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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 emf of the cell is zero, the `DeltaS^(@) ("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


`E = E^(@) - (RT)/(2 nF) ln ([A^(n+)]^(2))/([B^(2n+)])`
`E = E^(@) - (RT)/(2nF) ln (2)^(2)`
`or " " 0 = E^(@) - (RT)/(2 nF) ln 4`
`E^(@) = (RT)/(2nF) ln 4`
Now `Delta G^(@) = - 2n FE^(@) = (-2n F RT)/(2 nF) ln 4`
`= - RT ln 4`
`Delta G^(@) = Delta H^(@) - T Delta S^(@)`
`Delta G^(@) = 2 Delta G^(@) - T Delta S^(@)`
or `T Delta S^(@) = Delta G^(@)`
`Delta S^(@) = (Delta G^(@))/(T) = - (RT)/(T) ln 4 = - R ln 4 =- R xx 2 ln 2 `
`Delta S ^(@) = - 8.3 xx 2 xx 0.7`
`=- 11.62 JK^(-1) mol^(-1)`
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