Chapter 5

An aluminum can of a soft drink is placed in a freezer. Later, you find that the can is split open and its contents have frozen. Work was done on the can in splitting it open. Where did the energy for this work come from?

Consider a system consisting of the following apparatus, in which gas is confined in one flask and there is a vacuum in the other flask. The flasks are separated by a valve. Assume that the flasks are perfectly insulated and will not allow the flow of heat into or out of the flasks to the surroundings. When the valve is opened, gas flows from the filled flask to the evacuated one. (a) Is work performed during the expansion of the gas? (b) Why or why not? (c) Can you determine the value of \(\Delta E\) for the process?

The corrosion (rusting) of iron in oxygen-free water includes the formation of iron(II) hydroxide from iron by the follow. ing reaction: $$ \mathrm{Fe}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Fe}(\mathrm{OH})_{2}(s)+\mathrm{H}_{2}(g) $$ If 1 mol of iron reacts at \(298 \mathrm{~K}\) under \(101.3 \mathrm{kPa}\) pressure, the reaction performs \(2.48 \mathrm{~J}\) of \(P-V\) work, pushing back the atmosphere as the gaseous \(\mathrm{H}_{2}\) forms. At the same time, \(11.73 \mathrm{~kJ}\) of heat is released to the environment. What are the values of \(\Delta H\) and of \(\Delta E\) for this reaction?

Both oxyhydrogen torches and fuel cells use the following reaction to produce energy: $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) $$ Both processes occur at constant pressure. In both cases the change in state of the system is the same: the reactant is oxyhydrogen ("Knallgas") and the product is water. Yet, with an oxyhydrogen torch, the heat evolved is large and with a fuel cell it is small. If heat at constant pressure is considered to be a state function, why does it depend on path?

(a) When a 0.47-g sample of benzoic acid is combusted in a bomb calorimeter (Figure 5.19 ), the temperature rises by \(3.284^{\circ} \mathrm{C}\). When a \(0.53-\mathrm{g}\) sample of caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2}\), is burned, the temperature rises by \(3.05^{\circ} \mathrm{C}\). Using the value of \(26.38 \mathrm{~kJ} / \mathrm{g}\) for the heat of combustion of benzoic acid, calculate the heat of combustion per mole of caffeine at constant volume. (b) Assuming that there is an uncertainty of \(0.002^{\circ} \mathrm{C}\) in each temperature reading and that the masses of samples are measured to \(0.001 \mathrm{~g}\), what is the estimated uncertainty in the value calculated for the heat of combustion per mole of caffeine?

We can use Hess's law to calculate enthalpy changes that cannot be measured. One such reaction is the conversion of methane to ethane: $$ 2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2 (g) $$ Calculate the \(\Delta H^{\circ}\) for this reaction using the following thermochemical data: $$ \begin{aligned} \mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) & \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(I) & & \Delta H^{0}=-890.3 \mathrm{~kJ} \\ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) & \Delta H^{0} &=-571.6 \mathrm{~kJ} \\ 2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) & \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(I) & \Delta H^{0}=&-3120.8 \mathrm{~kJ} \end{aligned} $$

The hydrocarbons cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}(I), \Delta H_{i}^{\circ}=-156\right.\) \(\mathrm{kJ} / \mathrm{mol}\) ) and 1 -hexene \(\left.\left(\mathrm{C}_{6} \mathrm{H}_{12}(I), \Delta H_{f}^{\circ}=-74 \mathrm{k}\right] / \mathrm{mol}\right)\) have the same empirical formula. (a) Calculate the standard enthalpy change for the transformation of cyclohexane to 1-hexene. (b) Which has greater enthalpy, cyclohexane or 1 -hexene? (c) Without doing a further calculation and knowing the answer to (b), do you expect cyclohexane of 1-hexene to have the larger combustion enthalpy?

Three hydrocarbons that contain four carbons are listed here, along with their standard enthalpies of formation: \begin{tabular}{llc} \hline Hydrocarbon & Formula & \(\Delta H_{i}^{2}(\mathrm{k} \mathrm{U} / \mathrm{mol})\) \\ \hline Butane & \(\mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{~s})\) & -125 \\ 1-Butene & \(\mathrm{C}_{4} \mathrm{H}_{8}(g)\) & -1 \\ 1-Butyne & \(\mathrm{C}_{4} \mathrm{H}_{6}(\boldsymbol{g})\) & 165 \\ \hline \end{tabular} (a) For each of these substances, calculate the molar enthalpy of combustion to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) (b) Calculate the fuel value, in \(\mathrm{kJ} / \mathrm{g}\), for each of these compounds. (c) For each hydrocarbon, determine the percentage of hydrogen by mass. (d) By comparing your answers for parts (b) and (c), propose a relationship between hydrogen content and fuel value in hydrocarbons.

A \(100-\mathrm{kg}\) man decides to add to his exercise routine by walking up six flights of stairs \((30 \mathrm{~m}) 10\) times per day. He figures that the work required to increase his potential energy in this way will permit him to eat an extra order of French fries, at 245 Cal, without adding to his weight. Is he correct in this assumption?

Sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) is produced by plants as follows: \(12 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(I) \longrightarrow \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+12 \mathrm{O}_{2}(g)\) $$ \Delta H=5645 \mathrm{~kJ} $$ About \(4.8 \mathrm{~g}\) of sucrose is produced per day per square meter of the earth's surface. The energy for this endothermic reaction is supplied by the sunlight. About \(0.1 \%\) of the sunlight that reaches the earth is used to produce sucrose. Calculate the total energy the sun supplies for each square meter of surface area. Give your answer in kilowatts per square meter \(\left(\mathrm{kW} / \mathrm{m}^{2}\right.\) where \(\left.1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s}\right)\)

It is estimated that the net amount of carbon dioxide fixed by photosynthesis on the landmass of Earth is \(5.5 \times 10^{16} \mathrm{~g} / \mathrm{yr}\) of \(\mathrm{CO}_{2}\). Assume that all this carbon is converted into glucose. (a) Calculate the energy stored by photosynthesis on land per year, in \(\mathrm{kJ} .\) (b) Calculate the average rate of conversion of solar energy into plant energy in megawatts, MW \((1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s})\). A large nuclear power plant produces about \(10^{3} \mathrm{MW}\). The energy of how many such nuclear power plants is equivalent to the solar energy conversion?

At \(25^{\circ} \mathrm{C}\) (approximately room temperature) the \(\mathrm{rms}\) velocity of an Ar atom in air is \(1553 \mathrm{~km} / \mathrm{h}\). (a) What is the rms speed in \(\mathrm{m} / \mathrm{s}\) ? (b) What is the kinetic energy (in J) of an Ar atom moving at this speed? (c) What is the total kinetic energy of \(1 \mathrm{~mol}\) of Ar atoms moving at this speed?

Suppose an Olympic diver who weighs \(52.0 \mathrm{~kg}\) executes a straight dive from a \(10-\mathrm{m}\) platform. At the apex of the dive, the diver is \(10.8 \mathrm{~m}\) above the surface of the water. (a) What is the potential energy of the diver at the apex of the dive, relative to the surface of the water? (b) Assuming that all the potential energy of the diver is converted into kinetic energy at the surface of the water, at what speed, in \(\mathrm{m} / \mathrm{s}\), will the diver enter the water? (c) Does the diver do work on entering the water? Explain.

Consider two solutions, the first being \(50.0 \mathrm{~mL}\) of \(1.00 \mathrm{MCuSO}_{4}\) and the second \(50.0 \mathrm{~mL}\) of \(2.00 \mathrm{M} \mathrm{KOH}\). When the two solutions are mixed in a constant-pressure calorimeter, a precipitate forms and the temperature of the mixture rises from 21.5 to \(27.7^{\circ} \mathrm{C}\). (a) Before mixing, how many grams of Cu are present in the solution of \(\mathrm{CuSO}_{4} ?\) (b) Predict the identity of the precipitate in the reaction. (c) Write complete and net ionic equations for the reaction that occurs when the two solutions are mixed. \((\mathbf{d})\) From the calorimetric data, calculate \(\Delta H\) for the reaction that occurs on mixing. Assume that the calorimeter absorbs only a negligible quantity of heat, that the total volume of the solution is \(100.0 \mathrm{~mL},\) and that the specific heat and density of the solution after mixing are the same as those of pure water.