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Chapter 19: Problem 73

Explain qualitatively how \(\Delta G\) changes for each of the following reactions as the partial pressure of \(\mathrm{O}_{2}\) is increased: (a) \(2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)\) (b) \(2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)\) (c) \(2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)\)

Short Answer

Expert verified
As the partial pressure of \(\mathrm{O}_{2}\) increases: (a) \(\Delta G\) for reaction \(2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)\) becomes more negative, making the forward reaction more spontaneous. (b) \(\Delta G\) for reaction \(2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)\) becomes less negative or more positive, making the forward reaction less spontaneous and the reverse reaction more spontaneous. (c) \(\Delta G\) for reaction \(2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3\mathrm{O}_{2}(g)\) becomes less negative or more positive, making the forward reaction less spontaneous and the reverse reaction more spontaneous.

Step by step solution

01

Identify the change in partial pressure of \(\mathrm{O}_{2}\)

For this reaction, an increase in the partial pressure of \(\mathrm{O}_{2}\) will cause the concentration of one of the reactants to increase.
02

Determine the effect on reaction quotient \(Q\)

As the partial pressure of \(\mathrm{O}_{2}\) increases, the reaction quotient \(Q\) increases, because \(Q = \frac{[\mathrm{CO}_2]^2}{[\mathrm{CO}]^2[\mathrm{O}_2]}\). The increase in partial pressure of \(\mathrm{O}_{2}\) will cause \(Q\) to decrease since the denominator will become larger.
03

Determine the effect on the change in free energy \(\Delta G\)

According to the relationship \(\Delta G=\Delta G^{o}+RT \ln{Q}\), when \(Q\) decreases, \(\Delta G\) becomes more negative. So, as the partial pressure of \(\mathrm{O}_{2}\) is increased, \(\Delta G\) for the reaction will become more negative, indicating that the forward reaction will be increasingly spontaneous. (b) \(2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)\)
04

Identify the change in partial pressure of \(\mathrm{O}_{2}\)

For this reaction, an increase in the partial pressure of \(\mathrm{O}_{2}\) will cause the concentration of one of the products to increase.
05

Determine the effect on reaction quotient \(Q\)

As the partial pressure of \(\mathrm{O}_{2}\) increases, the reaction quotient \(Q = \frac{[\mathrm{O}_2]}{[\mathrm{H}_2\mathrm{O}_2]^2}\) will increase, since the numerator will become larger.
06

Determine the effect on the change in free energy \(\Delta G\)

According to the relationship \(\Delta G=\Delta G^{o}+RT \ln{Q}\), when \(Q\) increases, \(\Delta G\) becomes less negative or more positive. So, as the partial pressure of \(\mathrm{O}_{2}\) is increased, \(\Delta G\) for the reaction will become less negative or more positive, making the forward reaction less spontaneous and the reverse reaction more spontaneous. (c) \(2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3\mathrm{O}_{2}(g)\)
07

Identify the change in partial pressure of \(\mathrm{O}_{2}\)

For this reaction, an increase in the partial pressure of \(\mathrm{O}_{2}\) will cause the concentration of one of the products to increase.
08

Determine the effect on reaction quotient \(Q\)

As the partial pressure of \(\mathrm{O}_{2}\) increases, the reaction quotient \(Q = \frac{[\mathrm{O}_2]^3}{[\mathrm{KClO}_3]^2}\) will increase since the numerator will become larger.
09

Determine the effect on the change in free energy \(\Delta G\)

According to the relationship \(\Delta G=\Delta G^{o}+RT \ln{Q}\), when \(Q\) increases, \(\Delta G\) becomes less negative or more positive. So, as the partial pressure of \(\mathrm{O}_{2}\) is increased, \(\Delta G\) for the reaction will become less negative or more positive, making the forward reaction less spontaneous and the reverse reaction more spontaneous.

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Most popular questions from this chapter

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) Express the second law of thermodynamics in words. (b) If the entropy of the system increases during a reversible process, what can you say about the entropy change of the surroundings? (c) In a certain spontaneous process the system undergoes an entropy change, \(\Delta S=42 \mathrm{~J} / \mathrm{K} .\) What can you conclude about \(\Delta S_{\text {surr }} ?\)

Using data from Appendix \(C\), calculate \(\Delta G^{\circ}\) for the following reactions. Indicate whether each reaction is spontaneous under standard conditions. (a) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (b) \(\mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{NO}(g)\) (c) \(6 \mathrm{Cl}_{2}(g)+2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \longrightarrow 4 \mathrm{FeCl}_{3}(s)+3 \mathrm{O}_{2}(g)\) (d) \(\mathrm{SO}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{S}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)\)

Consider the vaporization of liquid water to steam at a pressure of 1 atm. (a) Is this process endothermic or exothermic? (b) In what temperature range is it a spontaneous process? (c) In what temperature range is it a nonspontaneous process? (d) At what temperature are the two phases in equilibrium?

(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?
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