Consider an electrochemical cell: A s    A n+   aq, 2 M    B 2n+ aq,&#160…

Consider an electrochemical cell: A s    A n+   aq, 2 M    B 2n+ aq, 1 M    B s . The value of ΔH o for the cell reaction is twice that of ΔG o at 300 K. If the emf of the cell is zero, the magnitude of ΔSo in  J −1 K −1   mol −1 of the cell reaction per mole of B formed at 300 K is ____
(Given: R = 8.3 JK−1mol−1. H, S and G are enthalpy, entropy and Gibbs energy, respectively.)

Solution

A(s) |  A +n (aq. 2 M) ||  B +2n (aq. 1 M) | B(s)
ΔHo = 2ΔGo    Ecell = 0
Cell Reaction    A→A+n+ne− × 2
B +2n +2  ne − →B(s)
2 A(s)+ B +2n 1 M (aq)→ 2  A +n 2 M (aq)+B(s)
ΔG =  ΔG o  + RT ln  A +n 2   B +2n
ΔG o  = −RT ln A +n 2   B +2n  = −RT × ln 2 2 1  = −RTln4
ΔG o  =  ΔH o − TΔS o
ΔG o  =  2ΔG o − TΔS o
ΔS o  =  ΔG o T  = − RT ln4 T
= −8.3 × 2 × 0.7 = -11.62 J/K mol−1

Asked in: JEE Advanced 2018 (Paper 2)

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