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Q.Represent the cell in which the following reaction takes place: Mg(s) + 2Ag⁺(0.0001M) → Mg²⁺(0.130M) + 2Ag(s). Calculate its E_cell; if E°_cell = 3.17 V.

Himachal HpboseHPBOSE Plus Two Board 2017Subjective· 2mImportance★★★★★
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Using the Nernst equation with n = 2, Ecell = E°cell − (0.0591/n) log Q ≈ 3.17 − 0.21 ≈ 2.96 V.

Cell representation (anode where oxidation occurs, written first; cathode where reduction occurs, written last; salt bridge shown by ||):

Mg(s)∣Mg2+(0.130 M)  ∣∣  Ag+(0.0001 M)∣Ag(s)\text{Mg}(s) \mid \text{Mg}^{2+}(0.130\,M) \;||\; \text{Ag}^+(0.0001\,M) \mid \text{Ag}(s)

Half reactions:

  • Anode (oxidation): Mg→Mg2++2e−\text{Mg} \rightarrow \text{Mg}^{2+} + 2e^-
  • Cathode (reduction, ×2): 2Ag++2e−→2Ag2\text{Ag}^+ + 2e^- \rightarrow 2\text{Ag}
  • Overall: Mg(s)+2Ag+(aq)→Mg2+(aq)+2Ag(s)\text{Mg}(s) + 2\text{Ag}^+(aq) \rightarrow \text{Mg}^{2+}(aq) + 2\text{Ag}(s), with n=2n = 2 electrons transferred.

Nernst equation:

Ecell=Ecell∘−0.0591nlog⁡[Mg2+][Ag+]2E_{cell} = E^{\circ}_{cell} - \dfrac{0.0591}{n}\log\dfrac{[\text{Mg}^{2+}]}{[\text{Ag}^+]^2}

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