Chapter 5

Complete combustion of 1 mol of acetone \(\left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\right)\) liberates \(1790 \mathrm{~kJ}\) : $$ \begin{aligned} \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}(l)+4 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+3 & \mathrm{H}_{2} \mathrm{O}(l) \\ & \Delta H^{\circ}=-1790 \mathrm{~kJ} \end{aligned} $$ Using this information together with data from Appendix \(C\), calculate the enthalpy of formation of acetone.

Calcium carbide \(\left(\mathrm{CaC}_{2}\right)\) reacts with water to form acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and \(\mathrm{Ca}(\mathrm{OH})_{2} .\) From the following enthalpy of reaction data and data in Appendix \(C\), calculate \(\Delta H_{f}^{\circ}\) for \(\mathrm{CaC}_{2}(s)\) \(\mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{C}_{2} \mathrm{H}_{2}(g)\) \(\Delta H^{\circ}=-127.2 \mathrm{~kJ}\)

Naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) is a solid aromatic compound often sold as mothballs. The complete combustion of this substance to yield \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(25^{\circ} \mathrm{C}\) yields \(5154 \mathrm{~kJ} / \mathrm{mol}\). (a) Write balanced equations for the formation of naphthalene from the elements and for its combustion. (b) Calculate the standard enthalpy of formation of naphthalene.

(a) What is meant by the term fuel value? (b) Which is a greater source of energy as food, \(5 \mathrm{~g}\) of fat or \(9 \mathrm{~g}\) of carbohydrate?

(a) Why are fats well suited for energy storage in the human body? (b) A particular chip snack food is composed of \(12 \%\) protein, \(14 \%\) fat, and the rest carbohydrate. What percentage of the calorie content of this food is fat? (c) How many grams of protein provide the same fuel value as \(25 \mathrm{~g}\) of fat?

The heat of combustion of fructose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), is \(-2812 \mathrm{~kJ} / \mathrm{mol}\). If a fresh golden delicious apple weighing \(4.23\) oz \((120 \mathrm{~g})\) contains \(16.0 \mathrm{~g}\) of fructose, what caloric content does the fructose contribute to the apple?

The heat of combustion of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\), is \(-1367 \mathrm{~kJ} / \mathrm{mol}\). A batch of Sauvignon Blanc wine contains \(10.6 \%\) ethanol by mass. Assuming the density of the wine to be \(1.0 \mathrm{~g} / \mathrm{mL}\), what caloric content does the alcohol (ethanol) in a 6-oz glass of wine (177 mL) have?

Thestandard enthalpies of formation of gaseous propyne \(\left(\mathrm{C}_{3} \mathrm{H}_{4}\right)\), propylene \(\left(\mathrm{C}_{3} \mathrm{H}_{6}\right)\), and propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) are \(+185.4,+20.4\), and \(-103.8 \mathrm{~kJ} / \mathrm{mol}\), respectively. (a) Calculate the heat evolved per mole on combustion of each substance to yield \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\) (b) Calculate the heat evolved on combustion of \(1 \mathrm{~kg}\) of each substance. (c) Which is the most efficient fuel in terms of heat evolved per unit mass?

At \(20^{\circ} \mathrm{C}\) (approximately room temperature) the average velocity of \(\mathrm{N}_{2}\) molecules in air is \(1050 \mathrm{mph}\). (a) What is the averagespeed in \(\mathrm{m} / \mathrm{s}\) ? (b) What is the kinetic energy (in J) of an \(\mathrm{N}_{2}\) molecule moving at this speed? (c) What is the total kinetic energy of 1 mol of \(\mathrm{N}_{2}\) molecules 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.

When a mole of dry ice, \(\mathrm{CO}_{2}(s)\), is converted to \(\mathrm{CO}_{2}(g)\) at atmospheric pressure and \(-78^{\circ} \mathrm{C}\), the heat absorbed by the system exceeds the increase in internal energy of the \(\mathrm{CO}_{2}\). Why is this so? What happens to the remaining energy?

The air bags that provide protection in autos in the event of an accident expand because of a rapid chemical reaction. From the viewpoint of the chemical reactants as the system, what do you expect for the signs of \(q\) and \(w\) in this process?

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

Limestone stalactites and stalagmites are formed in caves by the following reaction: $$ \mathrm{Ca}^{2+}(a q)+2 \mathrm{HCO}_{3}^{-}(a q) \longrightarrow $$ If 1 mol of \(\mathrm{CaCO}_{3}\) forms at \(298 \mathrm{~K}\) under 1 atm pressure, the reaction performs \(2.47 \mathrm{~kJ}\) of \(P-V\) work, pushing back the atmosphere as the gaseous \(\mathrm{CO}_{2}\) forms. At the same time, \(38.95 \mathrm{~kJ}\) of heat is absorbed from the environment. What are the values of \(\Delta H\) and of \(\Delta E\) for this reaction?

The enthalpy change for melting ice at \(0{ }^{\circ} \mathrm{C}\) and constant atmospheric pressure is \(6.01 \mathrm{~kJ} / \mathrm{mol}\). Calculate the quantity of energy required to melt a moderately large iceberg with a mass of \(1.25\) million metric tons. (A metric ton is \(1000 \mathrm{~kg}\).)

Comparing the energy associated with the rainstorm and that of a conventional explosive gives some idea of the immense amount of energy associated with a storm. (a) The heat of vaporization of water is \(44.0 \mathrm{~kJ} / \mathrm{mol}\). Calculate the quantity of energy released when enough water vapor condenses to form \(0.50\) inches of rain over an area of one square mile. (b) The energy released when one ton of dynamite explodes is \(4.2 \times 10^{6} \mathrm{~kJ} .\) Calculate the number of tons of dynamite needed to provide the energy of the storm in part (a).

(a) When a \(0.235-\mathrm{g}\) sample of benzoic acid is combusted in a bomb calorimeter, the temperature rises \(1.642^{\circ} \mathrm{C}\). When a \(0.265-\mathrm{g}\) sample of caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{O}_{2} \mathrm{~N}_{4}\), is burned, the temperature rises \(1.525^{\circ} \mathrm{C}\). Using the value \(26.38 \mathrm{~kJ} / \mathrm{g}\) 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?

How many grams of methane \(\left[\mathrm{CH}_{4}(g)\right]\) must be combusted to heat \(1.00 \mathrm{~kg}\) of water from \(25.0^{\circ} \mathrm{C}\) to \(90.0^{\circ} \mathrm{C}\), assuming \(\mathrm{H}_{2} \mathrm{O}(l)\) as a product and \(100 \%\) efficiency in heat transfer?

Burning methane in oxygen can produce three different carbon-containing products: soot (very fine particles of graphite), \(\mathrm{CO}(\mathrm{g})\), and \(\mathrm{CO}_{2}(\mathrm{~g})\). (a) Write three balanced equations for the reaction of methane gas with oxygen to produce these three products. In each case assume that \(\mathrm{H}_{2} \mathrm{O}(l)\) is the only other product. (b) Determine the standard enthalpies for the reactions in part (a). (c) Why, when the oxygen supply is adequate, is \(\mathrm{CO}_{2}(g)\) the predominant carbon- containing product of the combustion of methane?

From the following data for three prospective fuels, calculate which could provide the most energy per unit volume: $$ \begin{array}{lcc} \hline & \begin{array}{c} \text { Density } \\ \text { at } 20{ }^{\circ} \mathbf{C} \\ \left(\mathrm{g} / \mathrm{cm}^{3}\right) \end{array} & \begin{array}{c} \text { Molar Enthalpy } \\ \text { of Combustion } \\ \text { Fuel } \end{array} & \mathrm{kJ} / \mathrm{mol} \\ \hline \text { Nitroethane, } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NO}_{2}(l) & 1.052 & -1368 \\ \text { Ethanol, } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) & 0.789 & -1367 \\ \text { Methylhydrazine, } \mathrm{CH}_{6} \mathrm{~N}_{2}(I) & 0.874 & -1305 \\\ \hline \end{array} $$

A 200-lb man decides to add to his exercise routine by walking up three flights of stairs \((45 \mathrm{ft}) 20\) 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?

The sun supplies about \(1.0\) kilowatt of energy for each square meter of surface area \(\left(1.0 \mathrm{~kW} / \mathrm{m}^{2}\right.\), where a watt \(=1 \mathrm{~J} / \mathrm{s}\) ). Plants produce the equivalent of about \(0.20 \mathrm{~g}\) of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) per hour per square meter. Assuming that the sucrose is produced as follows, calculate the percentage of sunlight used to produce sucrose. $$ \begin{aligned} 12 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+12 \mathrm{O}_{2}(g) \\ \Delta H=5645 \mathrm{~kJ} \end{aligned} $$

Consider the following unbalanced oxidation-reduction reactions in aqueous solution: $$ \begin{aligned} \mathrm{Ag}^{+}(a q)+\mathrm{Li}(s) & \longrightarrow \mathrm{Ag}(s)+\mathrm{Li}^{+}(a q) \\ \mathrm{Fe}(s)+\mathrm{Na}^{+}(a q) & \longrightarrow \mathrm{Fe}^{2+}(a q)+\mathrm{Na}(s) \\ \mathrm{K}(s)+\mathrm{H}_{2} \mathrm{O}(l) & \longrightarrow \mathrm{KOH}(a q)+\mathrm{H}_{2}(g) \end{aligned} $$ (a) Balance each of the reactions. (b) By using data in Appendix \(C\), calculate \(\Delta H^{\circ}\) for each of the reactions. (c) Based on the values you obtain for \(\Delta H^{\circ}\), which of the reactions would you expect to be thermodynamically favored? (That is, which would you expect to be spontaneous?) (d) Use the activity series to predict which of these reactions should occur. ono (Section 4.4) Are these results in accord with your conclusion in part (c) of this problem?

Consider two solutions, the first being \(50.0 \mathrm{~mL}\) of \(1.00 \mathrm{M}\) \(\mathrm{CuSO}_{4}\) 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 \(21.5^{\circ} \mathrm{C}\) to \(27.7{ }^{\circ} \mathrm{C}\). (a) Before mixing, how many grams of Cu are present in the solution of \(\mathrm{CuSO}_{4} ?(\mathrm{~b})\) 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. (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 that of pure water.

A sample of a hydrocarbon is combusted completely in \(\mathrm{O}_{2}(g)\) to produce \(21.83 \mathrm{~g} \mathrm{CO}_{2}(g), 4.47 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}(g)\), and \(311 \mathrm{~kJ}\) of heat. (a) What is the mass of the hydrocarbon sample that was combusted? (b) What is the empirical formula of the hydrocarbon? (c) Calculate the value of \(\Delta H_{f}^{\circ}\) per empirical-formula unit of the hydrocarbon. (d) Do you think that the hydrocarbon is one of those listed in Appendix C? Explain your answer.