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Question

The equilibrium constant for the reaction
Sr(s)+Mg+2(aq)Sr+2(aq)+Mg(s)+2 is 2.69×1012 at 25oC.
The EO for a cell made up of the Sr/Sr+2 and Mg+2/Mq half cells is:

A
0.3667V
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B
0..7346V
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C
0.1836V
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D
0.1349V
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Solution

The correct option is A 0.3667V
Sr(s)+Mg+1(aq)Sr2+(aq)+Mg(s);Keq=2.69×1012
As we know that,
ΔG=nFE0cell..........(1)
and we also know that,
ΔG=RTln(Keq)..........(2)
From eqn(1)&(2), we have
lnKeq=nFE0cellRT
where as,
Keq= Equillibrium constant =2.69×1012
T= Temperature =25=(273+25)K=298K(Given)
n= no. of electrons involved =2
F= Faraday constant =96500C
R= Universal gas constant =8.314JK1mol1
E0cell=?
ln(2.69×1012)=2×96500×E0cell8.314×298
ln(2.69)+ln(1012)=193000×E0cell2477.572(lnab=lna+lnb)
0.99+(12×2.302)=77.9×E0cell
E0cell=28.61477.9=0.3670.3667V

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