If $E^{\circ }\left({\mathrm{Ag}}^{+}\mid \mathrm{Ag}\right)=0.8\mathrm{V}\text{ and }{E}^{\circ }\left({\mathrm{CNS}}^{-}\left|\mathrm{AgCNS}\right|\mathrm{Ag}\right)=0.1\mathrm{V}$ then the standard solubility product of $\mathrm{AgCNS}$ at 298 K is about

Consider the cell $\mathrm{Ag}\left(\mathrm{s}\right)\left|{\mathrm{Ag}}^{+}(\mathrm{aq},1\mathrm{M})\right|\left|\mathrm{KCNS}\right(\mathrm{aq},1.0\mathrm{M}\left)\right|\mathrm{AgCNS}\mid \mathrm{Ag}$

we have

$\begin{array}{lc}RHC& \mathrm{AgCNS}+{\mathrm{e}}^{-}\to {\mathrm{Ag}}^2+{\mathrm{CNS}}^{-}\\ LHS& \mathrm{Ag}\to {\mathrm{Ag}}^{+}+{\mathrm{e}}^{-}\end{array}$

add  $\mathrm{AgCNS}\to {\mathrm{Ag}}^{+}+{\mathrm{CNS}}^{-}$

$E_{\text{cell }}^{\circ }=E_{\mathrm{CNS}\rceil \mathrm{AgCNS}\mid \mathrm{Ag}}^{\circ }-E_{{\mathrm{Ag}}^{+}\mid \mathrm{Ag}}^{\circ }=0.1\mathrm{V}-0.8\mathrm{V}=-0.7\mathrm{V}$

Now   $-nF{E}_{\text{cell }}^{\circ }=-RT\ln K_{\mathrm{sp}}^{\circ }$

or $\log K_{\mathrm{sp}}^{\circ }=\frac{n{E}_{\mathrm{cell}}^{\circ }}{(RT/F)}=\frac{\left(1\right)(-0.7\mathrm{V})}{\left(0.059\mathrm{V}\right)}=-11.86\text{ i.e. }{K}_{\mathrm{sp}}^{\circ }=1.38\times {10}^{-12}$