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Q. What is the standard cell potential for the reaction with $K =1$ (equilibrium constant)

TS EAMCET 2020

Solution:

The relationship between cell potential and the equilibrium constant. We know.
$\Delta G=-R T \ln k=-n F E^{\circ}$
$\Delta G=-2.303 R T \log k=-n F E^{\circ}$
$\log K_{f}=\frac{n F \times E^{\circ}}{R T \times 2.303}$
$\log (1)=\frac{n}{0.059} \times E^{\circ}(n=1)$
$\Rightarrow 0 \times 0.059=E^{\circ}$
$ \Rightarrow E^{\circ}=$ zero