KCET · Chemistry · Electrochemistry
Given: \( E_{M n^{+7}}^{0} \mid M n^{+2}=1.5 \mathrm{~V} \) and \( E_{M n^{+4}}^{0} \mid M n^{+2}=1.2 \mathrm{~V} \), then \( E_{M n^{+7}}^{0} \mid M n^{+4} \) is
- A \( 1.7 \mathrm{~V} \)
- B \( 2.1 \mathrm{~V} \)
- C \( 0.3 \mathrm{~V} \)
- D \( 0.1 \mathrm{~V} \)
Answer & Solution
Correct Answer
(A) \( 1.7 \mathrm{~V} \)
Step-by-step Solution
Detailed explanation
(A)
\(M n^{+7}+5 e^{-} \rightarrow M n^{2+}\)
\(\Delta G^{0}=-n \mathrm{FE}^{0} \Rightarrow \Delta \mathrm{G}^{0}=-5 \mathrm{~F} 1.5\)
\(M n^{+4}+2 e^{-} \rightarrow M n^{2+}\)
\(\Delta \mathrm{G}^{0}=-2 \mathrm{~F} 1.2\)
Required equation
\(M n^{+7}+3 e^{-} \rightarrow M n^{4+}\)
\(\Delta \mathrm{G}^{0}=-3 \mathrm{FE}^{0}\)
\(\therefore-3 \mathrm{FE}^{0}=-7.5 \mathrm{~F}+2.4 \mathrm{~F}\)
\(\therefore \mathrm{E}^{0}=1.7 \mathrm{~V}\)
\(M n^{+7}+5 e^{-} \rightarrow M n^{2+}\)
\(\Delta G^{0}=-n \mathrm{FE}^{0} \Rightarrow \Delta \mathrm{G}^{0}=-5 \mathrm{~F} 1.5\)
\(M n^{+4}+2 e^{-} \rightarrow M n^{2+}\)
\(\Delta \mathrm{G}^{0}=-2 \mathrm{~F} 1.2\)
Required equation
\(M n^{+7}+3 e^{-} \rightarrow M n^{4+}\)
\(\Delta \mathrm{G}^{0}=-3 \mathrm{FE}^{0}\)
\(\therefore-3 \mathrm{FE}^{0}=-7.5 \mathrm{~F}+2.4 \mathrm{~F}\)
\(\therefore \mathrm{E}^{0}=1.7 \mathrm{~V}\)
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