Most chemical reactions used for the production of heat are combustion reactions. The energy released when 1 g of a material is combusted is often called its fuel value. Because fuel values represent the heat released in a combustion, fuel values are positive numbers. The fuel value of any food or fuel can be measured by calorimetry.
Most of the energy our bodies need comes from carbohydrates and fats. Carbohydrates are decomposed in the intestines into glucose, C6H12O6. Glucose is soluble in blood, and in the human body it is known as blood sugar. It is transported by the blood to cells, where it reacts with O2 in a series of steps, eventually producing CO2(g), H2O(l), and energy:
The breakdown of carbohydrates is rapid, so their energy is quickly supplied to the body. However, the body stores only a very small amount of carbohydrates. The average fuel value of carbohydrates is 17 kJ/g (4 kcal/g).
Like carbohydrates, fats produce CO2 and H2O in their metabolism and in their combustion in a bomb calorimeter. The reaction of tristearin, C57H110O6, a typical fat, is as follows:
The body puts the chemical energy from foods to different uses: to maintain body temperature, to drive muscles, and to construct and repair tissues. Any excess energy is stored as fats. Fats are well suited to serve as the body's energy reserve for at least two reasons: (1) They are insoluble in water, which permits their storage in the body; and (2) they produce more energy per gram than either proteins or carbohydrates, which makes them efficient energy sources on a mass basis. The average fuel value of fats is 38 kJ/g (9 kcal/g).
In the case of proteins, metabolism in the body produces less energy than does combustion in a calorimeter because the products are different. Proteins contain nitrogen, which is released in the bomb calorimeter as N2. In the body this nitrogen ends up mainly as urea, (NH2)2CO. Proteins are used by the body mainly as building materials for organ walls, skin, hair, muscle, and so forth. On average, the metabolism of proteins produces 17 kJ/g(4 kcal/g), the same as for carbohydrates.
The fuel values for a variety of common foods are shown in Table 5.4. Labels on packaged foods show the amounts of carbohydrate, fat, and protein contained in an average serving, as well as the energy value of the serving (Figure 5.21). The amount of energy our bodies require varies considerably depending on such factors as weight, age, and muscular activity. About 100 kJ per kilogram of body weight per day is required to keep the body functioning at a minimal level. An average 70-kg (154-lb.) person expends about 800 kJ/hr when doing light work, such as slow walking or light gardening. Strenuous activity, such as running, often requires 2000 kJ/hr or more. When the energy content of our food exceeds the energy we expend, our body stores the surplus as fat.
(a) A 28-g (1-oz) serving of a popular breakfast cereal served with 120 mL of skim milk provides 8 g protein, 26 g carbohydrates, and 2 g fat. Using the average fuel values of these kinds of substances, estimate the amount of food energy in this serving. (b) A person of average weight uses about 100 Cal/mi when running or jogging. How many servings of this cereal provide the fuel value requirements for running 3 mi?
SOLUTION (a) We are given the mass of protein, carbohydrates, and fat in the serving of cereal. We can use the data in Table 5.4 to convert these masses to their fuel values, which we can sum to get the total food energy:
This corresponds to 160 kcal:
Recall that the dietary Calorie is equivalent to 1 kcal. Thus, the serving provides 160 Cal.
(b) The problem statement provides a conversion factor between Calories and miles. The answer to part (a) provides us with a conversion factor between servings and Calories. We can use these factors in straightforward dimensional analysis to determine the number of servings needed, rounded to the nearest whole number:
(a) Dry red beans contain 62 percent carbohydrate, 22 percent protein, and 1.5 percent fat. Estimate the fuel value of these beans. (b) Very light activity like reading or watching television uses about 7 kJ/min. How many minutes of such activity can be sustained by the energy provided by a can of chicken noodle soup containing 13 g protein, 15 g carbohydrate, and 5 g fat? Answers: (a) 15 kJ/g; (b) 95 min.
The elemental compositions and fuel values of several common fuels are compared in Table 5.5. During the complete combustion of fuels, carbon is converted to CO2 and hydrogen is converted to H2O, both of which have large negative enthalpies of formation. Consequently, the greater the percentage of carbon and hydrogen in a fuel, the higher its fuel value. Compare, for example, the compositions and fuel values of bituminous coal and wood. The coal has a higher fuel value because of its greater carbon content.
In 1997 the United States consumed 9.89 1016 kJ of energy; that is, nearly 100 quadrillion kJ. This value corresponds to an average daily energy consumption per person of 1.0 106 kJ, which is roughly 100 times greater than the per capita food-energy needs. We are a very energy-intensive society. Figure 5.22 illustrates the sources of this energy consumption.
Figure 5.22 Sources of energy consumed in the United States. In 1997 the United States consumed a total of 9.9 1016 kJ of energy.
Coal, petroleum, and natural gas, which are our major sources of energy, are known as fossil fuels. All have formed over millions of years from the decomposition of plants and animals and are being depleted far more rapidly than they are being formed. Natural gas consists of gaseous hydrocarbons, compounds of hydrogen and carbon. It contains primarily methane, CH4, with small amounts of ethane, C2H6, propane, C3H8, and butane, C4H10. We determined the fuel value of propane in Sample Exercise 5.9. Petroleum is a liquid composed of hundreds of compounds. Most of these compounds are hydrocarbons, with the remainder being chiefly organic compounds containing sulfur, nitrogen, or oxygen. Coal, which is solid, contains hydrocarbons of high molecular weight as well as compounds containing sulfur, oxygen, or nitrogen. The sulfur in petroleum and coal is a major source of air pollution, as we will discuss in Chapter 18.
Coal is the most abundant fossil fuel; it constitutes 80 percent of the fossil fuel reserves of the United States and 90 percent of those of the world. However, the use of coal presents a number of problems. Coal is a complex mixture of substances, and it contains components that cause air pollution. Because it is a solid, recovery from its underground deposits is expensive and often dangerous. Furthermore, coal deposits are not always close to locations of high energy use, so there are often substantial shipping costs.
One promising way to utilize our coal reserves is to use them to produce a mixture of gaseous hydrocarbons called syngas (for "synthesis gas"). In this process, called coal gasification, the coal typically is pulverized and treated with superheated steam. Sulfur-containing compounds, water, and carbon dioxide can be removed from the products, leading to a mixture of CH4, H2, and CO gases, all of which have high fuel values:
Because it is gaseous, syngas can be easily transported in pipelines. Additionally, because much of the sulfur in coal is removed during the gasification process, combustion of syngas causes less air pollution than does the burning of coal. For these reasons, the economical conversion of coal and petroleum into "cleaner" fuels such as syngas and hydrogen (see the "Chemistry at Work" box that follows) is a very active area of current research in chemistry and engineering.
Nuclear energy is energy that is released in the splitting or fusion of the nuclei of atoms. Nuclear power is currently used to produce about 22 percent of the electric power in the United States, and comprises about 7 percent of the total U.S. energy production (Figure 5.22). Nuclear energy is, in principle, free of the polluting emissions that are a major problem in the generation of energy from fossil fuels. However, nuclear power plants produce radioactive waste products and their use has therefore been fraught with controversy. We will discuss issues related to the production of nuclear energy in Chapter 21.
Fossil fuel and nuclear energy are nonrenewable sources of energy; the fuels used are limited resources that we are consuming at a much greater rate than they are regenerated. Eventually these fuels will be expended, although estimates vary greatly as to when this will occur. Because nonrenewable sources of energy will eventually be used up, there is a great deal of research into sources of renewable energy, energy sources that are essentially inexhaustible. Renewable energy sources include solar energy from the Sun, wind energy harnessed by windmills, geothermal energy from the heat stored in the mass of Earth, hydroelectric energy from flowing rivers, and biomass energy from crops such as trees and corn and from biological waste matter. Currently, renewable sources provide about 7.6 percent of the U.S. annual energy consumption, with hydroelectric (4.2 percent) and biomass (2.9 percent) sources as the only significant contributors.
Providing our future energy needs will most certainly depend on developing the technology to harness solar energy with greater efficiency. Solar energy is the world's largest energy source. On a clear day about 1 kJ of solar energy reaches each square meter of Earth's surface every second. The solar energy that falls on only 0.1 percent of U.S. land area is equivalent to all the energy that this nation currently uses. Harnessing this energy is difficult because it is dilute (it is distributed over a wide area) and it fluctuates with time and weather conditions. The effective use of solar energy will depend on the development of some means of storing the collected energy for use at a later time. Any practical means for doing this will almost certainly involve use of an endothermic chemical process that can be later reversed to release heat. One such reaction is the following:
This reaction proceeds in the forward direction at high temperatures, which can be obtained in a solar furnace. The CO and H2 formed in the reaction could then be stored and allowed to react later, with the heat released being put to useful work.
Solar energy can be converted directly into electricity by use of photovoltaic devices, sometimes called solar cells. The efficiencies of solar energy conversion by use of such devices have increased dramatically during the past few years as a result of intensive research efforts. Photovoltaics are vital to the generation of power for satellites. However, for large-scale generation of useful energy at Earth's surface, they are not yet practical because of high unit cost. Even if the costs are reduced, some means must be found to store the energy produced by the solar cells, because the sun shines only intermittently and during only part of the day at any place. Once again, the solution to this problem will almost certainly be to use the energy to cause a chemical reaction to take place in the direction in which it is endothermic.
When 75.0 mL of 0.100 M Na2SO4(aq) and 25.0 mL of 0.200 M AgNO3(aq) are mixed together in a beaker, a white precipitate is formed. Assume that both solutions are initially at 25°C, and the final volume of the solution is 100.0 mL. (a) What is the net ionic equation for the reaction that occurs? (b) What is the limiting reactant in this reaction? (c) What is the theoretical yield in grams for the precipitate formed? (d) Given that for Ag2SO4(s) is -715.2 kJ/mol, calculate the quantity of heat absorbed or released during this reaction. (e) Will the temperature of the solution increase or decrease as the reaction occurs? Explain.
SOLUTION (a) Both Na2SO4 and AgNO3 are strong electrolytes. Because salts of Na+ and of NO3– ions are always soluble, the precipitate must be the salt formed by the reaction of Ag+ and SO42–, which, based on the charges of the ions, must be Ag2SO4. The net ionic equation is therefore:
(b) To determine the limiting reagent, we first calculate the number of moles of Ag+ and SO42– in the solutions that are mixed. Recall that the number of moles equals the volume of the solution times its molarity. Because AgNO3 and Na2SO4 are strong electrolytes, the concentrations of Ag+ and SO42– are equal to the molarities of the starting solutions:
The net ionic equation tells us that we will consume twice as many moles of Ag+ as we do SO42–. Thus, it takes only 2.50 10–3 mol of SO42– to react completely with 5.00 10–3 mol of Ag+. We conclude that Ag+ is the limiting reactant. (c) From the net ionic equation, we see that 2 mol Ag+ 1 mol Ag2SO4. We saw in part (b) that 5.00 10–3 mol of Ag+ are consumed in this reaction, so 2.50 10–3 mol of Ag2SO4 must be produced. We convert the moles to grams by using the formula weight of Ag2SO4:
This value is the theoretical yield of Ag2SO4 for this reaction. (d) We will use enthalpies of formation to calculate the enthalpy change for the net ionic reaction (Equation 5.29). The value of for Ag2SO4(s) is given in the problem, and those for Ag+(aq) and SO42–(aq) are given in Appendix C of the textbook.
Remember that in thermochemical reactions we assume that the coefficients correspond to moles of the reactants and products. Because the coefficient on Ag2SO4 in Equation 5.29 is one, our calculated value corresponds to H = -17.7 kJ per mole of Ag2SO4 produced. We saw in part (c) that we are producing 2.50 10–3 moles of Ag2SO4. Thus, the value of H for the quantities used in this particular reaction is H = (2.50 10–3 mol Ag2SO4)(-17.7 kJ/mol Ag2SO4) = -4.43 10–2 kJ. (e) The reaction is exothermic (H < 0), so heat is released into the solution by the reaction. We would therefore expect the temperature of the solution to rise. However, the amount of heat released is very small, only 0.044 kJ for 100 mL of solution. If we assume that the specific heat of the solution is the same as that of water (4.18 J/g-K), we can estimate that the temperature would rise by less than 0.001°C. We would not detect such a small change in temperature unless we had an extremely sensitive thermometer.