Exercises

Prepare a table identifying several energy transitions that take place during the typical operation of an automobile.

Calculate the heat capacity, in joules and in calories per degree, of the following:

(a) 28.4 g of water

(b) 1.00 oz of lead

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 °C to its melting temperature of 1535 °C?

How much would the temperature of 275 g of water increase if 36.5 kJ of heat were added?

A piece of unknown substance weighs 44.7 g and requires 2110 J to increase its temperature from 23.2 °C to 89.6 °C.

(a) What is the specific heat of the substance?

(b) If it is one of the substances found in Table 9.1, what is its likely identity?

An aluminum kettle weighs 1.05 kg.

(a) What is the heat capacity of the kettle?

(b) How much heat is required to increase the temperature of this kettle from 23.0 °C to 99.0 °C?

(c) How much heat is required to heat this kettle from 23.0 °C to 99.0 °C if it contains 1.25 L of water (density of 0.997 g/mL and a specific heat of 4.184 J/g °C)?

A 500-mL bottle of water at room temperature and a 2-L bottle of water at the same temperature were placed in a refrigerator. After 30 minutes, the 500-mL bottle of water had cooled to the temperature of the refrigerator. An hour later, the 2-L of water had cooled to the same temperature. When asked which sample of water lost the most heat, one student replied that both bottles lost the same amount of heat because they started at the same temperature and finished at the same temperature. A second student thought that the 2-L bottle of water lost more heat because there was more water. A third student believed that the 500-mL bottle of water lost more heat because it cooled more quickly. A fourth student thought that it was not possible to tell because we do not know the initial temperature and the final temperature of the water. Indicate which of these answers is correct and describe the error in each of the other answers.

Would the amount of heat absorbed by the dissolution in Example 9.6 appear greater, lesser, or remain the same if the experimenter used a calorimeter that was a poorer insulator than a coffee cup calorimeter? Explain your answer.

How many milliliters of water at 23 °C with a density of 1.00 g/mL must be mixed with 180 mL (about 6 oz) of coffee at 95 °C so that the resulting combination will have a temperature of 60 °C? Assume that coffee and water have the same density and the same specific heat.

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 °C. Explain why this is clearly an incorrect answer.

A 70.0-g piece of metal at 80.0 °C is placed in 100 g of water at 22.0 °C contained in a calorimeter like that shown in Figure 9.12. The metal and water come to the same temperature at 24.6 °C. How much heat did the metal give up to the water? What is the specific heat of the metal?

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 °C, what is the approximate amount of heat involved in the dissolution of the KCl, assuming the specific heat of the resulting solution is 4.18 J/g °C? Is the reaction exothermic or endothermic?

When 50.0 g of 0.200 M NaCl(aq) at 24.1 °C is added to 100.0 g of 0.100 M AgNO₃(aq) at 24.1 °C in a calorimeter, the temperature increases to 25.2 °C as AgCl(s) forms. Assuming the specific heat of the solution and products is 4.20 J/g °C, calculate the approximate amount of heat in joules produced.

The reaction of 50 mL of acid and 50 mL of base described in Example 9.5 increased the temperature of the solution by 6.9 degrees C. How much would the temperature have increased if 100 mL of acid and 100 mL of base had been used in the same calorimeter starting at the same temperature of 22.0 °C? Explain your answer.

When 1.0 g of fructose, C₆H₁₂O₆(s), a sugar commonly found in fruits, is burned in oxygen in a bomb calorimeter, the temperature of the calorimeter increases by 1.58 °C. If the heat capacity of the calorimeter and its contents is 9.90 kJ/°C, what is q for this combustion?

One method of generating electricity is by burning coal to heat water, which produces steam that drives an electric generator. To determine the rate at which coal is to be fed into the burner in this type of plant, the heat of combustion per ton of coal must be determined using a bomb calorimeter. When 1.00 g of coal is burned in a bomb calorimeter (Figure 9.17), the temperature increases by 1.48 °C. If the heat capacity of the calorimeter is 21.6 kJ/°C, determine the heat produced by combustion of a ton of coal (2.000 $\times$ 10³ pounds).

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 $\times$ 10³ Calories if the average number of Calories for fat is
9.1 Calories/g?

Which is the least expensive source of energy in kilojoules per dollar: a box of breakfast cereal that weighs 32 ounces and costs $4.23, or a liter of isooctane (density, 0.6919 g/mL) that costs $0.45? Compare the nutritional value of the cereal with the heat produced by combustion of the isooctane under standard conditions. A 1.0-ounce serving of the cereal provides 130 Calories.

Using the data in the check your learning section of Example 9.5, calculate ΔH in kJ/mol of AgNO₃(aq) for the reaction: $\text{NaCl}(aq)+{\text{AgNO}}_3(aq)⟶\text{AgCl}(s)+{\text{NaNO}}_3(aq)$

Calculate ΔH for the reaction described by the equation. (Hint: use the value for the approximate amount of heat absorbed by the reaction that you calculated in a previous exercise.)
$\text{Ba}{\left(\text{OH}\right)}_2\text{·}8{\text{H}}_2\text{O}(s)+2{\text{NH}}_4\text{SCN}(aq)⟶\text{Ba}{(\text{SCN})}_2(aq)+2{\text{NH}}_3(aq)+10{\text{H}}_2\text{O}\left(l\right)$

Although the gas used in an oxyacetylene torch (Figure 9.7) is essentially pure acetylene, the heat produced by combustion of one mole of acetylene in such a torch is likely not equal to the enthalpy of combustion of acetylene listed in Table 9.2. Considering the conditions for which the tabulated data are reported, suggest an explanation.

How much heat is produced by combustion of 125 g of methanol under standard state conditions?

What mass of carbon monoxide must be burned to produce 175 kJ of heat under standard state conditions?

How much heat is produced when 100 mL of 0.250 M HCl (density, 1.00 g/mL) and 200 mL of 0.150 M NaOH (density, 1.00 g/mL) are mixed?
$\text{HCl}\left(aq\right)+\text{NaOH}\left(aq\right)⟶\text{NaCl}\left(aq\right)+{\text{H}}_2\text{O}\left(l\right)\text{Δ}{H}_{298}^{°}=\mathrm{-58}\text{kJ}$

If both solutions are at the same temperature and the heat capacity of the products is 4.19 J/g °C, how much will the temperature increase? What assumption did you make in your calculation?

Before the introduction of chlorofluorocarbons, sulfur dioxide (enthalpy of vaporization, 6.00 kcal/mol) was used in household refrigerators. What mass of SO₂ must be evaporated to remove as much heat as evaporation of 1.00 kg of CCl₂F₂ (enthalpy of vaporization is 17.4 kJ/mol)?

The vaporization reactions for SO₂ and CCl₂F₂ are ${\text{SO}}_2(l)⟶{\text{SO}}_2(g)$ and ${\text{CCl}}_2\text{F}\left(l\right)⟶{\text{CCl}}_2{\text{F}}_2(g),$ respectively.

Which of the enthalpies of combustion in Table 9.2 the table are also standard enthalpies of formation?

Joseph Priestly prepared oxygen in 1774 by heating red mercury(II) oxide with sunlight focused through a lens. How much heat is required to decompose exactly 1 mole of red HgO(s) to Hg(l) and O₂(g) under standard conditions?

How many kilojoules of heat will be released when exactly 1 mole of iron, Fe, is burned to form Fe₂O₃(s) at standard state conditions?

Both graphite and diamond burn.
$\text{C}\left(s,\text{diamond}\right)+{\text{O}}_2(g)⟶{\text{CO}}_2(g)$

For the conversion of graphite to diamond:
$\text{C}\left(s,\text{graphite}\right)⟶\text{C}\left(s,\text{diamond}\right)\text{Δ}{H}_{298}^{°}=1.90\text{kJ}$

Which produces more heat, the combustion of graphite or the combustion of diamond?

Which produces more heat?
$\text{Os}\left(s\right)⟶2{\text{O}}_2(g)⟶{\text{OsO}}_4(s)$
or
$\text{Os}\left(s\right)⟶2{\text{O}}_2(g)⟶{\text{OsO}}_4(g)$

for the phase change ${\text{OsO}}_4(s)⟶{\text{OsO}}_4(g)\text{Δ}\text{H}=56.4\text{kJ}$

Calculate $\text{Δ}{H}_{298}^{°}$ for the process $\text{Zn}\left(s\right)+\text{S}\left(s\right)+2{\text{O}}_2(g)⟶{\text{ZnSO}}_4(s)$

from the following information:
$\begin{array}{l}\text{Zn}(s)+\text{S}(s)⟶\text{ZnS}(s)\text{Δ}{H}_{298}^{°}=\mathrm{-206.0}\text{kJ}\\ \text{ZnS}(s)+{\text{2O}}_2(g)⟶{\text{ZnSO}}_4(s)\text{Δ}{H}_{298}^{°}=\mathrm{-776.8}\text{kJ}\end{array}$

Calculate $\text{Δ}{H}_{298}^{°}$ for the process ${\text{Co}}_3{\text{O}}_4(s)⟶3\text{Co}\left(s\right)+2{\text{O}}_2(g)$

from the following information:
$\begin{array}{}\\ \text{Co}(s)+\frac{1}{2}{\text{O}}_2(g)⟶\text{CoO}(s)\text{Δ}{H}_{298}^{°}=\mathrm{-237.9}\text{kJ}\\ \text{3CoO}(s)+\frac{1}{2}{\text{O}}_2(g)⟶{\text{Co}}_3{\text{O}}_4(s)\text{Δ}{H}_{298}^{°}=\mathrm{-177.5}\text{kJ}\end{array}$

Using the data in Appendix G, calculate the standard enthalpy change for each of the following reactions:

(a) ${\text{N}}_2(g)+{\text{O}}_2(g)⟶2\text{NO}\left(g\right)$

(b) $\text{Si}\left(s\right)+2{\text{Cl}}_2(g)⟶{\text{SiCl}}_4(g)$

(c) ${\text{Fe}}_2{\text{O}}_3\left(s\right)+3{\text{H}}_2(g)⟶2\text{Fe}\left(s\right)+3{\text{H}}_2\text{O}\left(l\right)$

(d) $2\text{LiOH}(s)+{\text{CO}}_2(g)⟶{\text{Li}}_2{\text{CO}}_3(s)+{\text{H}}_2\text{O}(g)$

The following reactions can be used to prepare samples of metals. Determine the enthalpy change under standard state conditions for each.

(a) $2{\text{Ag}}_2\text{O}\left(s\right)⟶4\text{Ag}\left(s\right)+{\text{O}}_2(g)$

(b) $\text{SnO}\left(s\right)+\text{CO}\left(g\right)⟶\text{Sn}\left(s\right)+{\text{CO}}_2(g)$

(c) ${\text{Cr}}_2{\text{O}}_3(s)+3{\text{H}}_2(g)⟶2\text{Cr}\left(s\right)+3{\text{H}}_2\text{O}\left(l\right)$

(d) $2\text{Al}\left(s\right)+{\text{Fe}}_2{\text{O}}_3(s)⟶{\text{Al}}_2{\text{O}}_3(s)+2\text{Fe}\left(s\right)$

Calculate the enthalpy of combustion of propane, C₃H₈(g), for the formation of H₂O(g) and CO₂(g). The enthalpy of formation of propane is −104 kJ/mol.

Both propane and butane are used as gaseous fuels. Which compound produces more heat per gram when burned?

Water gas, a mixture of H₂ and CO, is an important industrial fuel produced by the reaction of steam with red hot coke, essentially pure carbon: $\text{C}\left(s\right)+{\text{H}}_2\text{O}\left(g\right)⟶\text{CO}\left(g\right)+{\text{H}}_2(g).$

(a) Assuming that coke has the same enthalpy of formation as graphite, calculate $\text{Δ}{H}_{298}^{°}$ for this reaction.

(b) Methanol, a liquid fuel that could possibly replace gasoline, can be prepared from water gas and additional hydrogen at high temperature and pressure in the presence of a suitable catalyst: $2{\text{H}}_2(g)+\text{CO}(g)⟶{\text{CH}}_3\text{OH}(g).$

Under the conditions of the reaction, methanol forms as a gas. Calculate $\text{Δ}{H}_{298}^{°}$ for this reaction and for the condensation of gaseous methanol to liquid methanol.

(c) Calculate the heat of combustion of 1 mole of liquid methanol to H₂O(g) and CO₂(g).

From the data in Table 9.2, determine which of the following fuels produces the greatest amount of heat per gram when burned under standard conditions: CO(g), CH₄(g), or C₂H₂(g).

Ethanol, C₂H₅OH, is used as a fuel for motor vehicles, particularly in Brazil.

(a) Write the balanced equation for the combustion of ethanol to CO₂(g) and H₂O(g), and, using the data in Appendix G, calculate the enthalpy of combustion of 1 mole of ethanol.

(b) The density of ethanol is 0.7893 g/mL. Calculate the enthalpy of combustion of exactly 1 L of ethanol.

(c) Assuming that an automobile’s mileage is directly proportional to the heat of combustion of the fuel, calculate how much farther an automobile could be expected to travel on 1 L of gasoline than on 1 L of ethanol. Assume that gasoline has the heat of combustion and the density of n–octane, C₈H₁₈ $(\text{Δ}{H}_{\text{f}}^{°}=\mathrm{-208.4}\text{kJ/mol;}$ density = 0.7025 g/mL).

How much heat is produced when 1.25 g of chromium metal reacts with oxygen gas under standard conditions?

The oxidation of the sugar glucose, C₆H₁₂O₆, is described by the following equation:
${\text{C}}_6{\text{H}}_{12}{\text{O}}_6(s)+6{\text{O}}_2(g)⟶6{\text{CO}}_2(g)+6{\text{H}}_2\text{O}\left(l\right)\text{Δ}\text{H}=\mathrm{-2816}\text{kJ}$

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 g of glucose?

(b) How many Calories can be produced by the metabolism of 1.0 g of glucose?

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 °F; at this temperature and a pressure of 1 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 [C₃H₈: density, 0.5318 g/mL; enthalpy of combustion, 2219 kJ/mol for the formation of CO₂(g) and H₂O(l)] 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 g/L.

(f) How many kilowatt–hours (1 kWh = 3.6 $\times$ 10⁶ J) 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) C–C or $\text{C}=\text{C}$

(b) C–N or $\text{C}\equiv \text{N}$

(c)$\text{C}\equiv \text{O}$ or $\text{C}=\text{O}$

(d) H–F or H–Cl

(e) C–H or O–H

(f) C–N or C–O

Using the bond energies in Table 9.3, determine the approximate enthalpy change for each of the following reactions:

(a) ${\text{Cl}}_2(g)+3{\text{F}}_2(g)⟶2{\text{ClF}}_3(g)$

(b) ${\text{H}}_2\text{C}={\text{CH}}_2(g)+{\text{H}}_2(g)⟶{\text{H}}_3{\text{CCH}}_3(g)$

(c) $2{\text{C}}_2{\text{H}}_6(g)+7{\text{O}}_2(g)⟶4{\text{CO}}_2(g)+6{\text{H}}_2\text{O}\left(g\right)$

Draw a curve that describes the energy of a system with H and Cl atoms at varying distances. Then, find the minimum energy of this curve two ways (Figure 5.2).

(a) Use the bond energy found in Table 9.3 and Table 9.4 to calculate the energy for one single HCl bond (Hint: How many bonds are in a mole?)

(b) Use the enthalpy of reaction and the bond energies for H₂ and Cl₂ to solve for the energy of one mole of HCl bonds.

How does the bond energy of HCl(g) differ from the standard enthalpy of formation of HCl(g)?

Using the standard enthalpy of formation data in Appendix G, calculate the bond energy of the carbon-sulfur double bond in CS₂.

Using the standard enthalpy of formation data in Appendix G, determine which bond is stronger: the P–Cl bond in PCl₃(g) or in PCl₅(g)?

Use the bond energy to calculate an approximate value of ΔH for the following reaction. Which is the more stable form of FNO₂?

The lattice energy of LiF is 1023 kJ/mol, and the Li–F distance is 200.8 pm. NaF crystallizes in the same structure as LiF but with a Na–F distance of 231 pm. Which of the following values most closely approximates the lattice energy of NaF: 510, 890, 1023, 1175, or 4090 kJ/mol? Explain your choice.

The reaction of a metal, M, with a halogen, X₂, proceeds by an exothermic reaction as indicated by this equation: $\text{M}\left(s\right)+{\text{X}}_2(g)⟶{\text{MX}}_2(s).$ For each of the following, indicate which option will make the reaction more exothermic. Explain your answers.

(a) a large radius vs. a small radius for M⁺²

(b) a high ionization energy vs. a low ionization energy for M

(c) an increasing bond energy for the halogen

(d) a decreasing electron affinity for the halogen

(e) an increasing size of the anion formed by the halogen

Which compound in each of the following pairs has the larger lattice energy? Note: Mg²⁺ and Li⁺ have similar radii; O^2– and F^– have similar radii. Explain your choices.

(a) MgO or MgSe

(b) LiF or MgO

(c) Li₂O or LiCl

(d) Li₂Se or MgO

Which of the following compounds requires the most energy to convert one mole of the solid into separate ions?

(a) MgO

(b) SrO

(c) KF

(d) CsF

(e) MgF₂

The lattice energy of KF is 794 kJ/mol, and the interionic distance is 269 pm. The Na–F

distance in NaF, which has the same structure as KF, is 231 pm. Which of the following values is the closest approximation of the lattice energy of NaF: 682 kJ/mol, 794 kJ/mol, 924 kJ/mol, 1588 kJ/mol, or 3175 kJ/mol? Explain your answer.