Chapter 9

How are energy and work related?

Explain the difference between potential energy and kinetic energy in molecules.

Explain what is meant by a state function.

Are kinetic energy and potential energy both state functions?

If the potential energy of a particle increases as it is moved away from another particle, do the two particles attract or repel each other?

Describe two ways to increase the internal energy of a gas sample.

How can the product of pressure and volume ( \(P-V\) work) have energy units?

Why is there a negative sign in front of the \(P \Delta V\) term in \(\Delta E=q-P \Delta V ?\)

Which of the following processes are exothermic, and which are endothermic? a. Molten aluminum solidifies. b. Rubbing alcohol evaporates from the skin. c. Fog forms over San Francisco Bay.

Which of the following processes are exothermic, and which are endothermic? a. Ice cubes solidify in the freezer. b. Ice cubes in a frost-free freezer slowly lose mass. c. Dew forms on a lawn overnight.

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 \(\mathrm{L} \cdot\) atm and joules \((\mathrm{J})\).

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 \(\Delta E\) when a. \(q=100.0 \mathrm{J} ; w=-50.0 \mathrm{J}\) b. \(q=6.2 \mathrm{kJ} ; w=0.70 \mathrm{L} \cdot\) atm c. \(q=-615 \mathrm{kJ} ; w=-3.25\) kilowatt-hours \((1 \mathrm{kWh}=\) \(3600 \mathrm{kJ})\)

Calculate \(\Delta E\) for a system that absorbs \(726 \mathrm{kJ}\) of heat from its surroundings and does \(526 \mathrm{kJ}\) of work on its surroundings.

Calculate \(\Delta E\) for 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.

Calculate \(\Delta E\) for a chemical reaction that releases \(90.7 \mathrm{kJ}\) of heat to its surroundings but does no work on them.

What is meant by an entbalpy change?

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

Why is the sign of \(\Delta H\) negative for an exothermic process?

What happens to the magnitude and sign of the enthalpy change when a process is reversed?

Adding Drano to a clogged sink causes the drainpipe to get warm. What is the sign of \(\Delta H\) when Drano dissolves in water?

Breaking the small pouch of water inside a chemical cold pack containing ammonium nitrate activates the pack, which is used by sports trainers for injured athletes. What is the sign of \(\Delta H\) for the process taking place in the cold pack?

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

In a simple "kitchen chemistry" experiment, some vinegar is poured into an empty soda bottle. A deflated balloon containing baking soda is stretched over the mouth of the bottle. Holding up the balloon and shaking it allows the baking soda to fall into the vinegar, which starts the following reaction and inflates the balloon: $$\begin{aligned} \mathrm{NaHCO}_{3}(a q)+\mathrm{CH}_{3} \mathrm{COOH}(a q) \rightarrow & \\ & \mathrm{CH}_{3} \mathrm{COONa}(a q)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(\ell) \end{aligned}$$ If the contents of the bottle are the system, is work being done on the surroundings or on the system?

Which has more heat capacity: one liter of water or one cubic meter of water? Which has more molar heat capacity?

Why is the heat of vaporization of water so much greater than its heat of fusion?

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 \(\left[6.1 \times 10^{-3} \mathrm{J} /(\mathrm{cm} \cdot \mathrm{s} \cdot \mathrm{K})\right] .\) The respective molar heat capacities are \(28.3 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})\) and \(75.3 \mathrm{kJ} /(\mathrm{mol} \cdot \mathrm{K})\). What is the advantage of using liquid sodium over water in this application?

How much heat must be absorbed by \(100.0 \mathrm{g}\) of water to raise its temperature from \(30.0^{\circ} \mathrm{C}\) to \(100.0^{\circ} \mathrm{C} ?\)

At an elevation where the boiling point of water is \(93^{\circ} \mathrm{C}\) \(1.33 \mathrm{kg}\) of water at \(30^{\circ} \mathrm{C}\) absorbs \(290.0 \mathrm{kJ}\) from a mountain climber's stove. Is this amount of thermal energy sufficient to heat the water to its boiling point?

Use the following data to sketch a heating curve for one mole of methanol. Start the curve at \(-100^{\circ} \mathrm{C}\) and end it at \(100^{\circ} \mathrm{C}\). $$\begin{array}{ll}\hline \text { Boiling point } & 65^{\circ} \mathrm{C} \\\\\hline \text { Melting point } & -94^{\circ} \mathrm{C} \\\\\hline \text { Heat of vaporization } & 35.3 \mathrm{kJ} / \mathrm{mol} \\\\\hline \text { Heat of fusion }\left(\Delta \mathrm{H}_{\text {fus }}\right) & 3.18 \mathrm{kJ} / \mathrm{mol} \\\\\hline \text { Molar heat capacity }(\ell) & 81.1 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\\\\hline \text { Molar heat capacity }(g) & 43.9 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\\\\hline \text { Molar heat capacity }(\mathrm{s}) & 48.7 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\\\\hline\end{array}$$

Use the following data to sketch a heating curve for 1.5 moles of acetic acid. Start the curve at \(+16^{\circ} \mathrm{C}\) and end it at \(130^{\circ} \mathrm{C}\). $$\begin{array}{ll}\hline \text { Boiling point } & 118^{\circ} \mathrm{C} \\\\\hline \text { Melting point } & 16^{\circ} \mathrm{C} \\\\\hline \text { Heat of vaporization } & 23.7 \mathrm{kJ} / \mathrm{mol} \\\\\hline \text { Heat of fusion }\left(\Delta H_{\text {fus }}\right) & 11.7 \mathrm{kJ} / \mathrm{mol} \\\\\hline \text { Molar heat capacity }(\ell) & 123.1 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\\\\hline \text { Molar heat capacity }(g) & 63.4 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\\\\hline\end{array}$$

During a strenuous workout, an athlete generates \(233 \mathrm{kJ}\) of thermal energy. What mass of water would have to evaporate from the athlete's skin to dissipate this energy?

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

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

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

When measuring the heat 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?

The complete combustion of \(1.200 \mathrm{g}\) of cinnamaldehyde \((\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O},\) 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 \(12.79^{\circ} \mathrm{C} .\) How much thermal energy is produced during the complete combustion of one mole of cinnamaldehyde?

Spices 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 \(19.35^{\circ} \mathrm{C} .\) How much thermal energy is produced during the complete combustion of one mole of cymene?

Hormone Mimics Phthalates that are 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. Combustion of one mole of one of these compounds, dimethyl phthalate \(\left(\mathrm{C}_{10} \mathrm{H}_{10} \mathrm{O}_{4}\right),\) produces \(4685 \mathrm{kJ}\) of thermal energy. If \(1.00 \mathrm{g}\) of dimethyl phthalate is combusted in a bomb calorimeter whose heat capacity ( \(C_{\text {calorimeter }}\) ) is \(7.854 \mathrm{kJ} /^{\circ} \mathrm{C},\) what is the change in temperature of the calorimeter?

The flavor of anise is due to anethole, a compound with the molecular formula \(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}\) Combustion of one mole of anethole produces \(5541 \mathrm{kJ}\) of thermal energy. If \(0.950 \mathrm{g}\) of anethole is combusted in a bomb calorimeter whose heat capacity ( \(C_{\text {calorimeter }}\) ) is \(7.854 \mathrm{kJ} /^{\circ} \mathrm{C},\) what is the change in temperature of the calorimeter?

A coffee-cup calorimeter contains \(100.0 \mathrm{mL}\) of \(1.00 M \mathrm{HCl}\) at \(22.4^{\circ} \mathrm{C} .\) When \(0.243 \mathrm{g}\) of \(\mathrm{Mg}\) metal is added to the acid, the ensuing reaction: $$\mathrm{Mg}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{MgCl}_{2}(a q)+\mathrm{H}_{2}(g) \quad \Delta H_{\mathrm{rxn}}=?$$ causes the temperature of the solution to increase to \(33.4^{\circ} \mathrm{C}\) What is the value of \(\Delta H_{\mathrm{rxn}}\) of the reaction? Assume the density of the solution is \(1.01 \mathrm{g} / \mathrm{mL}\) and that its specific heat is \(4.18 \mathrm{J} /\left(\mathrm{g} \cdot^{\circ} \mathrm{C}\right)\).

When \(4.00 \mathrm{g} \mathrm{NH}_{4} \mathrm{NO}_{3}(\mathscr{M}=80.04 \mathrm{g} /\)mol) - the active ingredient in some chemical cold packs is dissolved in \(96.0 \mathrm{g} \mathrm{H}_{2} \mathrm{O},\) the temperature of the resulting solution is \(3.07^{\circ} \mathrm{C}\) colder than the water and ammonium nitrate were before they were mixed together. What is the value of \(\Delta H\) for the following dissolution process? $$\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \rightarrow \mathrm{NH}_{4} \mathrm{NO}_{3}(a q) \quad \Delta H=?$$

How is Hess's law consistent with the law of conservation of energy?

Would Hess's law be valid if enthalpy were not a state function? Why or why not?

Use the \(\Delta H_{\mathrm{rxn}}^{\circ}\) values of the following reactions: $$\begin{aligned}2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) & \rightarrow 2 \mathrm{SO}_{3}(g) & \Delta H_{\mathrm{rsn}}^{\circ} &=-196 \mathrm{kJ} \\\\\frac{1}{4} \mathrm{S}_{8}(s)+3 \mathrm{O}_{2}(g) & \rightarrow 2 \mathrm{SO}_{3}(g) & \Delta H_{\mathrm{rxn}}^{\circ} &=-790 \mathrm{kJ}\end{aligned}$$ to calculate the \(\Delta H_{\mathrm{rxn}}^{\circ}\) value of this reaction: $$\frac{1}{8} \mathrm{S}_{\mathrm{g}}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{SO}_{2}(g) \quad \Delta H_{\mathrm{ran}}^{\circ}=?$$

The destruction of the ozone layer by chlorofluorocarbons (CFCs) can be described by the following reactions: $$\begin{aligned}\mathrm{ClO}(g)+\mathrm{O}_{3}(g) & \rightarrow \mathrm{Cl}(g)+2 \mathrm{O}_{2}(g) & \Delta H_{\mathrm{rxn}}^{\circ} &=-29.90 \mathrm{kJ} \\\2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g) & & \Delta H_{\mathrm{rxn}}^{\circ} &=+24.18 \mathrm{kJ}\end{aligned}$$ Use the preceding \(\Delta H_{\mathrm{rxn}}^{\circ}\) values to determine the value of the standard heat of reaction for this reaction: $$\mathrm{Cl}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=?$$