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 ∆ S ⊝ ( i n J K - 1 m o l - 1 ) of the cell reaction per mole of B formed at 300 K is ____ (Given: ln ⁡ 2 = 0.7 , R = 8 .3 J K − 1 mol − 1 . H, S and G are enthalpy, entropy and Gibbs energy, respectively.)

Step-by-step solution

A(s) | A +n (aq . 2 M) || B +2n (aq . 1 M) | B(s) ΔH o = 2ΔG o E cell = 0 Cell Rx 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 = − RT ln4 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 .6 J/K mol − 1