For the redox reaction Zn(s) + Cu^ 2+ (aq) rightleftharpoons Zn^ 2+ (aq) + Cu(s) at 300text K , given E^ 0 _ cell = 2text V , R = 8text J K ^ -1 text mol ^ -1 , and F = 96000text C mol ^ -1 , calculate the approximate equilibrium constant (K).

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EEJ MAIN Chemistry QUESTION #7111

Question 1

For the redox reaction $Zn(s) + Cu^{2+}(aq) \rightleftharpoons Zn^{2+}(aq) + Cu(s)$ at $300\text{ K}$, given $E^{0}_{cell} = 2\text{ V}$, $R = 8\text{ J K}^{-1}\text{ mol}^{-1}$, and $F = 96000\text{ C mol}^{-1}$, calculate the approximate equilibrium constant ($K$).

$e^{-80}$
$e^{-160}$
$e^{320}$
$e^{160}$✔️

Correct Answer Explanation

The relationship is $\Delta G^{0} = -nFE^{0} = -RT \ln K$. Here $n=2$.
$-2 \times 96000 \times 2 = -8 \times 300 \times \ln K$
$-384000 = -2400 \ln K$
$\ln K = \frac{384000}{2400} = 160$. Therefore, $K = e^{160}$.

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