Emf of the cell,$\mathrm{Zn}\left(\mathrm{s}\right)\left|{\mathrm{Zn}}^{2+}\left({10}^{-2}\mathrm{M}\right)\right|\left|{\mathrm{Cu}}^{2+}\left(1\mathrm{M}\right)\right|\mathrm{Cu}\left(\mathrm{s}\right)$ is 0.0886V. Equilibrium constant for the above reaction at 298K will be

$Zn+C{u}^{2+}\to Z{n}^{2+}+Cu$

$E_{cell}=E_{cell}^0\frac{-0.0591}{2}\log \frac{\left[Z{n}^{2+}\right]}{\left[C{u}^{2+}\right]}$

$0.0886=E_{cell}^0-\frac{0.0591}{2}\log \frac{{10}^{-2}}{1}$

$0.0886=E_{cell}^0+0.0591$

$0.0886=E_{cell}^0+0.0591$

$E_{cell}^0=0.0886-0.0591=0.0295$

$0.0295=\frac{0.0591}{2}\log k_c$.

$\log k_c=1\Rightarrow k_c={10}^1=10$