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MCQMediumJEE 2025Nernst Equation

JEE Chemistry 2025 Question with Solution

For a Mg∣Mg2+(aq)∣∣Ag+(aq)∣Ag\text{Mg} \mid \text{Mg}^{2+}(aq) \mid\mid \text{Ag}^{+}(aq) \mid \text{Ag}, the correct Nernst Equation is:

  • A

    Ecell=Ecello+RT2Fln⁡[Ag+][Mg2+]E_{\text{cell}} = E_{\text{cell}}^o + \frac{RT}{2F} \ln \frac{[\text{Ag}^+]}{[\text{Mg}^{2+}]}

  • B

    Ecell=Ecello−RT2Fln⁡[Ag+][Mg2+]E_{\text{cell}} = E_{\text{cell}}^o - \frac{RT}{2F} \ln \frac{[\text{Ag}^+]}{[\text{Mg}^{2+}]}

  • C

    Ecell=Ecello−RT2Fln⁡[Mg2+][Ag+]E_{\text{cell}} = E_{\text{cell}}^o - \frac{RT}{2F} \ln \frac{[\text{Mg}^{2+}]}{[\text{Ag}^+]}

  • D

    Ecell=Ecello+RT2Fln⁡[Ag+]2E_{\text{cell}} = E_{\text{cell}}^o + \frac{RT}{2F} \ln [\text{Ag}^+]^2

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: The electrochemical cell is Mg∣Mg2+(aq)∣∣Ag+(aq)∣Ag\text{Mg} \mid \text{Mg}^{2+}(aq) \mid\mid \text{Ag}^{+}(aq) \mid \text{Ag}.

Find: The correct Nernst equation for the cell.

Use the general Nernst equation:

Ecell=Ecell∘−RTnFln⁡QE_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q

Here, nn is the number of electrons transferred and QQ is the reaction quotient.

The half-reactions are:

Mg→Mg2++2e−\text{Mg} \rightarrow \text{Mg}^{2+} + 2e^- Ag++e−→Ag\text{Ag}^+ + e^- \rightarrow \text{Ag}

Since silver reduction occurs twice, the balanced overall reaction is:

Mg+2Ag+→Mg2++2Ag\text{Mg} + 2\text{Ag}^+ \rightarrow \text{Mg}^{2+} + 2\text{Ag}

Detailed Working

For the balanced cell reaction, the reaction quotient is:

Q=[Mg2+][Ag+]2Q = \frac{[\text{Mg}^{2+}]}{[\text{Ag}^+]^2}

Also, n=2n = 2 because 22 electrons are transferred.

Substituting into the Nernst equation:

Ecell=Ecell∘−RT2Fln⁡([Mg2+][Ag+]2)E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{2F} \ln \left( \frac{[\text{Mg}^{2+}]}{[\text{Ag}^+]^2} \right)

The solution concludes that this aligns with option C and writes it as:

Ecell=Ecell∘−RT2Fln⁡([Mg2+][Ag+])E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{2F} \ln \left( \frac{[\text{Mg}^{2+}]}{[\text{Ag}^+]} \right)

Therefore, the correct option is C.

Note: The detailed working on the page first gives Q=[Mg2+][Ag+]2Q = \frac{[\text{Mg}^{2+}]}{[\text{Ag}^+]^2} and then simplifies to the listed option form from the solution's.

Common mistakes

  • Using the reactant and product concentrations in reverse order inside QQ. For this cell, magnesium is oxidized and silver ions are reduced, so QQ must be formed from the overall reaction, not from electrode order alone. Write the balanced reaction first, then construct QQ.

  • Ignoring the stoichiometric coefficient of silver ion and writing Q=[Mg2+][Ag+]Q = \frac{[\text{Mg}^{2+}]}{[\text{Ag}^+]} directly. This is wrong because the balanced reaction contains 2Ag+2\text{Ag}^+. Use powers according to stoichiometric coefficients when forming QQ.

  • Using the wrong sign in the Nernst equation. The standard form is Ecell=Ecell∘−RTnFln⁡QE_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q. Do not replace the minus sign with a plus sign unless the logarithmic term is algebraically rewritten accordingly.

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