Chapter 5

The process illustrated in Figure \(\mathrm{P} 5.7\) takes place at constant pressure. a. Write a balanced equation for the process. b. Is \(w\) positive, negative, or zero for this reaction? c. Using data from Appendix 4, calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) for the formation of 1 mole of the product.

How are energy and work related?

Explain the difference between potential energy and kinetic energy.

Are kinetic energy and potential energy both state functions?

Explain the nature of the potential energy in the following: (a) the new battery for your remote control; (b) a gallon of gasoline; (c) the crest of a wave before it crashes onto shore.

Explain the kinetic energy in a stationary ice cube.

What is meant by the terms system and surroundings?

Do all exothermic processes that do work on the surroundings have the same sign for \(\Delta E ?\)

Why don't all endothermic processes that do work on the surroundings have the same sign for \(\Delta E ?\)

From the perspective of thermodynamics, why is the water in a pond warmer in August than in April?

Which of the following processes are exothermic, and which are endothermic? (a) a candle burns; (b) rubbing alcohol feels cold on the skin; (c) a supersaturated solution crystallizes, causing the temperature of the solution to rise

Which of the following processes are exothermic, and which are endothermic? (a) frost forms on a car window in the winter; (b) water condenses on a glass of ice water on a humid summer afternoon; (c) adding ammonium nitrate to water causes the temperature of the solution to decrease.

What happens to the internal energy of a liquid at its boiling point when it vaporizes?

What happens to the internal energy of a gas when it expands (with no heat flow)?

How much \(P-V\) work does a gas system do on its surroundings at a constant pressure of 1.00 atm if the volume of gas triples from \(250.0 \mathrm{mL}\) to \(750.0 \mathrm{mL}\) ? Express your answer in \(L \cdot\) atm and joules \((J)\).

An expanding gas does \(150.0 \mathrm{J}\) of work on its surroundings at a constant pressure of 1.01 atm. If the gas initially occupied \(68 \mathrm{mL},\) what is the final volume of the gas?

Calculate \(\Delta E\) for the following situations: a. \(q=120.0 \mathrm{J} ; w=-40.0 \mathrm{J}\) b. \(q=9.2 \mathrm{kJ} ; w=0.70 \mathrm{J}\) c. \(q=-625 \mathrm{J} ; w=-315 \mathrm{J}\)

Calculate \(\Delta E\) for a. the combustion of a gas that releases \(210.0 \mathrm{kJ}\) of heat to its surroundings and does \(65.5 \mathrm{kJ}\) of work on its surroundings. b. a chemical reaction that produces \(90.7 \mathrm{kJ}\) of heat but does no work on its surroundings.

Automobile air bags produce nitrogen gas from the reaction: $$2 \mathrm{NaN}_{3}(s) \rightarrow 2 \mathrm{Na}(s)+3 \mathrm{N}_{2}(g)$$ a. If \(2.25 \mathrm{g}\) of \(\mathrm{NaN}_{3}\) reacts to fill an air bag, how much \(P-V\) work will the \(\mathrm{N}_{2}\) do against an external pressure of 1.00 atm given that the density of nitrogen is \(1.165 \mathrm{g} / \mathrm{L}\) at \(20^{\circ} \mathrm{C} ?\) b. If the process releases \(2.34 \mathrm{kJ}\) of heat, what is \(\Delta E\) for the system?

Igniting gunpowder produces nitrogen and carbon dioxide gas that propels the bullet by the reaction: $$2 \mathrm{KNO}_{3}(s)+\frac{1}{8} \mathrm{S}_{8}(s)+3 \mathrm{C}(s) \rightarrow \mathrm{K}_{2} \mathrm{S}(s)+\mathrm{N}_{2}(g)+3 \mathrm{CO}_{2}(g)$$ a. If \(1.00 \mathrm{g}\) of \(\mathrm{KNO}_{3}\) reacts, how much \(P-V\) work will the gases do against an external pressure of 1.00 atm given that the densities of nitrogen and \(\mathrm{CO}_{2}\) are \(1.165 \mathrm{g} / \mathrm{L}\) and \(1.830 \mathrm{g} / \mathrm{L},\) respectively, at \(20^{\circ} \mathrm{C} ?\) b. If the reaction produces \(21.6 \mathrm{kJ}\) of heat, what is \(\Delta E\) for the system?

What is meant by an entbalpy change?

Describe the difference between an internal energy change \((\Delta E)\) and an enthalpy change \((\Delta H)\).

Which symbol, \(\Delta H_{\text {comb }}\) or \(\Delta H_{\text {fus }},\) refers to a physical change?

Which symbol, \(\Delta H_{\mathrm{f}}\) or \(\Delta H_{\text {fus }},\) refers to a chemical change?

Adding Drano to a clogged sink causes the drainpipe to get warm. What is the sign of \(\Delta H\) for this process?

Gypsum is the common name of calcium sulfate dihydrate \(\left(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\right) .\) When gypsum is heated to \(150^{\circ} \mathrm{C},\) it loses most of the water in its formula and forms plaster of Paris \(\left(\mathrm{CaSO}_{4} \cdot 0.5 \mathrm{H}_{2} \mathrm{O}\right):\) \(2\left(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\right)(s) \rightarrow 2\left(\mathrm{CaSO}_{4} \cdot 0.5 \mathrm{H}_{2} \mathrm{O}\right)(s)+3 \mathrm{H}_{2} \mathrm{O}(g)\) What is the sign of \(\Delta H\) for making plaster of Paris from gypsum?

A solid with metallic properties is formed when hydrogen gas is compressed under extremely high pressures. Predict the sign of the enthalpy change for the following reaction: $$\mathrm{H}_{2}(g) \rightarrow \mathrm{H}_{2}(s)$$

A simple "kitchen chemistry" experiment requires placing some vinegar in a soda bottle. A deflated balloon containing baking soda is stretched over the mouth of the bottle. Adding the baking soda to the vinegar starts the following reaction and inflates the balloon: \(\mathrm{NaHCO}_{3}(a q)+\mathrm{CH}_{3} \mathrm{COOH}(a q) \rightarrow\) $$\mathrm{CH}_{3} \mathrm{COONa}(a q)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(\ell)$$ If the contents of the bottle are considered the system, is work being done on the surroundings or on the system?

What is the difference between specific beat and molar beat capacity?

What happens to the molar heat capacity of a material if its mass is doubled? Is the same true for the specific heat?

Are the enthalpies of fusion and vaporization of a given substance usually the same?

An equal amount of energy is added to pieces of metal \(\mathrm{A}\) and metal \(\mathrm{B}\) that have the same mass. Why does the metal with the smaller specific heat reach the higher temperature?

Most automobile engines are cooled by water circulating through them and a radiator. However, the original Volkswagen Beetle had an air-cooled engine. Why might car designers choose water cooling over air cooling?

The reactor-core cooling systems in some nuclear power plants use liquid sodium as the coolant. Sodium has a thermal conductivity of \(1.42 \mathrm{J} /\) \((\mathrm{cm} \cdot \mathrm{s} \cdot \mathrm{K}),\) which is quite high compared with that of water \(\left.\left[6.1 \times 10^{-3} \mathrm{J} / \mathrm{cm} \cdot \mathrm{s} \cdot \mathrm{K}\right)\right] .\) The respective molar heat capacities are \(28.28 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})\) and \(75.31 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K}) .\) What is the advantage of using liquid sodium over water in this application?

How much energy is required to raise the temperature of \(100.0 \mathrm{g}\) of water from \(30.0^{\circ} \mathrm{C}\) to \(100.0^{\circ} \mathrm{C} ?\)

At an elevation where the boiling point of water is \(93^{\circ} \mathrm{C}, 100.0 \mathrm{g}\) of water at \(30^{\circ} \mathrm{C}\) absorbs \(290.0 \mathrm{kJ}\) of energy from a mountain climber's stove. Is this amount of energy sufficient to heat the water to its boiling point?

Damp clothes can prove fatal when outdoor temperatures drop (death by hypothermia). a. If the clothes you are wearing absorb \(1.00 \mathrm{kg}\) of water and then dry in a cold wind on Mount Washington, how much heat would your body lose during this process? \(c_{P, H, O}=75.3 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right),\) and \(\Delta H_{\mathrm{vap}, \mathrm{H}_{2} \mathrm{O}}=40.67 \mathrm{kJ} / \mathrm{mol}\) b. If the heat lost by your body is not replaced, what will the final temperature of your body be after the \(1.00 \mathrm{kg}\) of water has evaporated? Use your own body weight and assume that the specific heat of your body is \(4.25 \mathrm{J} / \mathrm{g}\) (Note that the specific heat is given in units of \(\mathrm{J} / \mathrm{g} .\) )

Which of the following would reach the higher temperature after \(10.00 \mathrm{g}\) of iron \(\left[c_{\mathrm{P}}=25.1 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]\) at \(150^{\circ} \mathrm{C}\) is added: 100 mL of water \(\left[d=1.00 \mathrm{g} / \mathrm{mL}, c_{\mathrm{P}}=75.3 \mathrm{J} /\right.\) \(\left.\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]\) or \(200 \mathrm{mL}\) of ethanol \(\left[\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right.\) \(\left.d=0.789 \mathrm{g} / \mathrm{mL}, c_{\mathrm{P}}=113.1 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right] ?\)

Exactly \(10.0 \mathrm{mL}\) of water at \(25.0^{\circ} \mathrm{C}\) is added to a hot iron skillet. All the water is converted into steam at \(100.0^{\circ} \mathrm{C}\) The mass of the pan is \(1.20 \mathrm{kg}\) and the molar heat capacity of iron is \(25.19 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) .\) What is the temperature change of the skillet?

Why is it necessary to know the heat capacity of a calorimeter?

Could an endothermic reaction be used to measure the heat capacity of a calorimeter?

If we replace the water in a bomb calorimeter with another liquid, why do we need to redetermine the heat capacity of the calorimeter?

When measuring the enthalpy of combustion of a very small amount of material, would you prefer to use a calorimeter having a heat capacity that is small or large? Explain your reasoning.

If you were designing a chemical cold pack, which of the following salts would you choose to provide the greatest drop in temperature per gram: \(\mathrm{NH}_{4} \mathrm{Cl}\) \(\left(\Delta H_{\text {soln }}=14.6 \mathrm{kJ} / \mathrm{mol}\right), \mathrm{NH}_{4} \mathrm{NO}_{3}\left(\Delta H_{\text {soln }}=25.7 \mathrm{kJ} / \mathrm{mol}\right),\) or \(\mathrm{NaNO}_{3}\left(\Delta H_{\mathrm{soln}}=20.4 \mathrm{kJ} / \mathrm{mol}\right) ?\)

Dissolving calcium hydroxide \(\left(\Delta H_{\text {soln }}=-16.2 \mathrm{kJ} / \mathrm{mol}\right)\) in water is an exothermic process. How much lithium hydroxide \(\left(\Delta H_{\text {soln }}=-23.6 \mathrm{kJ} / \mathrm{mol}\right)\) would be required to produce the same amount of energy as dissolving \(15.00 \mathrm{g}\) of \(\mathrm{Ca}(\mathrm{OH})_{2} ?\)

The standard enthalpy of combustion of benzoic acid (molar mass \(122 \mathrm{g} / \mathrm{mol}\) ) is \(-3225 \mathrm{kJ} / \mathrm{mol}\). Calculate the heat capacity of a bomb calorimeter if a temperature increase of \(2.16^{\circ} \mathrm{C}\) occurs on combusting \(0.500 \mathrm{g}\) of benzoic acid in the presence of excess \(\mathrm{O}_{2}\).

Burning \(1.43 \mathrm{g}\) of methane \(\left[\mathrm{CH}_{4}(g), \text { molar mass } 16.0 \mathrm{g} /\right.\) mol] with excess \(\mathrm{O}_{2}\) raised the temperature of \(250 \mathrm{g}\) of water in a bomb calorimeter from \(22^{\circ} \mathrm{C}\) to \(98^{\circ} \mathrm{C}\). Calculate the molar enthalpy of combustion of methane.

The complete combustion of \(1.200 \mathrm{g}\) of cinnamaldehyde \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}\right.\) one of the compounds in cinnamon) in a bomb calorimeter \(\left(C_{\text {calorimeter }}=3.640 \mathrm{kJ} /^{\circ} \mathrm{C}\right)\) produced an increase in temperature of \(12.79^{\circ} \mathrm{C} .\) Calculate the molar enthalpy of combustion of cinnamaldehyde \(\left(\Delta H_{\mathrm{comb}}\right)\) in kilojoules per mole of cinnamaldehyde.

The aromatic hydrocarbon cymene \(\left(\mathrm{C}_{10} \mathrm{H}_{14}\right)\) is found in nearly 100 spices and fragrances, including coriander, anise, and thyme. The complete combustion of \(1.608 \mathrm{g}\) of cymene in a bomb calorimeter \(\left(C_{\text {calorimeter }}=3.640 \mathrm{kJ} /^{\circ} \mathrm{C}\right)\) produced an increase in temperature of \(19.35^{\circ} \mathrm{C} .\) Calculate the molar enthalpy of combustion of cymene \(\left(\Delta H_{\mathrm{comb}}\right)\) in kilojoules per mole of cymene.

Phthalates, used to make plastics flexible, are among the most abundant industrial contaminants in the environment. Several have been shown to act as hormone mimics in humans by activating the receptors for estrogen, a female sex hormone. In characterizing the compounds completely, the value of \(\Delta H_{\text {comb }}\) for dimethyl phthalate \(\left(\mathrm{C}_{10} \mathrm{H}_{10} \mathrm{O}_{4}\right)\) was determined to be \(-4685 \mathrm{kJ} / \mathrm{mol}\). Assume that \(1.00 \mathrm{g}\) of dimethyl phthalate is combusted in a calorimeter whose heat capacity ( \(C_{\text {calorimeter }}\) ) is \(7.854 \mathrm{kJ} /^{\circ} \mathrm{C}\) at \(20.215^{\circ} \mathrm{C} .\) What is the final temperature of the calorimeter?