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Question: The correct Nernst equation for the given cell. \(Pt_{(s)}|Br_{2(l)}|Br^{- 1}(M)|H^{+}(M)|H_{2(g)}(...

The correct Nernst equation for the given cell.

Pt(s)∣Br2(l)∣Br−1(M)∣H+(M)∣H2(g)(1bar)∣Pt(s)Pt_{(s)}|Br_{2(l)}|Br^{- 1}(M)|H^{+}(M)|H_{2(g)}(1bar)|Pt_{(s)} is

A

Ecell=Eºcell−0.05912log⁡[Br2(l)][H2][H+]2[Br−]2E_{cell} = Eº_{cell} - \frac{0.0591}{2}\log\frac{\lbrack Br_{2(l)}\rbrack\lbrack H_{2}\rbrack}{\lbrack H^{+}\rbrack^{2}\lbrack Br^{-}\rbrack^{2}}

B

Ecell=Eºcell−0.05912log⁡[H+]2[Br−]2[Br2(l)][H2]E_{cell} = Eº_{cell} - \frac{0.0591}{2}\log\frac{\lbrack H^{+}\rbrack^{2}\lbrack Br^{-}\rbrack^{2}}{\lbrack Br_{2(l)}\rbrack\lbrack H_{2}\rbrack}

C

Ecell=Eºcell−0.05912log⁡[H+]2[H2][Br2(l)][Br−]2E_{cell} = Eº_{cell} - \frac{0.0591}{2}\log\frac{\lbrack H^{+}\rbrack^{2}\lbrack H_{2}\rbrack}{\lbrack Br_{2(l)}\rbrack\lbrack Br^{-}\rbrack^{2}}

D

Ecell=Eºcell−0.05912log⁡[Br2(l)][Br−]2[H+]2[H2]E_{cell} = Eº_{cell} - \frac{0.0591}{2}\log\frac{\lbrack Br_{2(l)}\rbrack\lbrack Br^{-}\rbrack^{2}}{\lbrack H^{+}\rbrack^{2}\lbrack H_{2}\rbrack}

Answer

Ecell=Eºcell−0.05912log⁡[Br2(l)][H2][H+]2[Br−]2E_{cell} = Eº_{cell} - \frac{0.0591}{2}\log\frac{\lbrack Br_{2(l)}\rbrack\lbrack H_{2}\rbrack}{\lbrack H^{+}\rbrack^{2}\lbrack Br^{-}\rbrack^{2}}

Explanation

Solution

At anode: 2Br−(M)→Br2(l)+2e−2Br^{-}(M) \rightarrow Br_{2(l)} + 2e^{-}

Atcathode2H+(M)+2e−→H2(1bar)Atcathode2H^{+}(M) + 2e^{-} \rightarrow H_{2}(1bar)

Netreaction:2H+(M)+2Br−(M)→Br2(l)+H2Netreaction:2H^{+}(M) + 2Br^{-}(M) \rightarrow Br_{2(l)} + H_{2}

Nernst equation for the given cell

Ecell=Eºcell−0.05912log⁡[Br2(l)][H2][H+]2[Br−]2E_{cell} = Eº_{cell} - \frac{0.0591}{2}\log\frac{\lbrack Br_{2(l)}\rbrack\lbrack H_{2}\rbrack}{\lbrack H^{+}\rbrack^{2}\lbrack Br^{-}\rbrack^{2}}