Question 7.17: A silver electrode is immersed into a dilute solution of sil......

The Nernst equation, Equation (7.41), for the silver couple is

E_{\mathrm{Ag}^{+},\mathrm{Ag}}=E_{\mathrm{Ag}^{+},\mathrm{Ag}}^{\\ \ominus}+{\frac{R T}{F}}\ln\left({\frac{a_{\mathrm{(Ag}^{+})}}{a_{\mathrm{(Ag)}}}}\right)

E_{\mathrm{O,R}}=E_{\mathrm{O,R}}^{\ominus}+{\frac{R T}{n F}}\ln\left({\frac{a_{\mathrm{(O)}}}{a_{\mathrm{(R)}}}}\right)           (7.41)

For simplicity, we assume that the concentration and activity of silver nitrate are the same, i.e. a_{(\mathrm{Ag}^{+})}=10^{-3}. We also assume that the silver is pure, so its activity is unity.

Inserting values into Equation (7.41):

E_{\mathrm{Ag}^{+},\mathrm{Ag}}=0.799\ \mathrm{V}+0.0257\ \mathrm{V}\ln\left({\frac{0.001}{1}}\right)

so

E_{\mathrm{Ag}^{+},\mathrm{Ag}}=0.799\ \mathrm{V}+(0.0257\ \mathrm{V}\times-6.91)

and

E_{\mathrm{Ag}^{+},\mathrm{Ag}}=0.799\mathrm{V}-0.178\mathrm{V}

E_{\mathrm{Ag}^{+},\mathrm{Ag}}=0.621\mathrm{~V}