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Chapter 2: Problem 50

A sample of \(\mathrm{H}_{2} \mathrm{S}\) gas is placed in an evacuated, sealed container and heated until the following decomposition reaction occurs at \(1000 \mathrm{K} :\) $$2 \mathrm{H}_{2} \mathrm{S}(g) \rightarrow 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \qquad K_{\mathrm{c}}=1.0 \times 10^{-6}$$ As the reaction progresses at a constant temperature of 1000 K, how does the value for the Gibbs free energy constant for the reaction change? (A) It stays constant. (B) It increases exponentially. (C) It increases linearly. (D) It decreases exponentially.

Short Answer

Expert verified
The Gibbs free energy constant for the reaction stays constant. Hence, the correct answer is (A).

Step by step solution

01

Identify the formula

Identify the correct equation that links Gibb's free energy, the temperature and the equilibrium constant. The appropriate equation is \(\Delta G^\circ = -RT \ln K\)
02

Examine the temperature

Examine the statement in the question, 'the reaction progresses at a constant temperature of 1000 K'. This means the variable \(T\) in the equation is constant.
03

Examine the equilibrium constant

One must also note the equilibrium constant \(K_c\), defined as \(K_c = 1.0 \times 10^{-6}\). This value does not change as the reaction progresses, since it is a function of the reaction and temperature, both of which are constant.
04

Conclusion

Since both \(T\) and \(K_c\) are constant, \(\Delta G^\circ \) must also remain constant. The variation in Gibbs free energy is a direct result of changes in either \(T\) or \(K_c\), and as they are continual, so too is \(\Delta G^\circ \).

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Most popular questions from this chapter

A sample of solid \(\mathrm{MgCl}_{2}\) would be most soluble in which of the following solutions? (A) \(\operatorname{LiOH}(a q)\) (B) \(\operatorname{CBr}_{4}(a q)\) (C) \(\operatorname{Mg}\left(\mathrm{NO}_{3}\right)_{2}(a q)\) (D) \(\mathrm{AlCl}_{3}(a q)\)

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