Chapter 19

What is a perpetual motion machine? Can such a machine exist given the laws of thermodynamics?

What is a spontaneous process? Provide an example.

Explain the difference between the spontaneity of a reaction (which depends on thermodynamics) and the speed at which the reaction occurs (which depends on kinetics). Can a catalyst nspontaneous reaction spontaneous?

Why does the entropy of a gas increase when it expands into a vacuum?

Explain the difference between macrostates (external arrangements of particles) and microstates (internal arrangements of particles).

Based on its fundamental definition, explain why entropy is a measure of energy dispersion.

State the second law of thermodynamics. How does the second law explain why heat travels from a substance at higher temperature to one at lower temperature?

What happens to the entropy of a sample of matter when it changes state from a solid to a liquid? From a liquid to a gas?

Explain why water spontaneously freezes to form ice below \(0^{\circ} \mathrm{C}\) even though the entropy of the water decreases during the state transition. Why is the freezing of water not spontaneous above \(0^{\circ} \mathrm{C} ?\)

What is the significance of the change in Gibbs free energy ( \(\Delta G\) ) for a reaction?

Predict the spontaneity of a reaction (and the temperature dependence of the spontaneity) for each possible combination of signs for \(\Delta H\) and \(\Delta S\) (for the system). a. \(\Delta H\) negative, \(\Delta S\) positive b. \(\Delta H\) positive, \(\Delta S\) negative c. \(\Delta H\) negative, \(\Delta S\) negative d. \(\Delta H\) positive, \(\Delta S\) positive

State the third law of thermodynamics and explain its significance.

Why is the standard entropy of a substance in the gas state greater than its standard entropy in the liquid state?

How can you calculate the standard entropy change for a reaction from tables of standard entropies?

Explain the difference between \(\Delta G^{\circ}\) and \(\Delta G\).

How do you calculate the change in free energy for a reaction under nonstandard conditions?

How does the value of \(\Delta G^{\circ}\) for a reaction relate to the equilibrium constant for the reaction? What does a negative \(\Delta G^{\circ}\) for a reaction imply about \(K\) for the reaction? A positive \(\Delta G^{\circ} ?\)

Which of these processes is spontaneous? a. the combustion of natural gas b. the extraction of iron metal from iron ore c. a hot drink cooling to room temperature d. drawing heat energy from the ocean's surface to power a ship

Which of these processes are nonspontaneous? Are the nonspontaneous processes impossible? a. a bike going up a hill b. a meteor falling to Earth c. obtaining hydrogen gas from liquid water d. a ball rolling down a hill

Without doing any calculations, determine the sign of \(\Delta S_{\text {sys }}\) for each chemical reaction. a. \(2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)\) b. \(\mathrm{CH}_{2}=\mathrm{CH}_{2}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{CH}_{3}(g)\) c. \(\mathrm{Na}(s)+1 / 2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NaCl}(s)\) d. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\)

Calculate \(\Delta S_{\text {surr }}\) at the indicated temperature for each reaction. a. \(\Delta H_{\mathrm{rxn}}^{\circ}=-385 \mathrm{~kJ} ; 298 \mathrm{~K}\) b. \(\Delta H_{\mathrm{rxn}}^{\circ}=-385 \mathrm{~kJ} ; 77 \mathrm{~K}\) c. \(\Delta H_{\mathrm{rxn}}^{\circ}=+114 \mathrm{~kJ} ; 298 \mathrm{~K}\) d. \(\Delta H_{\mathrm{rxn}}^{\circ}=+114 \mathrm{~kJ} ; 77 \mathrm{~K}\)

Given the values of \(\Delta H_{\mathrm{rxn}}^{\circ}, \Delta S_{\mathrm{rxn}}^{\circ},\) and \(T,\) determine \(\Delta S_{\text {univ }}\) and predict whether or not each reaction is spontaneous. (Assume that all reactants and products are in their standard states.) a. \(\Delta H_{\mathrm{rxn}}^{\circ}=+115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}\) b. \(\Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=+263 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}\) c. \(\Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}\) d. \(\Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{~J} / \mathrm{K} ; T=615 \mathrm{~K}\)

Given the values of \(\Delta H_{\mathrm{rxn}},\) and \(T,\) determine \(\Delta S_{\mathrm{rxn}},\) and predict whether or not each reaction is spontaneous. (Assume that all reactants and products are in their standard states.) a. \(\Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}\) b. \(\Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{~J} / \mathrm{K} ; T=855 \mathrm{~K}\) c. \(\Delta H_{\mathrm{rxn}}^{\circ}=+95 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}\) d. \(\Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=+157 \mathrm{~J} / \mathrm{K} ; T=398 \mathrm{~K}\)

Calculate the free energy change for this reaction at \(25^{\circ} \mathrm{C}\). Is the reaction spontaneous? (Assume that all reactants and products are in their standard states.) $$\begin{array}{c}\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g) \\\\\Delta H_{\mathrm{rxn}}^{\circ}=-2217 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=101.1 \mathrm{~J} / \mathrm{K}\end{array}$$

Calculate the free energy change for this reaction at \(25^{\circ} \mathrm{C}\). Is the reaction spontaneous? (Assume that all reactants and products are in their standard states.) $$ \begin{array}{c} 2 \mathrm{Ca}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CaO}(s) \\ \Delta H_{\mathrm{rxn}}^{\circ}=-1269.8 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-364.6 \mathrm{~J} / \mathrm{K} \end{array} $$

How does the molar entropy of a substance change with increasing temperature?

What is the molar entropy of a pure crystal at \(0 \mathrm{~K} ?\) What is the significance of the answer to this question?

For each pair of substances, choose the one that you expect to have the higher standard molar entropy \(\left(S^{\circ}\right)\) at \(25^{\circ} \mathrm{C} .\) Explain your choices. a. \(\mathrm{CO}(g) ; \mathrm{CO}_{2}(g)\) b. \(\mathrm{CH}_{3} \mathrm{OH}(l) ; \mathrm{CH}_{3} \mathrm{OH}(g)\) c. \(\operatorname{Ar}(g) ; \mathrm{CO}_{2}(g)\) d. \(\mathrm{CH}_{4}(g) ; \mathrm{SiH}_{4}(g)\) e. \(\mathrm{NO}_{2}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}(g)\) f. \(\operatorname{NaBr}(s) ; \operatorname{NaBr}(a q)\)

For each pair of substances, choose the one that you expect to have the higher standard molar entropy \(\left(S^{\circ}\right)\) at \(25^{\circ} \mathrm{C} .\) Explain your choices. a. \(\mathrm{NaNO}_{3}(s) ; \mathrm{NaNO}_{3}(a q)\) b. \(\mathrm{CH}_{4}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{3}(g)\) c. \(\operatorname{Br}_{2}(l) ; \mathrm{Br}_{2}(g)\) d. \(\mathrm{Br}_{2}(g) ; \mathrm{F}_{2}(g)\) e. \(\mathrm{PCl}_{3}(g) ; \mathrm{PCl}_{5}(g)\) f. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}(g) ; \mathrm{SO}_{2}(g)\)

Rank each set of substances in order of increasing standard molar entropy \(\left(S^{\circ}\right)\). Explain your reasoning. a. \(\mathrm{NH}_{3}(g) ; \operatorname{Ne}(g) ; \mathrm{SO}_{2}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(g) ; \operatorname{He}(g)\) b. \(\mathrm{H}_{2} \mathrm{O}(s) ; \mathrm{H}_{2} \mathrm{O}(l) ; \mathrm{H}_{2} \mathrm{O}(g)\) c. \(\mathrm{CH}_{4}(g) ; \mathrm{CF}_{4}(g) ; \mathrm{CCl}_{4}(g)\)

Nomex, a condensation copolymer used by firefighters because of its flame- resistant properties, forms from isophthalic acid and \(m\) -aminoaniline. Draw the structure of the dimer. (Hint: Water is eliminated when the bond between the monomers forms.)

Determine \(\Delta G^{\circ}\) for the reaction: $$\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{CO}_{2}(g)$$ Use the following reactions with known \(\Delta G_{\mathrm{rxn}}^{\circ}\) values: $2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)$$$ \Delta G_{\mathrm{rxn}}^{\circ}=-742.2 \mathrm{~kJ} $$$\mathrm{CO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)$$$\Delta G_{\mathrm{rxn}}^{\circ}=-257.2 \mathrm{~kJ}$$

Calculate \(\Delta G_{\mathrm{rxn}}^{\circ}\) for the reaction: $$\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) $$Use the following reactions and given \(\Delta G_{\mathrm{rxn}}^{\circ}\) values: \(\mathrm{Ca}(s)+\mathrm{CO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CaCO}_{3}(s) \Delta G_{\mathrm{rxn}}^{\circ}=-734.4 \mathrm{~kJ}\) \(2 \mathrm{Ca}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CaO}(s) \quad \Delta G_{\mathrm{rxn}}^{\circ}=-1206.6 \mathrm{~kJ}\)

Consider the reaction: $$\begin{array}{r} \mathrm{I}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{ICl}(g) \\ K_{\mathrm{p}}=81.9 \text { at } 25{ }^{\circ} \mathrm{C} \end{array}$$ Calculate \(\Delta G_{\mathrm{rxn}}\) for the reaction at \(25^{\circ} \mathrm{C}\) under each of the following conditions: a. standard conditions b. at equilibrium c. \(P_{\mathrm{ICl}}=2.55 \mathrm{~atm} ; P_{\mathrm{I}_{2}}=0.325 \mathrm{~atm} ; P_{\mathrm{Cl}_{2}}=0.221 \mathrm{~atm}\)

The \(\Delta G\) for the freezing of \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(-10^{\circ} \mathrm{C}\) is \(-210 \mathrm{~J} / \mathrm{mol},\) and the heat of fusion of ice at this temperature is \(5610 \mathrm{~J} / \mathrm{mol}\). Find the entropy change of the universe when 1 mol of water freezes at \(-10^{\circ} \mathrm{C}\)

Given the data, calculate \(\Delta S_{\text {vap }}\) for each of the first four liquids. \(\left(\Delta S_{\text {vap }}=\Delta H_{\text {vap }} / T,\right.\) where \(T\) is in \(\left.K\right)\) $$ \begin{array}{llcc} \text { Compound } & \text { Name } & \text { BP }\left({ }^{\circ} \mathrm{C}\right) & \Delta H_{\text {vap }}(\mathrm{kJ} / \mathrm{mol} \text { ) at BP } \\ \mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O} & \text { Diethyl ether } & 34.6 & 26.5 \\ \hline \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O} & \text { Acetone } & 56.1 & 29.1 \\ \hline \mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O} & \text { Benzene } & 79.8 & 30.8 \\ \hline \mathrm{CHCl}_{3} & \text { Chloroform } & 60.8 & 29.4 \\ \hline \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} & \text { Ethanol } & 77.8 & 38.6 \\ \hline \mathrm{H}_{2} \mathrm{O} & \text { Water } & 100 & 40.7 \\ \hline \end{array} $$ All four values should be close to each other. Predict whether the last two liquids in the table have \(\Delta S_{\text {vap }}\) in this same range. If not, predict whether it is larger or smaller and explain. Verify your prediction.

Which statement is true? a. A spontaneous reaction is always a fast reaction. b. A spontaneous reaction is always a slow reaction. c. The spontaneity of a reaction is not necessarily related to the speed of a reaction.

Which statement is true? a. A reaction in which the entropy of the system increases can be spontaneous only if it is exothermic. b. A reaction in which the entropy of the system increases can be spontaneous only if it is endothermic. c. A reaction in which the entropy of the system decreases can be spontaneous only if it is exothermic.

The free energy change of the reaction \(\mathrm{A}(g) \longrightarrow \mathrm{B}(g)\) is zero under certain conditions. The standard free energy change of the reaction is \(-42.5 \mathrm{~kJ}\). Which statement must be true about the reaction? a. The concentration of the product is greater than the concentration of the reactant. b. The reaction is at equilibrium. c. The concentration of the reactant is greater than the concentration of the product.

Imagine that you roll two dice. Write down all the possible rolls that sum to \(2 .\) Write all the possible rolls that sum to \(12 .\) Write all the possible rolls that sum to 7 . Which configuration has the greatest entropy: \(2,12,\) or \(7 ?\)

If you roll 1 million dice, what will be the average of all the dice? If there is a room with 1 million dice and they all have a 1 on the top face, and there is an earthquake strong enough to roll dice around, what is the likelihood that after the earthquake all the top faces will sum to 1 million? To 6 million? How does this thought experiment illustrate the second law of thermodynamics?

Not all processes in which the system increases in entropy are spontaneous. How can this observation be consistent with the second law? Provide an example and explain your answer in complete sentences.