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Q.Consider the following reaction : Zn(s)+Ag2O(s)+H2O(l)→Zn2+(aq)+2Ag(s)+2OH−(aq)Zn(s) + Ag_2O(s) + H_2O(l) \rightarrow Zn^{2+}(aq) + 2Ag(s) + 2OH^-(aq) Given : EAg+/Ago=0.80E^o_{Ag^+/Ag} = 0.80 V, EZn2+/Zno=−0.76E^o_{Zn^{2+}/Zn} = -0.76 V, 1 F=965001\,F = 96500 C mol−1^{-1} ΔrGo\Delta_r G^o for the above reaction is : (A) −301.080-301.080 kJ mol−1^{-1} (B) +310.080+310.080 kJ mol−1^{-1} (C) −326.070-326.070 kJ mol−1^{-1} (D) −375.060-375.060 kJ mol−1^{-1}

CBSECBSE Class XII Board 2026MCQ· 1mImportance★★★★★
✓ Free question

Zinc is oxidised and silver is reduced, giving Ecello=0.80−(−0.76)=1.56E^o_{cell} = 0.80 - (-0.76) = 1.56 V with n=2n = 2. Then ΔrGo=−nFEcello=−301.080\Delta_r G^o = -nFE^o_{cell} = -301.080 kJ mol−1^{-1}, which is option (A).

The standard Gibbs energy of a cell reaction is linked to its standard cell potential by

ΔrGo=−nFEcello\Delta_r G^o = -nFE^o_{cell}

so we first find EcelloE^o_{cell}, then nn, and finally ΔrGo\Delta_r G^o.

1. Identify the electrodes. Zinc is oxidised (anode) and silver is reduced (cathode):

Anode:Zn→Zn2++2e−\text{Anode:}\quad Zn \rightarrow Zn^{2+} + 2e^-

Cathode:Ag2O+H2O+2e−→2Ag+2OH−\text{Cathode:}\quad Ag_2O + H_2O + 2e^- \rightarrow 2Ag + 2OH^-

2. Standard cell potential. Using the given reduction potentials,

Ecello=Ecathodeo−Eanodeo=0.80−(−0.76)=1.56 VE^o_{cell} = E^o_{cathode} - E^o_{anode} = 0.80 - (-0.76) = 1.56\ \text{V}

3. Electrons transferred. Each half-reaction involves 2 electrons, so n=2n = 2.

4. Gibbs energy.

ΔrGo=−nFEcello=−(2)(96500 C mol−1)(1.56 V)\Delta_r G^o = -nFE^o_{cell} = -(2)(96500\ \text{C mol}^{-1})(1.56\ \text{V})

ΔrGo=−301080 J mol−1=−301.080 kJ mol−1\Delta_r G^o = -301080\ \text{J mol}^{-1} = -301.080\ \text{kJ mol}^{-1}

The negative value confirms the reaction is spontaneous, consistent with the positive EcelloE^o_{cell}.

✓Final answer

ΔrGo=−301.080 kJ mol−1\Delta_r G^o = \boxed{-301.080\ \text{kJ mol}^{-1}} — option (A).

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