Consider an electrochemical cell: $A(s)\left|A^{n+}(aq, 2 M) \right| B^{2n+}(aq, 1 M) \left| B(s)\right|$. The value of $\Delta H^{o}$ for the cell reaction is twice that of $\Delta G^{o}$ at 300 K. If the emf of the cell is $z \Delta S^{\ominus}$ in JK$^{-1}$ mol$^{-1}$ of the cell reaction per…

Question

Consider an electrochemical cell: $A(s)\left|A^{n+}(aq, 2 M) \right| B^{2n+}(aq, 1 M) \left| B(s)\right|$. The value of $\Delta H^{o}$ for the cell reaction is twice that of $\Delta G^{o}$ at 300 K. If the emf of the cell is $z \Delta S^{\ominus}$ in JK$^{-1}$ mol$^{-1}$ of the cell reaction per mole of B formed at 300 K is $\_\_\_\_\_$ (Given: $\ln (2)=0.7$, $R=8.3$ JK$^{-1}$ mol$^{-1}$. $H$, $S$, and $G$ are enthalpy, entropy and Gibbs energy, respectively.)

Aicharya · Accepted Answer

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

Consider an electrochemical cell: $A(s)\left|A^{n+}(aq, 2 M) \right| B^{2n+}(aq, 1 M) \left| B(s)\right|$.…

Solution