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Question
Write the Nernst equation and emf of the following cell at 298 K:
\[\ce{Mg_{(s)} | Mg^{2+} (0.001 M) || Cu^{2+} (0.0001 M) | Cu_{(s)}}\]
Solution
The cell reaction is as follows:
\[\ce{Mg_{(s)} + Cu^{2+} (0.0001 M) -> Mg^{2+} (0.001 M) + Cu_{(s)}}\]
Hence, n = 2,
According to this the Nernst equation will be as follows –
`"E"_"cell" = "E"_"cell"^Θ - 0.059/2 log_10 (["Mg"^(2+)])/(["Cu"^(2+)])`
∴ `"E"_"cell" = ("E"_("Cu"^(2+)//"Cu")^Θ - "E"_("Mg"^(2+)//"Mg")^Θ) - 0.059/2 log_10 0.001/0.0001`
= `[+ 0.34 - (-2.37)] - 0.059/2 log_10 10`
= 2.71 − 0.0295
= 2.68 V
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