Consider an electrochemical cell: $$A(s)$$ $$An+aq$$, $$2MB2n+aq$$, $$1MBs$$. The value of Δ$$H0$$ for the cell reaction is twice that of Δ$$G0$$ at $$300K$$. If the EMF of the cell is zero, the Δ$$S0$$ (in$$ JK−$$1mol$$−$$1) of the cell reaction per mole of B formed at $$300K$$ $$is___(Given$$ : ln (2) $$=$$ $$0.7$$, R (universal$$ gas $$constant) $$=$$ $$8.3$$ J $$K-1$$ $$mol-1$$. H, S and G are enthalpy, entropy and Gibbs energy, respectively.$$)$$

Question

Consider an electrochemical cell: $$A(s)$$ $$An+aq$$, $$2MB2n+aq$$, $$1MBs$$. The value of Δ$$H0$$ for the cell reaction is twice that of Δ$$G0$$ at $$300K$$. If the EMF of the cell is zero, the Δ$$S0$$ (in$$ JK−$$1mol$$−$$1)  of the cell reaction  per mole of B formed at $$300K$$ $$is___(Given$$ : ln (2) $$=$$ $$0.7$$, R (universal$$ gas $$constant) $$=$$ $$8.3$$ J $$K-1$$ $$mol-1$$. H, S and G are enthalpy, entropy and Gibbs energy, respectively.$$)$$

Infinity Learn · Accepted Answer

$$A(s)A+n(aq$$,$$2M)$$∥$$B+2n(aq$$,$$1M)B(s)$$ΔH∘$$=2$$Δ$$G0$$∘ Ecell $$=0$$ Cell Rx A→$$A+n+ne$$−×$$2$$ $$B+2n+2ne$$−→$$B(s)2A(s)+B1M+2n(aq)$$→$$2A+n(aq)+B(s)$$Δ$$G=$$ΔG∘$$+RTln$$⁡$$A+n2B+2n$$ΔG∘$$=$$−RTln⁡$$A+n2B+2n=$$−RT.ln⁡$$221=$$−RT⋅ln⁡$$4$$ΔG∘$$=$$ΔH∘−TΔS∘ΔG∘$$=2$$ΔG∘−TΔS∘ΔS∘$$=$$ΔG∘$$T=$$−RTln⁡$$4T=8.3$$×$$2$$×$$0.7=$$−$$11.62J/K$$⋅mol

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