification of Fats and Oils
Fats and oils are esters, they can be hydrolyzed in the presence of an acid, a base, or specific enzymes known as lipases. The hydrolysis of fats and oils in the presence of a base is used to make soap and is called saponification. Soaps are prepared through the hydrolysis of triglycerides (often from tallow, coconut oil, or both) using water and sodium hydroxide.
Figure \(\PageIndex{3}\): Saponification of a triglyceride.
Sodium salts of fatty acids make hard soaps while potassium salts make soft soaps. Three of the most common soaps are sodium stearate, sodium oleate, and sodium linoleate. Salts of saturated fatty acids make hard soap and those of polyunsaturated fatty acids make soft soap. Perfumes are added for scent and dyes for color, sand is added in scouring soap, and the air is blown into the soap to make it float on water.
Looking Closer: Soaps
Ordinary soap is a mixture of the sodium salts of various fatty acids, produced in one of the oldest organic syntheses practiced by humans (second only to the fermentation of sugars to produce ethyl alcohol ).  Even so, the widespread production of soap did not begin until the 1700s . Soap was traditionally made by treating molten lard or tallow with a slight excess of alkali in large open vats. The mixture was heated, and steam was bubbled through it. After saponification was completed, the soap was precipitated from the mixture by the addition of sodium chloride (NaCl), removed by filtration, and washed several times with water. It was then dissolved in water and reprecipitated by the addition of more NaCl. The glycerol produced in the reaction was also recovered from the aqueous wash solutions.
Pumice or sand is added to produce scouring soap, while ingredients such as perfumes or dyes are added to produce fragrant, colored soaps. Blowing air through molten soap produces a floating soap. Soft soaps, made with potassium salts, are more expensive but produce a finer lather and are more soluble. They are used in liquid soaps, shampoos, and shaving creams.
Figure \(\PageIndex{4}\): Micelle of Soap.
Dirt and grime usually adhere to skin, clothing, and other surfaces by combining with body oils, cooking fats , lubricating greases, and similar substances that act like glues. Because these substances are not miscible in water, washing with water alone does little to remove them. Soap removes them, because soap molecules have a dual nature. One end, called the head , carries an ionic charge (a carboxylate anion) and therefore dissolves in water; the other end, the tail , has a hydrocarbon structure and dissolves in oils. The hydrocarbon tails dissolve in the soil; the ionic heads remain in the aqueous phase. With the oil no longer “gluing” the dirt to the soiled surface (skin, cloth, dish), the soap-enclosed dirt can easily be rinsed away.
Hard water
Water is considered hard water, if it contains soluble Ca 2 + , Mg 2 + and Fe 3 + ions. These ions are present in water as soluble bicarbonate compounds. If these ions are removed or absent, the water is considered soft water. Hard water can be purified by using water softeners or ion-exchange resins that replace Ca 2 + and Mg 2 + with Na + ions.
Soaps
A soap is the sodium or potassium salt of a fatty acid. The tail part of the soap molecule is nonpolar, but the polar “head” at the carboxyl end permits a small portion of the molecule to be water soluble. Hence soaps are amphipathic. The cleansing power of soap is dependent on this water solubility. However, hard water containing Ca 2 + and Mg 2 + reacts with soap and forms insoluble scales (scum) with soap. Figure 11.5.5 shows the formation of insoluble precipitate of soap with Ca 2 + ion in hard water. This reduces the cleansing properties of soap since less soap molecules are available to form the micelle.
Figure \(\PageIndex{5}\): Formation of insoluble scales of soap with calcium ions in hard water.
Detergents
A detergent is the sodium salt of a sulfonic acid. It has similar cleansing properties to soap since detergents can form micelles just like soap. However, detergents differ from soaps in its interactions with hard water. The calcium and magnesium ions from hard water interact with a detergent and from compounds that are soluble in water. Figure 11.5.6 shows the formation of a soluble compound of detergent with Ca 2 + ion in hard water. So, calcium and magnesium ions from hard water have no effect on the cleansing properties of a detergent.
Figure \(\PageIndex{6}\): Formation of soluble compound of detergent with calcium ions in hard water.
Summary
Fatty acids can react with bases to form an amphipathic compound called soap. Soaps are made by the hydrolysis reaction of a triglyceride with an aqueous solution of a base.


1.2: The Westphalian System
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The European states emerged in the midst of struggle and strife, and struggle and strife have continued to characterise their existence. Yet, in early modern Europe it was no longer the competing claims of local and universal authorities that had to be combated but instead the competing claims of other states. The Thirty Years’ War, 1618–1648, was the bloodiest and most protracted military confrontation of the era. As a result of the war Germany’s population was reduced by around a third. What the Swiss or the Scottish mercenaries did not steal, the Swedish troops destroyed. Many of the people who did not die on the battlefield died of the plague. The Thirty Years’ War is often called a religious conflict since Catholic states confronted Protestants. Yet, Protestant and Catholic countries sometimes fought on the same side and religious dogma was clearly not the first thing on the minds of the combatants. Instead the war concerned which state should have hegemony (or dominance) over Europe. That is, which state, if any, would take over from the universal institutions of the Middle Ages. The main protagonists were two Catholic states, France and Austria, but Sweden – a Protestant country – intervened on France’s side and in the end no dominant power emerged.
The Treaty of Westphalia, 1648, which concluded the 30 years of warfare, has come to symbolise the new way of organising international politics. From this point onwards, international politics was a matter of relations between states and no other political units. All states were sovereign, meaning that they laid claims to the exclusive right to rule their own territories and to act, in relation to other states, as they themselves saw fit. All states were formally equal and they had the same rights and obligations. Taken together, the states interacted with each other in a system in which there was no overarching power. Sovereignty and formal equality led to the problem of anarchy. Within a country ‘anarchy’ refers to a breakdown of law and order, but in relations between states it refers to a system where power is decentralised and there are no shared institutions with the right to enforce common rules. An anarchical world is a world where everyone looks after themselves and no one looks after the system as a whole. Instead, states had to rely on their own resources or to form alliances through which the power of one alliance of states could be balanced against the power of another alliance. Yet, as soon became clear, such power balances were precarious, easily subverted, and given the value attached to territorial acquisitions, states had an incentive to engage in aggressive wars. As a result, the new international system was characterised by constant tensions and threats of war – which often enough turned into actual cases of warfare.
At the same time various practices developed which helped regulate common affairs. The foremost example was the practice of diplomacy as exemplified by the way peace treaties were negotiated. From the seventeenth century onward, European states met after each major war in order to reach a settlement and lay down the terms of their future interaction. These diplomatic practices had their origin in relations between the city-states of northern Italy. Once these states had made themselves independent both of the pope and the emperor, they soon discovered that their relations had become vastly more complicated. In order to avoid misunderstandings and unnecessary conflicts, the different rulers began dispatching ambassadors to each other’s courts. This diplomatic network provided a means of gathering information, of spying, but also a way of keeping in touch with one another, of carrying out negotiations and concluding deals. The practices of diplomacy soon expanded to include a number of mutually advantageous provisions: the embassies were given extraterritorial rights and legal immunity, diplomatic dispatches were regarded as inviolable and ambassadors had the right to worship the god of their choice. These originally north Italian practices gradually expanded to embrace more states and by the middle of the seventeenth century the system included France, Spain, Austria, England, Russia, Poland, Denmark, Sweden and the Ottoman Empire. Diplomatic practices were never powerful enough to prevent war, indeed wars continued to be common, but they did provide Europeans with a sense of a common identity. A European state was, more than anything, a state that participated in the system of shared diplomatic practices.


<IP_ADDRESS>: Harmony - Harmony in Pop/Rock Music
Harmony in pop/rock music does not always follow the same norms and patterns of classical-era music. Thus, functional-bass notation does not work for all situations. Instead, we will primarily use Roman numerals for our analysis of harmony in pop/rock music, occasionally using functional bass as a supplement to help us make sense of a particular harmonic pattern or relate it to what we’ve studied in classical harmony.
One key difference between rock and classical harmony is that chords in pop/rock music are almost always root-position triads or seventh chords. This affects the “rules” of harmonic syntax, as 6/3 chords in classical progressions are replaced by 5/3 chords in pop/rock progressions. (For instance, the classical progression IV–IV 6 becomes IV–VI . The same bass line does the same work, but by using a 5/3 chord instead of a 6/3 chord, the functional progression changes to something that would “break the rules” of classical syntax.) This can make harmonic analysis a little tricky in pop/rock music, especially since there is no published theory of rock harmony that is equal to Quinn’s functional theory of classical harmony. However, it makes chord labeling and harmonic dictation simpler. Most of the time, all you need is the scale degree of the bass.
Following is a chart of bass scale degrees and the roots/Roman numerals most typically associated with them. Keep this chart handy when transcribing and dictating rock harmonic progressions. As you can see, most bass notes typically go with a single chord.
Bass scale degrees and commonly associated harmonies in pop/rock music. Less common chords are enclosed in square brackets.
Harmonic functions in minor
Harmonic functions in minor keys of pop/rock songs, particularly in the last couple decades, tend to deviate from classical syntax in different ways than major-key songs. See the Harmonic functions in minor resource for more details about this.
Schemata
There are a number of common stock chord progressions that recur in many pop/rock songs. Typically, these stock progressions, or schemata, will occur in cyclical patterns; that is, the same progression will repeat multiple times in a row. This is particularly common in choruses of verse-chorus songs, but also happens in verses, strophes, and bridges. This is helpful for identifying harmonies by ear, since in addition to listening for bass scale degrees and considering whether the harmonies are chords of the fifth (5/3 or 7) or chords of the sixth (typically 6/3 or 6/5), we can listen for common patterns that we’ve heard in other songs. Following are a number of common schemata for pop/rock harmonic progressions.
||: I – VI – IV – V :||
or
||: I – VI – II – V :||
The “Singer/Songwriter” progression
||: VI – IV – I – V :||
(in major)
||: I – VI – III – VII :||
(in minor)
||: I – V – VI – IV :||
(“With or Without You” variant)
||: IV – I – V – VI :||
(“deceptive” variant)
I – III – IV . . . (to begin a phrase)
||: I - - - | IV - I - | V IV I - :||
(12-bar blues)
||: I - - - | I - - - | IV - I - | V IV I -:||
(16-bar blues)
||: I – V – VI – III – IV – I – IV – V :||
||: I – V
6
– VI – III
6
– IV – I
6
– IV – V :||
(stepwise bass version)
I – V – VI – III . . .
(to begin a phrase; “truncated” version)
||: I – VII – VI – V :||
The circle-of-fifths progression (in minor)
||: I – IV – VII – III :||
||: I - IV :||
||: I - bVII - IV - I :||
||: bVI - bIII - bVII - IV - I :||
Rock’s “tonal systems”
Walter Everett has posited six tonal systems to which most pop/rock songs belong. The following sections summarize four of these with examples (all but 1 and 6—the most and least tonal). See Everett’s 2004 article in Music Theory Online for a more detailed exploration of these “systems.”
System 1: Pop/rock tonality that strongly resembles common-practice classical tonality (major and minor keys, with parallel-key borrowing).
System 2: Pop/rock tonality that draws on diatonic modes (such as Dorian, Mixolydian, Aeolian).
System 4: Blues-based pop/rock tonality.
System 5: Minor-pentatonic-based pop/rock tonality.
System 6: Chromatically inflected minor-pentatonic-based pop/rock tonality.


10.2.1: Complexation Equilibrium
- To be introduced to complex ions, including ligands.
Previously, you learned that metal ions in aqueous solution are hydrated—that is, surrounded by a shell of usually four or six water molecules. A hydrated ion is one kind of a complex ion (or, simply, complex), a species formed between a central metal ion and one or more surrounding ligands , molecules or ions that contain at least one lone pair of electrons, such as the [Al(H 2 O) 6 ] 3+ ion.
A complex ion forms from a metal ion and a ligand because of a Lewis acid–base interaction. The positively charged metal ion acts as a Lewis acid, and the ligand, with one or more lone pairs of electrons, acts as a Lewis base. Small, highly charged metal ions, such as Cu 2 + or Ru 3 + , have the greatest tendency to act as Lewis acids, and consequently, they have the greatest tendency to form complex ions.
As an example of the formation of complex ions, consider the addition of ammonia to an aqueous solution of the hydrated Cu 2 + ion {[Cu(H 2 O) 6 ] 2+ }. Because it is a stronger base than H 2 O, ammonia replaces the water molecules in the hydrated ion to form the [Cu(NH 3 ) 4 (H 2 O) 2 ] 2+ ion. Formation of the [Cu(NH 3 ) 4 (H 2 O) 2 ] 2+ complex is accompanied by a dramatic color change, as shown in Figure \(\PageIndex{1}\). The solution changes from the light blue of [Cu(H 2 O) 6 ] 2+ to the blue-violet characteristic of the [Cu(NH 3 ) 4 (H 2 O) 2 ] 2+ ion.
Figure \(\PageIndex{1}\): The Formation of Complex Ions. An aqueous solution of \(\ce{CuSO4}\) consists of hydrated Cu 2 + ions in the form of pale blue [Cu(H 2 O) 6 ] 2+ (left). The addition of aqueous ammonia to the solution results in the formation of the intensely blue-violet [Cu(NH 3 ) 4 (H 2 O) 2 ] 2+ ions, usually written as [Cu(NH 3 ) 4 ] 2+ ion (right) because ammonia, a stronger base than H 2 O, replaces water molecules from the hydrated Cu 2 + ion. For a more complete description, see www.youtube.com/watch?v=IQNcLH6OZK0.
The Formation Constant
The replacement of water molecules from [Cu(H 2 O) 6 ] 2+ by ammonia occurs in sequential steps. Omitting the water molecules bound to Cu 2 + for simplicity, we can write the equilibrium reactions as follows:
\\ \mathrm{[Cu(NH_3)]^{2+}_{(aq)}}+\mathrm{NH_{3(aq)}}&\rightleftharpoons\mathrm{[Cu(NH_3)_2]^{2+}_{(aq)}}\hspace{3mm}K_2
\\ \mathrm{[Cu(NH_3)_2]^{2+}_{(aq)}}+\mathrm{NH_{3(aq)}}&\rightleftharpoons\mathrm{[Cu(NH_3)_3]^{2+}_{(aq)}}\hspace{3mm}K_3
\\ \mathrm{[Cu(NH_3)_3]^{2+}_{(aq)}}+\mathrm{NH_{3(aq)}}&\rightleftharpoons \mathrm{[Cu(NH_3)_4]^{2+}_{(aq)}}\hspace{3mm}K_4 \end{align} \label{17.3.1}\]
The sum of the stepwise reactions is the overall equation for the formation of the complex ion: The hydrated Cu 2 + ion contains six H 2 O ligands, but the complex ion that is produced contains only four \(\ce{NH_3}\) ligands, not six.
\[Cu^{2+}_{(aq)} + 4NH_{3(aq)} \rightleftharpoons [Cu(NH_3)_4]^{2+}_{(aq)} \label{17.3.2}\]
The equilibrium constant for the formation of the complex ion from the hydrated ion is called the formation constant ( K f ) . The equilibrium constant expression for K f has the same general form as any other equilibrium constant expression. In this case, the expression is as follows:
The formation constant ( K f ) has the same general form as any other equilibrium constant expression.
Water, a pure liquid, does not appear explicitly in the equilibrium constant expression, and the hydrated Cu 2 + (aq) ion is represented as Cu 2 + for simplicity. As for any equilibrium, the larger the value of the equilibrium constant (in this case, K f ), the more stable the product. With K f = 2.1 × 10 13 , the [Cu(NH 3 ) 4 (H 2 O) 2 ] 2+ complex ion is very stable. The formation constants for some common complex ions are listed in Table \(\PageIndex{1}\) .
| Complex Ion | Equilibrium Equation | K f | |
|---|---|---|---|
| *Reported values are overall formation constants. Source: Data from Lange’s Handbook of Chemistry, 15th ed. (1999). | |||
| Ammonia Complexes | [Ag(NH 3 ) 2 ] + | Ag + + 2NH 3 ⇌ [Ag(NH 3 ) 2 ] + | 1.1 × 10 7 |
| [Cu(NH 3 ) 4 ] 2+ | Cu 2 + + 4NH 3 ⇌ [Cu(NH 3 ) 4 ] 2+ | 2.1 × 10 13 | |
| [Ni(NH 3 ) 6 ] 2+ | Ni 2 + + 6NH 3 ⇌ [Ni(NH 3 ) 6 ] 2+ | 5.5 × 10 8 | |
| Cyanide Complexes | [Ag(CN) 2 ] − | Ag + + 2CN − ⇌ [Ag(CN) 2 ] − | 1.1 × 10 18 |
| [Ni(CN) 4 ] 2− | Ni 2 + + 4CN − ⇌ [Ni(CN) 4 ] 2− | 2.2 × 10 31 | |
| [Fe(CN) 6 ] 3− | Fe 3 + + 6CN − ⇌ [Fe(CN) 6 ] 3− | 1 × 10 42 | |
| Hydroxide Complexes | [Zn(OH) 4 ] 2− | Zn 2 + + 4OH − ⇌ [Zn(OH) 4 ] 2− | 4.6 × 10 17 |
| [Cr(OH) 4 ] − | Cr 3 + + 4OH − ⇌ [Cr(OH) 4 ] − | 8.0 × 10 29 | |
| Halide Complexes | [HgCl 4 ] 2− | Hg 2 + + 4Cl − ⇌ [HgCl 4 ] 2− | 1.2 × 10 15 |
| [CdI 4 ] 2− | Cd 2 + + 4I ⇌ [CdI 4 ] 2− | 2.6 × 10 5 | |
| [AlF 6 ] 3− | Al 3 + + 6F − ⇌ [AlF 6 ] 3− | 6.9 × 10 19 | |
| Other Complexes | [Ag(S 2 O 3 ) 2 ] 3− | Ag + + 2S 2 O 3 2− ⇌ [Ag(S 2 O 3 ) 2 ] 3− | 2.9 × 10 13 |
| [Fe(C 2 O 4 ) 3 ] 3− | Fe 3 + + 3C 2 O 4 2− ⇌ [Fe(C 2 O 4 ) 3 ] 3− | 2.0 × 10 20 |
If 12.5 g of \(\ce{Cu(NO3)2•6H2O}\) is added to 500 mL of 1.00 M aqueous ammonia, what is the equilibrium concentration of Cu 2 + (aq)?
Given: mass of Cu 2 + salt and volume and concentration of ammonia solution
Asked for: equilibrium concentration of Cu 2 + (aq)
Strategy:
- Calculate the initial concentration of Cu 2 + due to the addition of copper(II) nitrate hexahydrate. Use the stoichiometry of the reaction shown in Equation \(\ref{17.3.2}\) to construct a table showing the initial concentrations, the changes in concentrations, and the final concentrations of all species in solution.
- Substitute the final concentrations into the expression for the formation constant ( Equation \(\ref{17.3.3}\) ) to calculate the equilibrium concentration of Cu 2 + (aq).
Solution
Adding an ionic compound that contains Cu 2 + to an aqueous ammonia solution will result in the formation of [Cu(NH 3 ) 4 ] 2+ (aq), as shown in Equation \(\ref{17.3.2}\) . We assume that the volume change caused by adding solid copper(II) nitrate to aqueous ammonia is negligible.
A The initial concentration of Cu 2 + from the amount of added copper nitrate prior to any reaction is as follows:
\[12.5\mathrm{\;\cancel{g}\;Cu(NO_3)_2}\cdot\mathrm{6H_2O}\left(\dfrac{\textrm{1 mol}}{\textrm{295.65} \cancel{g}} \right )\left(\dfrac{1}{\textrm{500}\; \cancel{mL}} \right )\left(\dfrac{\textrm{1000}\; \cancel{mL}}{\textrm{1 L}} \right )=\textrm{0.0846 M}\]
Because the stoichiometry of the reaction is four NH 3 to one Cu 2 + , the amount of NH 3 required to react completely with the Cu 2 + is 4(0.0846) = 0.338 M. The concentration of ammonia after complete reaction is 1.00 M − 0.338 M = 0.66 M. These results are summarized in the first two lines of the following table. Because the equilibrium constant for the reaction is large (2.1 × 10 13 ), the equilibrium will lie far to the right. Thus we will assume that the formation of [Cu(NH 3 ) 4 ] 2+ in the first step is complete and allow some of it to dissociate into Cu 2 + and NH 3 until equilibrium has been reached. If we define x as the amount of Cu 2 + produced by the dissociation reaction, then the stoichiometry of the reaction tells us that the change in the concentration of [Cu(NH 3 ) 4 ] 2+ is − x , and the change in the concentration of ammonia is +4 x , as indicated in the table. The final concentrations of all species (in the bottom row of the table) are the sums of the concentrations after complete reaction and the changes in concentrations.
\[\ce{Cu^{2+} + 4NH3 <=> [Cu(NH3)4]^{2+}} \nonumber\]
| [Cu 2 + ] | [NH 3 ] | [[Cu(NH 3 ) 4 ] 2+ ] | |
|---|---|---|---|
| initial | 0.0846 | 1.00 | 0 |
| after complete reaction | 0 | 0.66 | 0.0846 |
| change | + x | +4 x | − x |
| final | x | 0.66 + 4 x | 0.0846 − x |
B Substituting the final concentrations into the expression for the formation constant ( Equation \(\ref{17.3.3}\) ) and assuming that x << 0.0846, which allows us to remove x from the sum and difference,
\[\begin{align*}K_\textrm f&=\dfrac{\left[[\mathrm{Cu(NH_3)_4}]^{2+}\right]}{[\mathrm{Cu^{2+}}][\mathrm{NH_3}]^4}=\dfrac{0.0846-x}{x(0.66+4x)^4}\approx\dfrac{0.0846}{x(0.66)^4}=2.1\times10^{13} \\x&=2.1\times10^{-14}\end{align*}\]
The value of x indicates that our assumption was justified. The equilibrium concentration of Cu 2 + (aq) in a 1.00 M ammonia solution is therefore 2.1 × 10 −14 M.
The ferrocyanide ion {[Fe(CN) 6 ] 4− } is very stable, with a K f of 1 × 10 35 . Calculate the concentration of cyanide ion in equilibrium with a 0.65 M solution of K 4 [Fe(CN) 6 ].
- Answer
-
2 × 10 −6 M
The Effect of the Formation of Complex Ions on Solubility
What happens to the solubility of a sparingly soluble salt if a ligand that forms a stable complex ion is added to the solution? One such example occurs in conventional black-and-white photography. Recall that black-and-white photographic film contains light-sensitive microcrystals of AgBr, or mixtures of AgBr and other silver halides. AgBr is a sparingly soluble salt, with a K sp of 5.35 × 10 −13 at 25°C. When the shutter of the camera opens, the light from the object being photographed strikes some of the crystals on the film and initiates a photochemical reaction that converts AgBr to black Ag metal. Well-formed, stable negative images appear in tones of gray, corresponding to the number of grains of AgBr converted, with the areas exposed to the most light being darkest. To fix the image and prevent more AgBr crystals from being converted to Ag metal during processing of the film, the unreacted AgBr on the film is removed using a complexation reaction to dissolve the sparingly soluble salt.
The reaction for the dissolution of silver bromide is as follows:
\[AgBr_{(s)} \rightleftharpoons Ag^+_{(aq)} + Br^{−}_{(aq)} \label{17.3.4a}\]
with
\[K_{sp} = 5.35 \times 10^{−13} \text{ at 25°C} \label{17.3.4b}\]
The equilibrium lies far to the left, and the equilibrium concentrations of Ag + and Br − ions are very low (7.31 × 10 −7 M). As a result, removing unreacted AgBr from even a single roll of film using pure water would require tens of thousands of liters of water and a great deal of time. Le Chatelier’s principle tells us, however, that we can drive the reaction to the right by removing one of the products, which will cause more AgBr to dissolve. Bromide ion is difficult to remove chemically, but silver ion forms a variety of stable two-coordinate complexes with neutral ligands, such as ammonia, or with anionic ligands, such as cyanide or thiosulfate (S 2 O 3 2− ). In photographic processing, excess AgBr is dissolved using a concentrated solution of sodium thiosulfate.
The reaction of Ag + with thiosulfate is as follows:
\[Ag^+_{(aq)} + 2S_2O^{2−}_{3(aq)} \rightleftharpoons [Ag(S_2O_3)_2]^{3−}_{(aq)} \label{17.3.5a}\]
with
\[K_f = 2.9 \times 10^{13} \label{17.3.5b}\]
The magnitude of the equilibrium constant indicates that almost all Ag + ions in solution will be immediately complexed by thiosulfate to form [Ag(S 2 O 3 ) 2 ] 3− . We can see the effect of thiosulfate on the solubility of AgBr by writing the appropriate reactions and adding them together:
\[\begin{align}\mathrm{AgBr(s)}\rightleftharpoons\mathrm{Ag^+(aq)}+\mathrm{Br^-(aq)}\hspace{3mm}K_{\textrm{sp}}&=5.35\times10^{-13}
\\ \mathrm{Ag^+(aq)}+\mathrm{2S_2O_3^{2-}(aq)}\rightleftharpoons\mathrm{[Ag(S_2O_3)_2]^{3-}(aq)}\hspace{3mm}K_\textrm f&=2.9\times10^{13}
\\ \mathrm{AgBr(s)}+\mathrm{2S_2O_3^{2-}(aq)}\rightleftharpoons\mathrm{[Ag(S_2O_3)_2]^{3-}(aq)}+\mathrm{Br^-(aq)}\hspace{3mm}K&=K_{\textrm{sp}}K_{\textrm f}=15\end{align} \label{17.3.6}\]
Comparing K with K sp shows that the formation of the complex ion increases the solubility of AgBr by approximately 3 × 10 13 . The dramatic increase in solubility combined with the low cost and the low toxicity explains why sodium thiosulfate is almost universally used for developing black-and-white film. If desired, the silver can be recovered from the thiosulfate solution using any of several methods and recycled.
If a complex ion has a large K f , the formation of a complex ion can dramatically increase the solubility of sparingly soluble salts.
Due to the common ion effect, we might expect a salt such as AgCl to be much less soluble in a concentrated solution of KCl than in water. Such an assumption would be incorrect, however, because it ignores the fact that silver ion tends to form a two-coordinate complex with chloride ions (AgCl 2 − ). Calculate the solubility of AgCl in each situation:
- in pure water
- in 1.0 M KCl solution, ignoring the formation of any complex ions
- the same solution as in part (b) except taking the formation of complex ions into account, assuming that AgCl 2 − is the only Ag + complex that forms in significant concentrations
At 25°C, K sp = 1.77 × 10 −10 for AgCl and K f = 1.1 × 10 5 for AgCl 2 − .
Given: K sp of AgCl, K f of AgCl 2 − , and KCl concentration
Asked for: solubility of AgCl in water and in KCl solution with and without the formation of complex ions
Strategy:
- Write the solubility product expression for AgCl and calculate the concentration of Ag + and Cl − in water.
- Calculate the concentration of Ag + in the KCl solution.
- Write balanced chemical equations for the dissolution of AgCl and for the formation of the AgCl 2 − complex. Add the two equations and calculate the equilibrium constant for the overall equilibrium.
- Write the equilibrium constant expression for the overall reaction. Solve for the concentration of the complex ion.
Solution
- A If we let x equal the solubility of AgCl, then at equilibrium [Ag + ] = [Cl − ] = x M. Substituting this value into the solubility product expression,
Thus the solubility of AgCl in pure water at 25°C is 1.33 × 10 −5 M.
- B If x equals the solubility of AgCl in the KCl solution, then at equilibrium [Ag + ] = x M and [Cl − ] = (1.0 + x ) M. Substituting these values into the solubility product expression and assuming that x << 1.0,
If the common ion effect were the only important factor, we would predict that AgCl is approximately five orders of magnitude less soluble in a 1.0 M KCl solution than in water.
- C To account for the effects of the formation of complex ions, we must first write the equilibrium equations for both the dissolution and the formation of complex ions. Adding the equations corresponding to K sp and K f gives us an equation that describes the dissolution of AgCl in a KCl solution. The equilibrium constant for the reaction is therefore the product of K sp and K f :
\(\begin{align}\mathrm{AgCl(s)}\rightleftharpoons\mathrm{Ag^+(aq)}+\mathrm{Cl^-(aq)}\hspace{3mm}K_{\textrm{sp}}&=1.77\times10^{-10}
\\ \mathrm{Ag^+(aq)}+\mathrm{2Cl^{-}}\rightleftharpoons\mathrm{[AgCl_2]^{-}}\hspace{3mm}K_\textrm f&=1.1\times10^{5}
\\ \mathrm{AgCl(s)}+\mathrm{Cl^{-}}\rightleftharpoons\mathrm{[AgCl_2]^{-}}\hspace{3mm}K&=K_{\textrm{sp}}K_{\textrm f}=1.9\times10^{-5}\end{align}\)
D If we let x equal the solubility of AgCl in the KCl solution, then at equilibrium [AgCl 2 − ] = x and [Cl − ] = 1.0 − x . Substituting these quantities into the equilibrium constant expression for the net reaction and assuming that x << 1.0,
That is, AgCl dissolves in 1.0 M KCl to produce a 1.9 × 10 −5 M solution of the AgCl 2 − complex ion. Thus we predict that AgCl has approximately the same solubility in a 1.0 M KCl solution as it does in pure water, which is 10 5 times greater than that predicted based on the common ion effect. (In fact, the measured solubility of AgCl in 1.0 M KCl is almost a factor of 10 greater than that in pure water, largely due to the formation of other chloride-containing complexes.)
Calculate the solubility of mercury(II) iodide (HgI 2 ) in each situation:
- pure water
- a 3.0 M solution of NaI, assuming [HgI 4 ] 2− is the only Hg-containing species present in significant amounts
K sp = 2.9 × 10 −29 for HgI 2 and K f = 6.8 × 10 29 for [HgI 4 ] 2− .
- Answer a
-
1.9 × 10 −10 M
- Answer a
-
1.4 M
Complexing agents, molecules or ions that increase the solubility of metal salts by forming soluble metal complexes, are common components of laundry detergents. Long-chain carboxylic acids, the major components of soaps, form insoluble salts with Ca 2 + and Mg 2 + , which are present in high concentrations in “hard” water. The precipitation of these salts produces a bathtub ring and gives a gray tinge to clothing. Adding a complexing agent such as pyrophosphate (O 3 POPO 3 4− , or P 2 O 7 4− ) or triphosphate (P 3 O 10 5− ) to detergents prevents the magnesium and calcium salts from precipitating because the equilibrium constant for complex-ion formation is large:
with
However, phosphates can cause environmental damage by promoting eutrophication, the growth of excessive amounts of algae in a body of water, which can eventually lead to large decreases in levels of dissolved oxygen that kill fish and other aquatic organisms. Consequently, many states in the United States have banned the use of phosphate-containing detergents, and France has banned their use beginning in 2007. “Phosphate-free” detergents contain different kinds of complexing agents, such as derivatives of acetic acid or other carboxylic acids. The development of phosphate substitutes is an area of intense research.
Commercial water softeners also use a complexing agent to treat hard water by passing the water over ion-exchange resins, which are complex sodium salts. When water flows over the resin, sodium ion is dissolved, and insoluble salts precipitate onto the resin surface. Water treated in this way has a saltier taste due to the presence of Na + , but it contains fewer dissolved minerals.
Figure \(\PageIndex{2}\): An MRI Image of the Heart, Arteries, and Veins. When a patient is injected with a paramagnetic metal cation in the form of a stable complex known as an MRI contrast agent, the magnetic properties of water in cells are altered. Because the different environments in different types of cells respond differently, a physician can obtain detailed images of soft tissues.
Another application of complexing agents is found in medicine. Unlike x-rays, magnetic resonance imaging (MRI) can give relatively good images of soft tissues such as internal organs. MRI is based on the magnetic properties of the 1 H nucleus of hydrogen atoms in water, which is a major component of soft tissues. Because the properties of water do not depend very much on whether it is inside a cell or in the blood, it is hard to get detailed images of these tissues that have good contrast. To solve this problem, scientists have developed a class of metal complexes known as “MRI contrast agents.” Injecting an MRI contrast agent into a patient selectively affects the magnetic properties of water in cells of normal tissues, in tumors, or in blood vessels and allows doctors to “see” each of these separately ( Figure \(\PageIndex{2}\) ). One of the most important metal ions for this application is Gd 3 + , which with seven unpaired electrons is highly paramagnetic. Because Gd 3 + (aq) is quite toxic, it must be administered as a very stable complex that does not dissociate in the body and can be excreted intact by the kidneys. The complexing agents used for gadolinium are ligands such as DTPA 5− (diethylene triamine pentaacetic acid), whose fully protonated form is shown here.
Summary
The formation of complex ions can substantially increase the solubility of sparingly soluble salts if the complex ion has a large K f . A complex ion is a species formed between a central metal ion and one or more surrounding ligands, molecules or ions that contain at least one lone pair of electrons. Small, highly charged metal ions have the greatest tendency to act as Lewis acids and form complex ions. The equilibrium constant for the formation of the complex ion is the formation constant ( K f ). The formation of a complex ion by adding a complexing agent increases the solubility of a compound.


7.5.1: HIV/AIDS
In chapter 3 we covered a brief history of HIV/AIDS, which was first discovered in the U.S. the early 1980’s, but had likely been a zoonotic disease transmitted to humans at least a century prior.  This can lead to dangerously low levels of these cells, which disarms the cell-mediated immune response. If the disease progresses to the advanced stage, it can cause acquired immunodeficiency syndrome (AIDS), in which so-called opportunistic infections and cancers take hold. HIV is a uniquely devastating infection in this way: it attacks the body’s defenses themselves, allowing other infections or cancers to easily overwhelm the person’s weakened immune system. HIV is transmitted via direct contact with bodily fluids, whether from sex, sharing needles, infected blood transfusion, or perinatally and via breastmilk (Contributors to Wikimedia projects, 2024). Although some people get flu-like symptoms 2-4 weeks after infection with HIV, it may take between 9-11 years for HIV to progress to AIDS (untreated). Within that time frame, a person who does not know their HIV status may transmit it to many more people.(CDC, 2022).
The most current estimated rates in the U.S. from 2021 are below.
- Incidence: 32,100 new cases.
- Prevalence: 1.2 million people currently living with HIV. The CDC estimates that 13% of HIV positive people are unaware of their status.
- Mortality: 19,986 deaths in people who were HIV positive, from any cause including COVID-19 (HIV.gov, 2023).
Significant medical advancements in testing, prevention and treatment have been made, including: antiretroviral therapy (ART) for those HIV positive, prophylactic medicines for pre-exposure (PrEP) and post-exposure (PEP) treatment. These medicines can decrease viral load to the point that not only is the virus undetectable, it is also not transmissible to a partner (HIV.gov, 2024). There is still a significant negative stigma associated with an HIV positive status, which deters many at-risk individuals from getting tested (CDC, 2022b). Self-tests that can be taken at home may help to reduce testing avoidance.
In 2021, President Joseph Biden’s administration began the National HIV/AIDS Strategy (NHAS) 2022-2025 which set goals for reducing the number of new infections by 75% by 2025, and 90% by 2030. This plan coordinates national and local efforts, increases public health messaging on HIV, releases funding for testing and PrEP and PEP medications, and focuses on reducing disparities in HIV and addressing the associated social determinants of health (SDOH) (The White House, 2021). According to the 2023 Interim Report, estimated new infections had dropped by 12% between 2017-2023, and the number of people receiving PrEP treatment had increased significantly. Still, the report recognizes that racial, ethnic, and gender disparities still need to be addressed. Also of note in the report is that over half of those living with diagnosed HIV in the U.S. are over the age of 50 (The White House, 2023).


4.3: Procedure, flowchart, and datasheets for separation and confirmation of group II cations
|
Chemical |
Hazard |
|---|---|
|
0.1M ammonium chloride (\(\ce{NH4Cl}\)) |
Toxic and irritant |
|
0.1M bismuth nitrate in 0.3M \(\ce{HNO3}\) |
Toxic, irritant, and oxidant |
|
0.1M cadmium chloride in 0.3M \(\ce{HNO3}\) |
Toxic and suspected carcinogen |
|
0.1M copper(II) nitrate in 0.3M \(\ce{HNO3}\) |
Toxic, irritant, and oxidant |
|
0.1M Tin(IV) chloride in 0.3M \(\ce{HNO3}\) |
Corrosive and irritant |
- *Hazards of 6M ammonia, 6M hydrochloric acid, 6M nitric acid, 3M potassium hydroxide, and 1M thioacetamide are listed in the common reagents table in chapter 2.
- Used heavy metal ion solutions or precipitates are disposed of in a labeled metal waste disposal container, do not drain these solutions down the drain or in the regular trash.
- Take 15 drops of the test solution if the group I cations are not present in the sample or take the supernatant of step 1 of group I analysis . Find its pH using a short-range pH paper. If the pH is 0.5 ±3 there is no need to adjust the pH. If pH is lower, increase it to 0.5 ±3 by adding drops of 0.5M ammonia solution, one drop at a time while stirring. If pH is higher, decrease to 0.5 ±3 by adding drops of 0.5M \(\ce{HCl}\), one drop at a time while stirring. Then add 10 drops of 1M thioacetamide stir and heat for 10 min in a water bath. Add 1 drop of 0.5M \(\ce{NH3}\),stir, centrifuge for 2 min, and add 5 drops of 1M thioacetamide, stir, and heat again for 2 min. Cool in room temperature water bath and add 1 more drop of 0.5M ammonia while stirring and centrifuge for 2 min. Decant and keep the supernatant for group III cations and keep the precipitate for separation and analysis of group II cations. The precipitate may be one or more of the following: \(\ce{SnS2}\) (yellow), \(\ce{CdS}\) (yellow-orange), \(\ce{CuS}\) (black-brown), \(\ce{Bi2S3}\) (black). Record the observation in the datasheet.
- Wash the precipitate from step 1 by re-suspending it in 1 mL (20 drops) of 0.1M \(\ce{NH4Cl}\), centrifuge for 2 min, decant, and discard the supernatant which is just the washing liquid. Re-suspend the precipitate in 1 mL (20 drops) of 3M \(\ce{KOH}\) + 1 drop of 1M thioacetamide, stir, loosely stopper the test tube, and heat in a water bath for 2 min. Centrifuge the hot mixture for 2 min and decant while it is hot. Keep the supernatant for analysis of \(\ce{Sn^{4+}}\) which exists as soluble \(\ce{Sn(OH)_{6}^{2-}}\) ion at this stage and keep the precipitate , if there is any, for analysis of the rest of the group II cations. Record the observation in the datasheet.
- Add 6M \(\ce{HCl}\) drop by drop to the supernatant from step 2 and keep testing with blue litmus paper until the mixture turns acidic. Then add 5 drops of 1M thioacetamide, stir, and heat in a water bath for 2 min. Yellow precipitate at this stage is \(\ce{SnS2}\) which confirms \(\ce{Sn^{4+}}\) is present in the test sample, no yellow precipitate means \(\ce{Sn^{4+}}\) was not present. Record the observation in the datasheet and discard the mixture in a waste container.
- Wash the precipitate from step 2 by re-suspending it in 10 drops of distilled water and then centrifuge for 2 min. Decant and discard the supernatant and wash the precipitate again by re-suspension in 10 drops of distilled water followed by centrifuge for 2 min, decant and discard the supernatant. Re-suspend the precipitate in 10 drops of distilled water + 2 drops of 6M \(\ce{HCl}\) and heat for 2 min. Centrifuge and decant while the mixture is still hot. If the supernatant appears turbid due to some precipitate left in it, use the cotton plug technique to aspire clean supernatant and filter out the residual precipitate. Keep the supernatant for analysis of \(\ce{Cd^{2+}}\) which may exist as dissolved \(\ce{[CdCl4]^{2-}}\) ion at this stage and keep the precipitate , if there is any, for analysis of remaining group II cations. Record the observation in the datasheet.
- Add 6M \(\ce{NH3}\) drop by drop to the clear supernatant from step 4 and keep testing with red litmus paper until the solution turns basic. Add 2 drops of 1M thioacetamide, stir, and heat for 2 min in a water bath. If a yellow precipitate forms at this stage it is \(\ce{CdS}\) that confirms \(\ce{Cd^{2+}}\) was present in the test sample, otherwise \(\ce{Cd^{2+}}\) was not present. Record the observation in the datasheet and discard the mixture in a metal waste container.
- Wash the precipitate from step 4, if there is any, by re-suspending it in 10 drops of distilled water, centrifuge for 2 min, decant and discard the supernatant. Re-suspend the precipitate in 10 drops of 6M HNO 3 and heat in a boiling water bath for 5 min. The precipitate, i.e., \(\ce{CuS}\) and/or \(\ce{Bi2S3}\) will dissolve in the liquid, and \(\ce{Cu^{2+}}\) and/or \(\ce{Bi^{3+}}\) hydrated ions and yellow sulfur particles may form. Remove the sulfur particles by centrifugation and decantation and discard them as there is no ion in them. Keep the supernatant for the analysis of \(\ce{Cu^{2+}}\) and \(\ce{Bi^{3+}}\) and record the observation in the datasheet.
- Add 6M NH 3 drop by drop to the supernatant from step 6 and keep testing with red litmus paper till the solution turns alkaline. Add 10 more drops of 6M \(\ce{NH3}\) solution after the solution turns alkaline to make it strongly alkaline. If the mixture becomes blue color at this stage, it is due to the blue \(\ce{[Cu(NH3)4]^{2+}}\) ion that confirms \(\ce{Cu^{2+}}\) is present in the test solution. If there is a white suspension in the mixture, keep it for testing \(\ce{Bi^{3+}}\). Record the observation in the datasheet.
- Centrifuge the mixture from step 7 for 2 min and decant and discard the supernatant. If there is any white precipitate left after decantation, it is most likely \(\ce{Bi(OH)3}\). Wash the precipitate by re-suspending it in 10 drops of 6M \(\ce{NH3}\), centrifuge for 2 min, and decant. If the white precipitate remains there after the washing, it is \(\ce{Bi(OH)3}\) that confirms \(\ce{Bi^{3+}}\) is present in the test solution, otherwise, \(\ce{Bi^{3+}}\) is absent. Discard the mixture in a metal waste container and record the observation in the datasheet.
- Step number refers to the corresponding step number in the procedure sub-section.
- In “the expected chemical reaction and expected observations column”, write an overall net ionic equation of the reaction that will happen if the ion being processed in the step was present, write the expected color change of the solution, the expected precipitate formed and its expected color, etc.
- In the “the actual observations and conclusion” column write the color change, the precipitate formed and its color, etc. that is actually observed as evidence, and state the specific ion as present or absent.
- In “the overall conclusion” row write one by one symbol of the ions being tested with a statement “present” or “absent” followed by evidence/s to support your conclusion.


7.S: Carboxylic Acid Derivatives (Summary)
Summary of Reactions by type of Reactions
Synthesis of Acid Chlorides
Synthesis of Anhydrides
Synthesis of Carboxylic Acids (Hydrolysis)
Synthesis of Esters (Alcoholysis)
Synthesis of Amides (Aminolysis)
Reduction Reactions
Organometallic Reactions
Grignard Reactions
Gilman Reaction
Concepts & Vocabulary
7.1 Chapter Objectives and Introduction to Carboxylic Acid Derivatives
- Carboxylic acid derivatives formed when the hydroxyl group of the carboxylic acid is replaced by a different group.
- Carboxylic acid derivatives are also known as acyl derivatives.
- Many types of carboxylic acid derivatives, the chapter focused on acid halides (acyl halides), anhydrides, esters, amides, thioesters, and acylphosphates.
- Cyclic esters are referred to as lactones and cyclic amides are referred to as lactams.
- Nucleophilic acyl substitution reactions convert the carboxylic acid to one of the derivatives.
7.2 Naming Carboxylic Acid Derivatives
- Acid halides are named following the IUPAC rules with the carboxylic acid ending with -oyl or -yl and the halide ending in an -ide.
- Anhydrides are named following the IUPAC rules with the carboxylic acid ending -acid being replaced by -anhydride.
- Esters are named following the IUPAC rules with the carboxylic acid ending with -oic acid being replaced by -ate and the alkoxy alkyl chain as a substituent.
- Thioesters are named following the IUPAC rules with the carboxylic acid ending with -oic acid being replaced by -thioate and the sulfide alkyl chain as a substituent.
- Primary amides are named following the IUPAC rules with the carboxylic acid ending with -oic acid being replaced by -amide.
- Secondary or tertiary amides are named as primary amides are, but in additon an upper case N is used to designate the alkyl groups attached to the nitrogen atom, which are names as substituents.
- Cyclic amides (lactams) use a Greek letter to identify the location of the nitrogen in relation the carbonyl group.
- Acyl phosphates are named following the IUPAC rules with the carboxylic acid ending with -oyl or -yl and -phosphate.
7.3 Nucleophilic Acyl Substitution Reactions
- Carboxylic acid derivatives contain an electronegative heteroatom (typically oxygen, nitrogen, sulfur, or phosphorus) bonded directly to the carbonyl carbon represented by the symbol Y.
- The acyl group is the remainder of the molecule, which includes the carbonyl and the attached alkyl group.
- The Y group acts as a leaving group during the nucleophilic acyl substitution reaction.
- Stability of the negative charge on the Y group can be guaged by the pK a of its corresponding acid (HY).
- Carboxylic acid derivatives undergo a reaction called nucleophilic acyl substitution.
- The electrophile is the carbon of the carbonyl, which undergoes an attack by a nucelophile followed by the elimination of the Y group in the carboxylic acid derivative.
- The Y group is substituted for the nucleophile.
- The reactivity of the carboxylic acid derivatives depends on the stability of the carbonyl and the effectiveness of the leaving group.
- Stabilization of the carbonyl reduces the electrophilic character of the carbonyl group.
- The ability of the leaving group to stabilize negative charge creates a more effective leaving group.
- More reactive carboxylic acid derivatives can be used to make less reactive carboxylic acid derivatives.
7.4 Nucleophilic Acyl Substitution Reactions of Carboxylic Acids
- The hydroxyl of a carboxylic acid is a poor leaving group, but activating the carbonyl and converting the hydroxyl to a better leaving group allow for reactions to occur.
- Carboxylic acids can be converted to acid chlorides using thionyl chloride (SOCl 2 ).
- Carboxylic acids can be converted into anhydrides by condensing two carboxylic acids together and the loss of water.
-
Carboxylic acids can be converted into esters in two ways.
- Using the carboxylate in an S N 2 mechanism.
-
The Fischer Esterification
- Acid catalyzed
- Pushing equilibrium in the forward direction using Le Chatelier's principle
-
Carboxylic acids can be converted into amides in two ways.
- Direct conversion by heating ammonium carboxylate salts
- Using a coupling agent like dicyclohexylcarbodiimide (DCC)
- Carboxylic acids can be reduced to primary alcohols using lithium aluminum hydride or borane tetrahydrofurane (THF).
- In biological chemistry, carboxylate anions are converted to an acyl phosphate, which requires phosphrylation using TAP as the phosphate donor or thioesters using coenzyme A.
7.5 Chemistry of Acid Halides
- Carboxylic acids react with thionyl chloride to form acid chlorides.
- Carboxylic acids react with phosphorus tribromide to form acid bromides.
- Acid chlorides are the most reactive carboxylic acid derivative, which allows them to easily convert to other acyl compounds.
- Acid chlorides undergo hydrolysis to form carboxylic acids.
- Acid chlorides react with carboxylic acid to form anhydrides through a nucleophilic acyl substitution.
- Acid chlorides react with alcohol nucleophiles to produce esters with pyridine being used to neutralize the HCl produced.
- Acid chlorides can be reduced to aldehydes using hindered reducing agents that have only one equivalent of hydride.
- Acid chlorides react with amines to form amides, usually an excess of amine is used to neutralize the HCl produced.
- Acid chlorides react with Grignard reagents to form tertiary alcohols.
- Acid chlorides react with Gillman reagents to produce ketones.
7.6 Chemistry of Acid Anhydrides
- Anhydrides are generally made by nucleophilic acyl substitution reactions using an acid chloride and a carboxylic acid or carboxylate anion.
- Anhydrides are not as reactive as acid chlorides, but still undergo many of the same reactions.
- Asymmetrical anhydrides not used to make amides or esters since multiple products can be formed.
- Anhydrides undergo hydrolysis to form carboxylic acids.
- Anhydrides react with alcohol nucleophiles to produce esters.
- Anhydrides can react with amines to form the corresponding amides.
7.7 Chemistry of Esters
- Esters are present in many biologically important molecules.
- Esters are often the sources of pleasant aromas of many fruits and perfumes.
- Esters are also present in commercial and synthetic applications.
-
Esters are prepared
- most often using nucleophilic acyl substitution using an acid chloride and an alcohol
- using nucleophilic acyl substitution using an anhydride and an alcohol
- using nucleophilic acyl substitution using a carboxylic acid and an alcohol
- deprotonating a carboxlylic acid for an SN 2 reaction
- Esters can be converted to a carboxylic acid through a reaction witt water and a catalytic amount of strong acid.
- Saponification is the reaction between an ester and water under basic conditions to produce a carboxylate anion.
- Esters can be inter-converted using a transesterfication reaction.
- Esters can be converted into amides using an ester and a large excess of amine.
- Esters can be reduced to primary alcohols using lithium aluminum hydride.
- Like acid chlorides, esters can be reduced to aldehydes using weak, bulky reducing agents.
- Esters can react with Grignard reagents to form tertiary alcohols.
7.8 Chemistry of Amides
- Amides make up the backbone of proteins when the amino group of one amino acid reacts with the carboxylate carbon of another amino acid and from an amide linkage (peptide bond).
- Amides are most commonly prepared through the reaction of an acid chloride and amine.
- Amides are relatively unreactive towards nucleophilic acyl substitutions due to the poor leaving group ability of its nitrogen containing Y group.
- Amides can be hydrolzyed to a carboxylic acid and ammonia or amine by heating the reaction under acidic or basic aqueous solutions.
- Hydrolysis of amines is the first step in metabolism of dietary proteins.
- Primary amines can be converted into a nitrile through a reaction with thionyl chloride.
- Amides are reduced to amines by treatment with lithium aluminum hydride.
7.9 Chemistry of Thioesters and Acyl Phosphates - Biological Carboxylic Acid Derivatives
- Acyl phosphates, acyl adenosine phosphophates, and thioesters are all activated forms of carboxylate groups in biochemical reactions.
- Carboxylate groups of fatty acids are converted to thioesters using coenzyme A
- Thioesters are a good substrate for a number of metabolic transformations.
- Thioesters can be hydrolyzed, resulting back to a carboxylate anion.
- Thioesters and acyl phosphates are the most reactive biologically relevant acyl groups, but not as reactive as an acid chloride or anhydride.
7.10 Polyamides and Polyesters - Step-Growth Polymers
- Step-growth is one of two broad classes of polymerization methods.
- Step-growth polymerizations are linked by a carbon-heteroatom bond formed in non-sequential steps.
- A step-growth polymerization starts with two complementary functional groups on different monomers reacting to form a dimer.
- Using a difunctional monomer, allows step-growth polymers to grow in two directions at once.
- Fibers are made from some form of polymer.
-
Nylon
- First successful fully synthetic polymer was nylon-6,6 in 1938 by the company DuPont, which is a polyamide.
- Nylons are widely used synthetic fibers, which are found in commercial products such as rope, sails, clothing, and more.
-
Esterfication
- Can also be used to form primary linkages in step-growth polymers.
- Polyester is typically produced when a dicarboxylic acid and a diol react together.
- The most important polyester is polyethylene terephthalate (PET), which is used to make bottles for soda.
- Polyesters are fibers often used in many fabrics.
-
Polycarbonates
- Monomer is a carbonate, which acts like a double ester and can undergo a type of double transesterification reaction with two alcohols.
- A carbonate is difunctional and can react with a diol to form polymers called polycarbonates.
- Used in engineering because they are strong materials, but easily molded.
- Polycarbonates are found in DVDs, compact discs, and Blu-ray discs.
7.11 Spectroscopy of Carboxylic Acid Derivatives
- IR of acid chlorides shows a strong carbonyl stretch around 1800 cm -1 .
- IR of anhydrides show two strong carbonyl stretch around 1750 and 1820 cm -1 .
- IR of esters shows a strong carbonyl stretch around 1740 cm -1 and a strong CO-O stretch around 1150 to 1250 cm -1 .
- IR of amides shows a strong carbonyl stretch around 1700 cm -1 , primary and secondary amides have two bands and tertiary amides have one band and a strong N-H stretch around 3170 to 3500 cm -1 in primary and secondary amides.
- 1 H NMR of acid halides do not have any distinctive peaks.
- 1 H NMR of anhydrides do not have any distinctive peaks, but symmetrical anhydrides will produce equivalent protons on either side.
- 1 H NMR of esters and thioesters have an alkyl group attached to the heteroatom. For esters, the alkoxide protons will show up in the 3.5-4.5 ppm region, while those attached to the sulfur in thioesters will show up in the 2.0-3.0 ppm region.
- 1 H NMR of amides have the possibility of alkyl groups or hydrogens attached. Resonances for protons attached to the carbon bonded to the nitrogen of the amide resonate between 2.0-3.0 ppm region. The NH protons of primary and secondary amides resonate in the 7.5-8.5 ppm regions, which will be broad.
- 13 C NMR of carboxylic acid derivatives show the carbonyl carbon at 160-180 ppm.
- 1 3 C NMR of esters also have the carbon attached to the alkoxide of the ester, which appears at 50-90 ppm.
- 13 C NMR of amides also have the carbon attached to the nitrogen of the amide, which appears at 20-65 ppm.
- 13 C NMR of thioesters also have the carbon attached to the sulfur, which appears at 20-45 ppm.
- Mass spectra of carboxylic acid derivatives show a base peak due to the acylium ion.
Skills to Master
- 1 Name carboxylic acid derivatives using IUPAC rules.
- 2 Draw the structure of carboxylic acid derivatives from the IUPAC name.
- 3 Compare the stability of different carboxylic acid derivatives to determine reactivity.
- 4 Determine the products for nucleophilic acyl substitution reactions.
- 5 Provide step-by-step mechanism for the Fischer esterification.
- 6 Show how to synthesize an ester from a carboxylic acid and alcohol.
- 7 Show mechanisms for the different carboxylic acid derivatives starting from an acid chloride.
- 8 Show how to synthesize the different carboxylic acid derivatives starting from an acid chloride.
- 9 Provide step-by-step mechanisms for the different carboxylic acid derivatives starting from an anhydride.
- 10 Show how to synthesize the different carboxylic acid derivatives starting from an anhydride.
- 11 Understand why the hydrolysis of an ester is not reversible under basic conditions and why the reverse does not produce an ester.
- 12 Be able to synthesize tertiary alcohols from esters.
- 13 Provide a step-by-step mechanism for the hydrolysis of an amide under acidic and basic conditions.
- 14 Provide the structure of different polymers using the bracketed notation and the monomers from the polymer.
- 15 Use IR, NMR, and MS to identify different carboxylic acid derivatives.
Summary of Reactions by Functional Groups
Carboxylic Acid Reactions
Amide Reactions
Acid Chloride Reactions
Acid Anhydride Reactions
Ester Reactions


4.10: Key Terms Defined
Commodification : The process of transforming a cultural activity into a saleable product.
Cultural ecology : Study of human adaptations to physical environments.
Cultural Landscape : Landscapes produced by the interaction of physical and human inputs.
Cultural reproduction : The process of inculcating cultural values into successive generations.
Cultural tourism : A variety of tourism concerned with exploring the culture of a place.
Culture : Learned human behavior associated with groups.
Culture Hearth : Historic location of cultural formation.
Fashion : The latest and most socially esteemed style of clothing or other products and behaviors.
Folk Culture : Culture practiced by a small, homogeneous, usually rural group. AKA Traditional culture.
Formal region : A region that has defined boundaries, often a governmental unit such as a country, province, or county.
Functional region : A region defined by a relationship, such as the market area of a product, a commuter zone or an employment market.
Globalization : The global movement of money, technology, and culture.
Heterogeneous : A population composed of dissimilar people.
Homogeneous : A population composed of similar people.
Material culture : The objects and materials related to a particular culture.
Perceptual region : Internally defined region that exists as the expression of a cultural type.
Placelessness : The state of having no place. In the modern context, a place exactly like any other place.
Popular Culture : Culture created for consumption by the mass of population.
Resistance : Actively pursuing a policy of obstruction of a particular process or undertaking.


1.1: The Need for Efficiency
In the next section, we look at the operations supported by the most commonly used data structures. Anyone with a bit of programming experience will see that these operations are not hard to implement correctly. We can store the data in an array or a linked list and each operation can be implemented by iterating over all the elements of the array or list and possibly adding or removing an element.
This kind of implementation is easy, but not very efficient. Does this really matter? Computers are becoming faster and faster. Maybe the obvious implementation is good enough. Let's do some rough calculations to find out.
Number of operations:
Imagine an application with a moderately-sized data set, say of one million (\(10^6\)), items. It is reasonable, in most applications, to assume that the application will want to look up each item at least once. This means we can expect to do at least one million (\(10^6\)) searches in this data. If each of these \(10^6\) searches inspects each of the \(10^6\) items, this gives a total of \(10^6\times 10^6=10^{12}\) (one thousand billion) inspections.
Processor speeds:
At the time of writing, even a very fast desktop computer can not do more than one billion (\(10^9\)) operations per second. 1 This means that this application will take at least \(10^{12}/10^9 = 1000\) seconds, or roughly 16 minutes and 40 seconds. Sixteen minutes is an eon in computer time, but a person might be willing to put up with it (if he or she were headed out for a coffee break).
Bigger data sets:
Now consider a company like Google, that indexes over 8.5 billion web pages. By our calculations, doing any kind of query over this data would take at least 8.5 seconds. We already know that this isn't the case; web searches complete in much less than 8.5 seconds, and they do much more complicated queries than just asking if a particular page is in their list of indexed pages. At the time of writing, Google receives approximately \(\textrm{4,500}\) queries per second, meaning that they would require at least \(\textrm{4,500}\times 8.5=\textrm{38,250}\) very fast servers just to keep up.
The solution:
These examples tell us that the obvious implementations of data structures do not scale well when the number of items, \(\mathtt{n}\), in the data structure and the number of operations, \(m\), performed on the data structure are both large. In these cases, the time (measured in, say, machine instructions) is roughly \(\mathtt{n}\times m\).
The solution, of course, is to carefully organize data within the data structure so that not every operation requires every data item to be inspected. Although it sounds impossible at first, we will see data structures where a search requires looking at only two items on average, independent of the number of items stored in the data structure. In our billion instruction per second computer it takes only \(0.000000002\) seconds to search in a data structure containing a billion items (or a trillion, or a quadrillion, or even a quintillion items).
We will also see implementations of data structures that keep the items in sorted order, where the number of items inspected during an operation grows very slowly as a function of the number of items in the data structure. For example, we can maintain a sorted set of one billion items while inspecting at most 60 items during any operation. In our billion instruction per second computer, these operations take \(0.00000006\) seconds each.
Footnotes
1 Computer speeds are at most a few gigahertz (billions of cycles per second), and each operation typically takes a few cycles.


1.1: Employee Benefits - An Overview
Why Do We Have Employee Benefits?
- Began as a form of social insurance during industrialization and the Great Depression
- Retirement plans were the earliest benefit - begun in the late 1800s
- Welfare practices described anything for the comfort of the employee and not required by law
- Today, employees view benefits as entitlements.. Why do you think this is?
Three Roles of Benefits Programs
- Protection programs - guards against loss of income caused by illness, disability, or unemployment
- Paid time-off - guarantees payment for holidays, vacation, or illness
- Accommodation and enhancement benefits - promotes opportunities for employees and their families
Legal and Regulatory Influences
-
Social Security Act of 1935
- Mandates a variety of programs such as federal retirement and unemployment insurance
- Learn more: Historical Background and Development of Social Security
-
Employee Retirement Income Security Act of 1974 (ERISA)
Sets minimum standard for most voluntarily established retirement and health plans in private industry
- Provides protection for individuals in these plans
- Learn more: ERISA website
Strategic Planning and Benefits
- Todays's market is competitive!!
- Companies need to offer benefits that employees want or need
-
According to the
US Chamber of Commerce: The top 3 reasons employees are changing jobs
- Work-life balance
- Flexible scheduling
- Positive culture
Informations Sources to Consider in Strategic Planning
-
External Market Environment
- Economic conditions and forecasts
-
Employer costs for compensations and benefits
- benefits average 30% of total compensation costs
- Government regulations of employee benefits
- Changing demographics of the labor force
-
Internal Company Environment
- Workforce demographics
- Collective bargaining agreements


2.1.4: Religions of the World
There are numerous religions and spiritual beliefs throughout the world. Religious beliefs influence people’s values, morals, behaviors, and traditions. Religion may be important to some people and unimportant to others. Some people consider themselves to be spiritual, but may not practice or be affiliated with a particular religion. Other people do not believe in any religion or God. Only some of the more common religions are discussed here. Remember, even if a patient practices one of the religions discussed, they may or may not adhere to the beliefs or practices described. Always ask a patient what their individual beliefs and practices are.
Agnostics and Atheists
Agnostics are people who do not know if there is a God. They do not necessarily think that God does not exist, but they feel God’s existence cannot be proven.Atheism, on the other hand is the belief that there are no gods. According to American Atheists, Atheism is not a belief system or religion. They further state that Atheism is not a disbelief in God or a denial of gods, but is a lack of belief in gods and supernatural systems. For many atheists, their beliefs are as strong as those who believe in a particular religion or specific God/gods. Home Health Aides/Personal Care Aides must take care to never judge a person based on their beliefs.
Buddhism
Buddhism is based on the teachings of Siddhartha Gautama, known as Buddha (PBS, 1999). While this religion started in Asia, it is practiced worldwide. According to PBS, Buddhists believe in The Four Noble Truths: that suffering exists, that there is a cause to the suffering, there is an end to the suffering, and there is a way to bring the suffering to an end. Desiring material belongings, immortality, and pleasure leads to suffering. To end suffering, one must achieve Nirvana, which is a state of spiritual heightening in which there are no desires or suffering. To achieve this, Buddhists believe they must follow the Noble Eightfold Path which includes: Right Understanding, Right Thought, Right Speech, Right Action, Right Livelihood, Right Effort, Right Mindfulness, and Right Concentration (PBS). Practicing meditation, good moral conduct, and achieving insight are the ways to follow this path. Death is viewed as the ending of the physical body, and the spirit will live on in a new form, or rebirth occurs. After the death of a person who practices Buddhism, the body should be left alone for 3-8 hours untouched, as the Buddhists believe that the spirit lingers for some time (Carteret, 2010e).
Christianity
Christianity is the world’s largest religion and is based on the teachings of Jesus Christ, who lived 2,000 years ago (BBC, 2011a). Christians believe that Jesus was the Son of God who was sent to Earth to save humans from the consequences of their sins. Important holy days include Easter and Christmas. Christians believe that Jesus gave his life on the cross (Crucifixion), which occurs on Good Friday, and that he rose on the third day (Resurrection), which is Easter day. Christmas marks the day of Jesus’ birth. The Christian holy book is called The Holy Bible, which consists of the Old and the New Testaments. Most Christians worship in a church and communicate with God through prayer. Christians believe in baptism, which is the process in which a formal commitment is made to God (BBC, 2009e). There are many denominations of Christianity, each with a different set of practices. Some of these groups include Methodist, Mormon, Presbyterian, Baptist, Episcopalian, Seventh-day Adventists, Lutheran, and Roman Catholic. Religious leaders may be called priests, pastors, preachers, or deacons, depending on the denomination. Some Christians may practice dietary restrictions, such as not eating meat or fasting during the Lenten season, which is approximately 40 days prior to Easter, starting on Ash Wednesday. Mormon diet prohibits tea, cola, and coffee. Some Christians may have sacred objects in their homes or worn as jewelry, such as images of saints and holy crosses.
Hinduism
Hinduism is largely practiced in India. It is the world’s oldest religion, and there is no founder. There are four sects, or divisions, of Hinduism: Shaivism, Shaktism, Vaishnavism, and Smartism (Kauai’s Hindu Monastery, 2015.). Each has some different beliefs and practices, but all believe in one Supreme Being, who is the creator of all things. According to Kauai’s Hindu Monastery, Hindus follow the four Vedas, which are ancient scriptures. Hindus also believe in reincarnation, which is the belief that the soul reincarnates, or returns after the physical body has died into a new body. This process is meant to help karma become resolved. Karma is the belief that consequences are caused by actions, and that people create their own destinies by their thoughts and actions. Hindus believe that all life is sacred. Many may be vegetarians. After the death of a person who practices Hinduism, the body must be bathed, massaged with oil, dressed, and cremated prior to the next sunrise (Carteret, 2010e).
Islam
Islam, the second largest religion in the world, began in Mecca, Arabia over 1400 years ago (BBC, 2009b). People who practice Islam are called Muslims. Prophets of this religion include Adam, Moses, Abraham, David, Jesus, and the final prophet to whom credit for the start of Islam is given; Muhammad (BBC, 2011d). Muslims believe in one God, called Allah. Many Muslims pray five times per day, facing Mecca, the holy city. Mosques are the places of worship for Muslims.  Prayer is done sitting on the floor and facing the direction of Mecca. Mostly men attend prayer services in mosques, and when women do, they pray in a section separate from the men. The Qur’an, which is the sacred word of God as revealed to the prophet Muhammad over 23 years is the holy book of the Islamic faith (BBC, 2011c).
Muslims believe in predestination, that Allah has knowledge of all that will happen (BBC, 2011d). However, Muslims do believe in free will, that they can make their own choices in life. Muslims also believe in the Day of Judgment, in which every human will be judged to determine if they will go to heaven or hell (BBC, 2011d). According to BBC (2009i), the most important practices of Muslims are the Five Pillars. These are obligations that every Muslim must meet within their life in order to get to heaven. They include being sincere within one’s Muslim faith, praying five times per day, paying charity to the poor, fasting during Ramadan, and making a pilgrimage (a visit of faith) to Mecca once in their lifetimes (BBC, 2009i). Ramadan, a holy period, is the ninth month in the Islamic calendar (BBC, 2011b). According to BBC (2011b), during this month, adults must give up food and drink, smoking, and sexual activity during daylight hours. The month of Ramadan ends with the festival known as Eid al-Fitr, in which Muhammad is thanked for giving Muslims strength to practice self-control over the last month (BBC, 2011e). Celebrations with family and services are attended at mosques in which Muslims wear new or their best clothing (BBC, 2011e).
There are special rules regarding diet and dress that many Muslims follow. Most Muslims do not consume alcohol or pork. Women dress modestly with long skirts and shirts within the Muslim faith and may wear a hijab, a veil covering the head and chest (BBC, 2009h). Some Muslims believe all parts of a female should be covered except the eyes, while others believe all parts should be covered except the face and hands. The name for the garment which covers all of a woman except her eyes is called a burqa. It may be forbidden for members of the opposite sex to touch. It is important for healthcare workers to be aware of these dietary restrictions and any special way of dressing their patient may practice.
Judaism
Judaism originated in the Middle East over 3500 years ago and was founded by Moses, although Jews trace their history back to Abraham (BBC, 2009a). Abraham was a leader appointed by God and was the first to teach that there was only one God. The Torah, written in Hebrew, which is the oldest Jewish language, is the religious book of the Jews and consists of the 5 books of Moses (BBC, 2009e). According to BBC (2009e), Jewish people believe that God dictated the words found within the Torah to Moses on Mount Sinai, after the Jews were exiled from their slavery in Egypt. Additionally, the Torah is read in completion every year during synagogue or temple, which is where Jewish people attend services (BBC, 2009a). The Torah contains 613 commandments by which Jews live their life (BBC, 2009e). A rabbi usually conducts services within synagogues and temples, and serves as a religious leader for Jewish people.
Judaism is divided into Reform, Conservative, and Orthodox movements, all with some differences in practice and belief. In Orthodox Judaism, men and women sit separately in synagogues and services are conducted in ancient Hebrew. Some Jewish men wear a yarmulke or kippah, a small cap to cover their head. Health care providers should take care to respect religious dress and special traditions their patients may follow during prayers and religious holy days.
The holy day is called the Sabbath, which begins at nightfall on Friday and lasts until nightfall on Saturday (BBC, 2009d). The Sabbath is a time of rest and worship, in which candles may be lit, the Sabbath wine and meals with prayer shared. Hanukkah is the Jewish Festival of Lights, lasting 8 days, in which a menorah with 8 candles is lit, one each day. This holiday celebrates the Jewish people’s struggle for religious freedom (BBC, 2009c). Rosh Hashanah is another holy day which lasts two days, in which the creation of the world is celebrated on this Jewish New Year (BBC, 2011f). According to BBC (2011f), this day is also known as Judgment Day, in which God reviews one’s good versus bad days throughout the year. On Yom Kippur, or Day of Atonement, which is the most sacred day of the year for Jewish people, marks the day when God’s judgment comes to an end (BBC, 2011g). The Book of Life, in which one’s year has been reviewed closes. This determines how the course of the next year will go for each person (BBC, 2011g). During holy days and the Sabbath, special foods are shared and fasting may occur, such as in the 25 hours prior to Yom Kippur (BBC, 2009c; 2009d; 2011g). Healthcare providers should take special care to honor these dietary and fasting practices in order to best uphold their patient’s religious beliefs.