Chapter 9

Explain the difference between heat capacity and specific heat of a substance.

How much heat, in joules and in calories, must be added to a 75.0-g iron block with a specific heat of 0.449 J/g "C to increase its temperature from \(25^{\circ} \mathrm{C}\) to its melting temperature of \(1535^{\circ} \mathrm{C}\) ?

A 45-g aluminum spoon (specific heat 0.88 J/g ^ C) at 24 ^ C is placed in 180 mL (180 g) of coffee at 85 ^ C and the temperature of the two become equal. (a) What is the final temperature when the two become equal? Assume that coffee has the same specific heat as water. (b) The first time a student solved this problem she got an answer of \(88^{\circ} \mathrm{C}\). Explain why this is clearly an incorrect answer.

A 0.500-g sample of KCl is added to 50.0 g of water in a calorimeter (Figure 9.12). If the temperature decreases by \(1.05^{\circ} \mathrm{C},\) what is the approximate amount of heat involved in the dissolution of the \(\mathrm{KCl}\), assuming the specific heat of the resulting solution is \(4.18 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C}\) ? Is the reaction exothermic or endothermic?

The addition of 3.15 g of \(\mathrm{Ba}(\mathrm{OH})_{2} \cdot 8 \mathrm{H}_{2} \mathrm{O}\) to a solution of \(1.52 \mathrm{g}\) of \(\mathrm{NH}_{4} \mathrm{SCN}\) in \(100 \mathrm{g}\) of water in a calorimeter caused the temperature to fall by \(3.1^{\circ} \mathrm{C} .\) Assuming the specific heat of the solution and products is \(4.20 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C}\) calculate the approximate amount of heat absorbed by the reaction, which can be represented by the following equation: $$\mathrm{Ba}(\mathrm{OH})_{2} \cdot 8 \mathrm{H}_{2} \mathrm{O}(s)+2 \mathrm{NH}_{4} \mathrm{SCN}(a q) \longrightarrow \mathrm{Ba}(\mathrm{SCN})_{2}(a q)+2 \mathrm{NH}_{3}(a q)+10 \mathrm{H}_{2} \mathrm{O}(I)$$

When \(1.0 \mathrm{g}\) of fructose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)\), a sugar commonly found in fruits, is bumed in oxygen in a bomb calorimeter, the temperature of the calorimeter increases by \(1.58^{\circ} \mathrm{C}\). If the heat capacity of the calorimeter and its contents is \(9.90 \mathrm{kJ} /^{\circ} \mathrm{C}\), what is \(q\) for this combustion?

When a 0.740-g sample of trinitrotoluene (TNT), \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{N}_{2} \mathrm{O}_{6}\), is bumed in a bomb calorimeter, the temperature increases from \(23.4^{\circ} \mathrm{C}\) to \(26.9^{\circ} \mathrm{C}\). The heat capacity of the calorimeter is \(534 \mathrm{J} /^{\circ} \mathrm{C}\), and it contains \(675 \mathrm{mL}\) of water. How much heat was produced by the combustion of the TNT sample?

The amount of fat recommended for someone with a daily diet of 2000 Calories is \(65 \mathrm{g}\). What percent of the calories in this diet would be supplied by this amount of fat if the average number of Calories for fat is 9.1 Calories/g?

A teaspoon of the carbohydrate sucrose (common sugar) contains 16 Calories (16 kcal). What is the mass of one teaspoon of sucrose if the average number of Calories for carbohydrates is 4.1 Calories/g?

A pint of premium ice cream can contain 1100 Calories. What mass of fat, in grams and pounds, must be produced in the body to store an extra \(1.1 \times 10^{3}\) Calories if the average number of Calories for fat is 9.1 Calories/g?

A serving of a breakfast cereal contains 3 g of protein, 18 g of carbohydrates, and 6 g of fat. What is the Calorie content of a serving of this cereal if the average number of Calories for fat is 9.1 Calories/g, for carbohydrates is 4.1 Calories/g, and for protein is 4.1 Calories/g?

When 2.50 g of methane burns in oxygen, 125 kJ of heat is produced. What is the enthalpy of combustion per mole of methane under these conditions?

Does the standard enthalpy of formation of \(\mathrm{H}_{2} \mathrm{O}(g)\) differ from \(\Delta H^{\circ}\) for the reaction \(2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) ?\)

Both graphite and diamond burn. \(\mathrm{C}(s, \text { diamond })+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)\) For the conversion of graphite to diamond: \(\mathbf{C}(s, \text { graphite }) \longrightarrow \mathbf{C}(s, \text { diamond })\) \(\Delta H^{\circ}=1.90 \mathrm{kJ}\) Which produces more heat, the combustion of graphite or the combustion of diamond?

Calculate \(\Delta H^{\circ}\) for the process \(\mathrm{Sb}(s)+\frac{5}{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SbCl}_{5}(s)\) from the following information: \(\mathrm{Sb}(s)+\frac{3}{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SbCl}_{3}(s) \quad \Delta H^{\circ}=-314 \mathrm{kJ}\) \(\mathrm{SbCl}_{3}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SbCl}_{5}(s) \quad \Delta H^{\circ}=-80 \mathrm{kJ}\)

Calculate \(\Delta H^{\circ}\) for the process \(\mathrm{Zn}(s)+\mathrm{S}(s)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{ZnSO}_{4}(s)\) from the following information: \(\mathrm{Zn}(s)+\mathrm{S}(s) \longrightarrow \mathrm{ZnS}(s) \quad \Delta H^{\circ}=-206.0 \mathrm{kJ}\) \(\mathrm{ZnS}(s)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{ZnSO}_{4}(s) \quad \Delta H^{\circ}=-776.8 \mathrm{kJ}\)

Calculate \(\Delta H\) for the process \(\mathrm{Hg}_{2} \mathrm{Cl}_{2}(s) \longrightarrow 2 \mathrm{Hg}(l)+\mathrm{Cl}_{2}(g)\) from the following information: \(\mathrm{Hg}(l)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{HgCl}_{2}(s) \quad \Delta H=-224 \mathrm{kJ}\) \(\mathrm{Hg}(l)+\mathrm{HgCl}_{2}(s) \longrightarrow \mathrm{Hg}_{2} \mathrm{Cl}_{2}(s) \quad \Delta H=-41.2 \mathrm{kJ}\)

Calculate \(\Delta H^{\circ}\) for the process \(\mathrm{Co}_{3} \mathrm{O}_{4}(s) \longrightarrow 3 \mathrm{Co}(s)+2 \mathrm{O}_{2}(g)\) from the following information: \(\operatorname{Co}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \operatorname{CoO}(s) \quad \Delta H^{\circ}=-237.9 \mathrm{kJ}\) \(3 \operatorname{CoO}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{Co}_{3} \mathrm{O}_{4}(s) \quad \Delta H^{\circ}=-177.5 \mathrm{kJ}\)

Calculate the standard molar enthalpy of formation of \(\mathrm{NO}(g)\) from the following data: \(\mathrm{N}_{2}(g)+2 \mathrm{O}_{2} \longrightarrow 2 \mathrm{NO}_{2}(g) \quad \Delta H^{\circ}=66.4 \mathrm{kJ}\) \(2 \mathrm{NO}(g)+\mathrm{O}_{2} \longrightarrow 2 \mathrm{NO}_{2}(g) \quad \Delta H^{\circ}=-114.1 \mathrm{kJ}\)

The enthalpy of combustion of hard coal averages \(-35 \mathrm{kJ} / \mathrm{g}\), that of gasoline, \(1.28 \times 10^{5} \mathrm{kJ} / \mathrm{gal}\). How many kilograms of hard coal provide the same amount of heat as is available from 1.0 gallon of gasoline? Assume that the density of gasoline is \(0.692 \mathrm{g} / \mathrm{mL}\) (the same as the density of isooctane).

The oxidation of the sugar glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), is described by the following equation: \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-2816 \mathrm{kJ}\) The metabolism of glucose gives the same products, although the glucose reacts with oxygen in a series of steps in the body. (a) How much heat in kilojoules can be produced by the metabolism of \(1.0 \mathrm{g}\) of glucose? (b) How many Calories can be produced by the metabolism of \(1.0 \mathrm{g}\) of glucose?

Propane, \(C_{3} \mathrm{H}_{8}\), is a hydrocarbon that is commonly used as a fuel. (a) Write a balanced equation for the complete combustion of propane gas. (b) Calculate the volume of air at \(25^{\circ} \mathrm{C}\) and 1.00 atmosphere that is needed to completely combust 25.0 grams of propane. Assume that air is 21.0 percent \(\mathrm{O}_{2}\) by volume. (Hint: We will see how to do this calculation in a later chapter on gases - for now use the information that \(1.00 \mathrm{L}\) of air at \(25^{\circ} \mathrm{C}\) and 1.00 atm contains \(0.275 \mathrm{g}\) of \(\mathrm{O}_{2}\) per liter.) (c) The heat of combustion of propane is \(-2,219.2 \mathrm{kJ} / \mathrm{mol}\). Calculate the heat of formation, \(\Delta H_{\mathrm{f}}^{\circ}\) of propane given that \(\Delta H_{\mathrm{f}}^{\circ} \quad\) of \(\mathrm{H}_{2} \mathrm{O}(l)=-285.8 \mathrm{kJ} / \mathrm{mol}\) and \(\Delta H_{\mathrm{f}}^{\circ} \quad\) of \(\mathrm{CO}_{2}(g)=-393.5 \mathrm{kJ} / \mathrm{mol}\) (d) Assuming that all of the heat released in burning 25.0 grams of propane is transferred to 4.00 kilograms of water, calculate the increase in temperature of the water.

During a recent winter month in Sheboygan, Wisconsin, it was necessary to obtain 3500 kWh of heat provided by a natural gas furnace with \(89 \%\) efficiency to keep a small house warm (the efficiency of a gas furnace is the percent of the heat produced by combustion that is transferred into the house). (a) Assume that natural gas is pure methane and determine the volume of natural gas in cubic feet that was required to heat the house. The average temperature of the natural gas was \(56^{\circ} \mathrm{F} ;\) at this temperature and a pressure of \(1 \mathrm{atm}\) natural gas has a density of 0.681 g/L. (b) How many gallons of LPG (liquefied petroleum gas) would be required to replace the natural gas used? Assume the LPG is liquid propane \(\left[\mathrm{C}_{3} \mathrm{H}_{8}:\right.\) density, \(0.5318 \mathrm{g} / \mathrm{mL}\); enthalpy of combustion, \(2219 \mathrm{kJ} / \mathrm{mol}\) for the formation of \(\left.\mathrm{CO}_{2}(g) \text { and } \mathrm{H}_{2} \mathrm{O}(l)\right]\) and the furnace used to burn the LPG has the same efficiency as the gas furnace. (c) What mass of carbon dioxide is produced by combustion of the methane used to heat the house? (d) What mass of water is produced by combustion of the methane used to heat the house? (e) What volume of air is required to provide the oxygen for the combustion of the methane used to heat the house? Air contains \(23 \%\) oxygen by mass. The average density of air during the month was \(1.22 \mathrm{g} / \mathrm{L}\). (f) How many kilowatt-hours \(\left(1 \mathrm{kWh}=3.6 \times 10^{6} \mathrm{J}\right)\) of electricity would be required to provide the heat necessary to heat the house? Note electricity is \(100 \%\) efficient in producing heat inside a house. (g) Although electricity is 100\% efficient in producing heat inside a house, production and distribution of electricity is not \(100 \%\) efficient. The efficiency of production and distribution of electricity produced in a coal- fired power plant is about 40\%. A certain type of coal provides 2.26 kWh per pound upon combustion. What mass of this coal in kilograms will be required to produce the electrical energy necessary to heat the house if the efficiency of generation and distribution is 40\%?

Which bond in each of the following pairs of bonds is the strongest? (a) \(\mathrm{C}-\mathrm{C}\) or \(\mathrm{C}=\mathrm{C}\) (b) C-N or C \(\equiv \mathrm{N}\) (c) \(\mathrm{C} \equiv \mathrm{O}\) or \(\mathrm{C}=\mathrm{O}\) (d) H-F or H-Cl (e) C-H or O-H (f) C-N or C-O

Explain why bonds occur at specific average bond distances instead of the atoms approaching each other infinitely close.

Use principles of atomic structure to answer each of the following: \(^{[4]}\) (a) The radius of the Ca atom is 197 pm; the radius of the \(C a^{2+}\) ion is 99 pm. Account for the difference. (b) The lattice energy of \(\mathrm{CaO}(s)\) is \(-3460 \mathrm{kJ} / \mathrm{mol}\); the lattice energy of \(\mathrm{K}_{2} \mathrm{O}\) is \(-2240 \mathrm{kJ} / \mathrm{mol}\). Account for the difference. (c) Given these ionization values, explain the difference between \(\mathrm{Ca}\) and \(\mathrm{K}\) with regard to their first and second ionization energies. $$\begin{array}{|c|c|c|} \hline \text { Element } & \text { First lonkation anerey (caluol) } & \text { Second lonkation anary (Calmo) } \\ \hline \mathrm{K} & 419 & 3050 \\ \hline \mathrm{Ca} & 590 & 1140 \\ \hline \end{array}$$ (d) The first ionization energy of \(\mathrm{Mg}\) is \(738 \mathrm{kJ} / \mathrm{mol}\) and that of \(\mathrm{Al}\) is \(578 \mathrm{kJ} / \mathrm{mol}\). Account for this difference.

Which compound in each of the following pairs has the larger lattice energy? Note: \(\mathrm{Mg}^{2+}\) and \(\mathrm{Li}^{+}\) have similar radii; O \(^{2-}\) and \(\mathrm{F}^{-}\) have similar radii. Explain your choices. (a) MgO or MgSe (b) LiF or MgO (c) \(\mathrm{Li}_{2} \mathrm{O}\) or \(\mathrm{LiCl}\) (d) Li_se or MgO

Which compound in each of the following pairs has the larger lattice energy? Note: \(\mathrm{Ba}^{2+}\) and K 'have similar radii; S^- and Cl- have similar radii. Explain your choices. (a) \(\mathrm{K}_{2} \mathrm{O}\) or \(\mathrm{Na}_{2} \mathrm{O}\) (b) \(\mathrm{K}_{2} \mathrm{S}\) or \(\mathrm{BaS}\) (c) KCl or BaS (d) BaS or BaCl_

Which of the following compounds requires the most energy to convert one mole of the solid into separate ions? (a) \(\mathrm{K}_{2} \mathrm{S}\) (b) \(\mathrm{K}_{2} \mathrm{O}\) (c) CaS (d) \(\mathrm{Cs}_{2} \mathrm{S}\) (e) CaO