Chapter 6

A \(10.0-\mathrm{g}\) sample of a mixture of \(\mathrm{CH}_{4}\) and \(\mathrm{C}_{2} \mathrm{H}_{4}\) reacts with oxygen at \(25^{\circ} \mathrm{C}\) and 1 atm to produce \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) If the reaction produces \(520 \mathrm{~kJ}\) of heat, what is the mass percentage of \(\mathrm{CH}_{4}\) in the mixture?

Consider the Haber process: $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) ; \Delta H^{\circ}=-91.8 \mathrm{~kJ} $$ The density of ammonia at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) is \(0.696 \mathrm{~g} / \mathrm{L}\). The density of nitrogen, \(\mathrm{N}_{2}\), is \(1.145 \mathrm{~g} / \mathrm{L}\), and the molar heat capacity is \(29.12 \mathrm{~J} /\left(\mathrm{mol} \cdot{ }^{\circ} \mathrm{C}\right)\). (a) How much heat is evolved in the production of \(1.00 \mathrm{~L}\) of ammonia at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm} ?\) (b) What percentage of this heat is required to heat the nitrogen required for this reaction \((0.500 \mathrm{~L})\) from \(25^{\circ} \mathrm{C}\) to \(400^{\circ} \mathrm{C}\), the temperature at which the Haber process is run?

An industrial process for manufacturing sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4}\), uses hydrogen sulfide, \(\mathrm{H}_{2} \mathrm{~S}\), from the purification of natural gas. In the first step of this process, the hydrogen sulfide is burned to obtain sulfur dioxide, \(\mathrm{SO}_{2}\). $$ \begin{aligned} 2 \mathrm{H}_{2} \mathrm{~S}(g)+3 \mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{SO}_{2}(g) \\ \Delta H^{\circ} &=-1124 \mathrm{~kJ} \end{aligned} $$ The density of sulfur dioxide at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) is \(2.62 \mathrm{~g} / \mathrm{L}\) and the molar heat capacity is \(30.2 \mathrm{~J} /\left(\mathrm{mol} \cdot{ }^{\circ} \mathrm{C}\right) .\) (a) How much heat would be evolved in producing \(1.00 \mathrm{~L}\) of \(\mathrm{SO}_{2}\) at \(25^{\circ} \mathrm{C}\) and \(1.00\) atm? (b) Suppose heat from this reaction is used to heat \(1.00 \mathrm{~L}\) of \(\mathrm{SO}_{2}\) from \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) to \(500^{\circ} \mathrm{C}\) for its use in the next step of the process. What percentage of the heat evolved is required for this?

The carbon dioxide exhaled in the breath of astronauts is often removed from the spacecraft by reaction with lithium hydroxide. $$ 2 \mathrm{LiOH}(s)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{Li}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) $$ Estimate the grams of lithium hydroxide required per astronaut per day. Assume that each astronaut requires \(2.50 \times 10^{3}\) kcal of energy per day. Further assume that this energy can be equated to the heat of combustion of a quantity of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\). From the amount of glucose required to give \(2.50 \times 10^{3}\) kcal of heat, calculate the amount of \(\mathrm{CO}_{2}\) produced and hence the amount of LiOH required. The \(\Delta H_{f}^{\circ}\) for glucose \((s)\) is \(-1273 \mathrm{~kJ} / \mathrm{mol}\).

A rebreathing gas mask contains potassium superoxide, \(\mathrm{KO}_{2}\), which reacts with moisture in the breath to give oxygen. $$ 4 \mathrm{KO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 4 \mathrm{KOH}(s)+3 \mathrm{O}_{2}(g) $$ Estimate the grams of potassium superoxide required to supply a person's oxygen needs for one hour. Assume a person requires \(1.00 \times 10^{2}\) kcal of energy for this time period. Further assume that this energy can be equated to the heat of combustion of a quantity of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) From the amount of glucose required to give \(1.00 \times 10^{2} \mathrm{kcal}\) of heat, calculate the amount of oxygen consumed and hence the amount of \(\mathrm{KO}_{2}\) required. The \(\Delta H_{f}^{\circ}\) for glucose \((s)\) is \(-1273 \mathrm{~kJ} / \mathrm{mol}\).