For a M g ? M g 2 + ( a q ) ? A g + ( a q ) ? A g the correct Nernst Equation is: [2025]

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Q.
For a $M g ∣ M g^{2 +} (a q) ∥ A g^{+} (a q) ∣ A g$ the correct Nernst Equation is: [2025]

1 $E_{cell} = E_{cell}^{\circ} + \frac{R T}{2 F} \ln \frac{{[{Ag}^{+}]}^{2}}{[{Mg}^{2 +}]}$

2 $E_{cell} = E_{cell}^{\circ} - \frac{R T}{2 F} \ln \frac{[{Ag}^{+}]}{[{Mg}^{2 +}]}$

3 $E_{cell} = E_{cell}^{\circ} - \frac{R T}{2 F} \ln \frac{[{Mg}^{2 +}]}{[{Ag}^{+}]}$

4 $E_{cell} = E_{cell}^{\circ} - \frac{R T}{2 F} \ln \frac{{[{Ag}^{+}]}^{2}}{[{Mg}^{2 +}]}$

Ans.
(1)

Cell reaction: $Mg (s) + 2 {Ag}^{+} (a q) \to {Mg}^{2 +} (a q) + 2 Ag (s)$

Nernst equation: $E_{cell} = E_{cell}^{\circ} - \frac{R T}{n F} \ln Q$

$E_{cell} = E_{cell}^{\circ} - \frac{R T}{2 F} \ln \frac{[{Mg}^{2 +}]}{{[{Ag}^{+}]}^{2}}$

$E_{cell} = E_{cell}^{\circ} + \frac{R T}{2 F} \ln \frac{{[{Ag}^{+}]}^{2}}{[{Mg}^{2 +}]}$

Solution

Q.
For a $M g ∣ M g^{2 +} (a q) ∥ A g^{+} (a q) ∣ A g$ the correct Nernst Equation is: [2025]

1 $E_{cell} = E_{cell}^{\circ} + \frac{R T}{2 F} \ln \frac{{[{Ag}^{+}]}^{2}}{[{Mg}^{2 +}]}$

2 $E_{cell} = E_{cell}^{\circ} - \frac{R T}{2 F} \ln \frac{[{Ag}^{+}]}{[{Mg}^{2 +}]}$

3 $E_{cell} = E_{cell}^{\circ} - \frac{R T}{2 F} \ln \frac{[{Mg}^{2 +}]}{[{Ag}^{+}]}$

4 $E_{cell} = E_{cell}^{\circ} - \frac{R T}{2 F} \ln \frac{{[{Ag}^{+}]}^{2}}{[{Mg}^{2 +}]}$

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Solution

Q. For a Mg∣Mg2+(aq)∥Ag+(aq)∣Ag the correct Nernst Equation is: [2025]

1 Ecell=Ecell∘+RT2Fln[Ag+]2[Mg2+]

2 Ecell=Ecell∘-RT2Fln[Ag+][Mg2+]

3 Ecell=Ecell∘-RT2Fln[Mg2+][Ag+]

4 Ecell=Ecell∘-RT2Fln[Ag+]2[Mg2+]

Ans. (1) Cell reaction: Mg(s)+2Ag+(aq)→Mg2+(aq)+2Ag(s) Nernst equation: Ecell=Ecell∘-RTnFlnQ Ecell=Ecell∘-RT2Fln[Mg2+][Ag+]2 Ecell=Ecell∘+RT2Fln[Ag+]2[Mg2+]

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Q.
For a $M g ∣ M g^{2 +} (a q) ∥ A g^{+} (a q) ∣ A g$ the correct Nernst Equation is: [2025]

1 $E_{cell} = E_{cell}^{\circ} + \frac{R T}{2 F} \ln \frac{{[{Ag}^{+}]}^{2}}{[{Mg}^{2 +}]}$

2 $E_{cell} = E_{cell}^{\circ} - \frac{R T}{2 F} \ln \frac{[{Ag}^{+}]}{[{Mg}^{2 +}]}$

3 $E_{cell} = E_{cell}^{\circ} - \frac{R T}{2 F} \ln \frac{[{Mg}^{2 +}]}{[{Ag}^{+}]}$

4 $E_{cell} = E_{cell}^{\circ} - \frac{R T}{2 F} \ln \frac{{[{Ag}^{+}]}^{2}}{[{Mg}^{2 +}]}$