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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 300K . If the emf of the cell is zero, the `DeltaS^(@)` (in JK^(-1mol^(-1))` of the cell reaction per mole of B formed at 300 K is _________.
(Given ln (2)= 0.7, R (universal gas constant ) = `8.3JK^(-1)mol^(-1)`. H, S and G are enthalpy , entropy and gibbs energy, respectively).

Text Solution

Verified by Experts

The correct Answer is:
A, B
`(-11.62)`
`underset(DeltaH^(o)=2DeltaG_(O)^(o))(A(s)|A^(+n)(aq,2M))||B^(+2n)underset(E_(cell)=0)((aq,1M)|B(s))`
Cell Rx `[AtoA^(+n)+ n e^(-)]xx2`
`B^(+2n)+2n e^(-)toB(s)`
`2A(s)+underset(1M)(B^(+2n))(aq)tounderset(2M)(2A^(+n))(aq)+B(s)`
`DeltaG=DeltaG^(o)+RT" ln "([A^(+n)]^(2))/([B^(+2n)])`
`DeltaG^(o)=-RT" ln "([A^(+n)]^(2))/([B^(+2n)])=-RT.ln(2^(2))/(1)=-RT.ln4`
`DeltaG^(o)=DeltaH^(o)-TDeltaS^(o)`
`DeltaG^(o)=2DeltaG^(o)-TDeltaS^(o)`
`DeltaS^(o)=(DeltaG^(o))/(T)=-(RTln4)/(T)=-8.3xx2xx0.7=-11.62J//K.mol`
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