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Consider an electrochemical cell : A(s...

Consider an electrochemical cell :
`A(s)|A^(n+) (aq. 2M)||B^(2n+) (aq. 1M)|B(s)`. The value of `DeltaH^(@)` for the cell reaction is twice that of `DeltaG^(@)` at 300 K. If the amf of the cell is zero, the `DelatS^(@) ("in "JK^(-1) mol^(-1))` of the cell reaction per mole of B formed at 300 K is ______ .
(Given : In (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.)

Text Solution

Verified by Experts

`A (s) | A^(n+) (aq, 2M)||B^(2n+) (aq, 1M)|B(s)`
E=0 i.e., Redox process of cell is at equilibrium.
Cell Reaction : `{:([A (s) rarr A^(n+)+n e^(-)]2),(B^(2n+)+2n e^(-) rarr B(s)),(ulbar(2A(s)+B^(2n+) hArr 2A^(n+)+B(s))):}`
`K=([A^(n+)]^(2))/([B^(2n+)])=2^(2)/1=4`
`DeltaG^(@)=-2.303 RT log_(10) K`
`=-2.303xx8.3xx300 log_(10) 4`
`=-3452.5 J`
We know,
`DeltaG^(@)=DeltaH^(@)-T DeltaS^(@)`
`=2 DeltaG^(@)-T DeltaS^(@)`
`DeltaS^(@)=(DeltaG^(@))/T=(-3452.5)/(300) =-11.5 JK^(-1) mol^(-1)`
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