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Chapter 19: Problem 74

Indicate whether \(\Delta G\) increases, decreases, or does not change when the partial pressure of \(\mathrm{H}_{2}\) is increased in each of the following reactions: (a) \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) (b) \(2 \mathrm{HBr}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g)\) (c) \(2 \mathrm{H}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)\)

Short Answer

Expert verified
For the given reactions, when the partial pressure of H鈧�(g) is increased: (a) 鈭咷 increases in the reaction N鈧�(g) + 3H鈧�(g) 鈫� 2NH鈧�(g). (b) 鈭咷 decreases in the reaction 2HBr(g) 鈫� H鈧�(g) + Br鈧�(g). (c) 鈭咷 increases in the reaction 2H鈧�(g) + C鈧侶鈧�(g) 鈫� C鈧侶鈧�(g).

Step by step solution

01

Recall the relationship between 鈭咷, Q, and K

The Gibbs free energy change (鈭咷) helps us understand whether a reaction is spontaneous or not. When 鈭咷 = 0, the system is at equilibrium, and when 鈭咷 < 0, the reaction is spontaneous in the forward direction. Recall the relationship between 鈭咷, reaction quotient (Q), and equilibrium constant (K) as: \[ 鈭咷 = RT \ln (\frac{Q}{K})\] where R is the gas constant, T is the temperature, Q is the reaction quotient, and K is the equilibrium constant.
02

Use Le Chatelier's Principle

According to Le Chatelier's principle, if a change is imposed on a system at equilibrium, the system will adjust itself to counteract that change and reestablish equilibrium. When the partial pressure of H鈧� is increased in the given reactions, the system will try to consume more H鈧� gas to reestablish equilibrium. Let's analyze the reactions to predict how 鈭咷 will change. (a) N鈧�(g) + 3H鈧�(g) 鈫� 2NH鈧�(g)
03

Analyze the forward direction of Reaction (a)

An increase in the partial pressure of H鈧�(g) will cause the system to produce more NH鈧�(g) to consume the excess H鈧�(g). This will increase the number of moles of the products and decrease the number of moles of the reactants, which leads to an increase in the reaction quotient (Q). According to 鈭咷 = RTln(Q/K), as Q increases, 鈭咷 will increase.
04

鈭咷 for Reaction (a)

For Reaction (a), an increase in the partial pressure of H鈧�(g) causes 鈭咷 to increase. (b) 2HBr(g) 鈫� H鈧�(g) + Br鈧�(g)
05

Analyze the forward direction of Reaction (b)

An increase in the partial pressure of H鈧�(g) will cause the system to consume more H鈧�(g) by shifting the equilibrium towards the reactants, which means it will convert the products back into the reactants. This will decrease the number of moles of the products and increase the number of moles of the reactants, which leads to a decrease in the reaction quotient (Q). According to 鈭咷 = RTln(Q/K), as Q decreases, 鈭咷 will decrease.
06

鈭咷 for Reaction (b)

For Reaction (b), an increase in the partial pressure of H鈧�(g) causes 鈭咷 to decrease. (c) 2H鈧�(g) + C鈧侶鈧�(g) 鈫� C鈧侶鈧�(g)
07

Analyze the forward direction of Reaction (c)

An increase in the partial pressure of H鈧�(g) will cause the system to produce more C鈧侶鈧�(g) to consume the excess H鈧�(g). This will increase the number of moles of the products and decrease the number of moles of the reactants, which leads to an increase in the reaction quotient (Q). According to 鈭咷 = RTln(Q/K), as Q increases, 鈭咷 will increase.
08

鈭咷 for Reaction (c)

For Reaction (c), an increase in the partial pressure of H鈧�(g) causes 鈭咷 to increase.

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Most popular questions from this chapter

The value of \(K_{a}\) for nitrous acid \(\left(\mathrm{HNO}_{2}\right)\) at \(25^{\circ} \mathrm{C}\) is given in Appendix D. (a) Write the chemical equation for the equilibrium that corresponds to \(K_{a} .\) (b) By using the value of \(K_{a}\) calculate \(\Delta G^{\circ}\) for the dissociation of nitrous acid in aqueous solution. (c) What is the value of \(\Delta G\) at equilibrium? (d) What is the value of \(\Delta G\) when \(\left[\mathrm{H}^{+}\right]=5.0 \times 10^{-2} \mathrm{M}\), \(\left[\mathrm{NO}_{2}^{-}\right]=6.0 \times 10^{-4} M\), and \(\left[\mathrm{HNO}_{2}\right]=0.20 \mathrm{M?}\)

A certain reaction is nonspontaneous at \(-25^{\circ} \mathrm{C}\). The entropy change for the reaction is \(95 \mathrm{~J} / \mathrm{K}\). What can you conclude about the sign and magnitude of \(\Delta H ?\)

(a) What is meant by calling a process irreversible? (b) After an irreversible process the system is restored to its original state. What can be said about the condition of the surroundings after the system is restored to its original state? (c) Under what conditions will the condensation of a liquid be an irreversible process?

The oxidation of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) in body tissue produces \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O} .\) In contrast, anaerobic decomposition, which occurs during fermentation, produces ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and \(\mathrm{CO}_{2} .\) (a) Using data given in Appendix \(\mathrm{C}\), compare the equilibrium constants for the following reactions: $$ \begin{aligned} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) & \rightleftharpoons 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \\ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) & \rightleftharpoons 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+2 \mathrm{CO}_{2}(g) \end{aligned} $$ (b) Compare the maximum work that can be obtained from these processes under standard conditions.

The conversion of natural gas, which is mostly methane, into products that contain two or more carbon atoms, such as ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\), is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen: $$ 2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g) $$ In practice, this reaction is carried out in the presence of oxygen: $$ 2 \mathrm{CH}_{4}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ (a) Using the data in Appendix \(C\), calculate \(K\) for these reactions at \(25^{\circ} \mathrm{C}\) and \(500^{\circ} \mathrm{C}\). (b) Is the difference in \(\Delta G^{\circ}\) for the two reactions due primarily to the enthalpy term \((\Delta H)\) or the entropy term \((-T \Delta S) ?\) (c) Explain how the preceding reactions are an example of driving a nonspontaneous reaction, as discussed in the "Chemistry and Life" box in Section 19.7. (d) The reaction of \(\mathrm{CH}_{4}\) and \(\mathrm{O}_{2}\) to form \(\mathrm{C}_{2} \mathrm{H}_{6}\) and \(\mathrm{H}_{2} \mathrm{O}\) must be carried out carefully to avoid a competing reaction. What is the most likely competing reaction?
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