Question
Given the data at $${25^ \circ }C$$
$$\eqalign{
& Ag + {I^ - } \to AgI + {e^ - }\,\,\,\,\,\,{E^ \circ } = 0.152\,V \cr
& Ag \to A{g^ + } + {e^ - }\,\,\,\,\,\,\,\,\,\,\,\,\,\,{E^ \circ } = - 0.800\,V \cr} $$
What is the value of log $${K_{sp}}$$ for $$AgI?$$ $$( 2.303 RT/F = 0.059 V )$$
A.
$$- 37.83$$
B.
$$- 16.13$$
C.
$$- 8.12$$
D.
$$+ 8.612$$
Answer :
$$- 16.13$$
Solution :
$$\eqalign{
& \left( {\text{i}} \right)\,\,Ag \to A{g^ + } + {e^ - }\,\,\,\,\,\,{E^ \circ } = - 0.800\,V \cr
& {\text{(ii)}}Ag + {I^ - } \to AgI + {e^ - }\,\,\,{E^ \circ } = 0.152\,V \cr
& {\text{From (i) and (ii) we have,}} \cr
& AgI \to A{g^ + } + {I^ - }\,\,\,\,{E^ \circ } = - 0.952\,V \cr
& E_{cell}^o = \frac{{0.059}}{n}\log \,K \cr
& \therefore \,\, - 0.952 = \frac{{0.059}}{1}\log \,\left[ {A{g^ + }} \right]\left[ {{I^ - }} \right]\,\,\left[ {\because \,\,k = \left[ {A{g^ + }} \right]\left[ {{I^ - }} \right]} \right] \cr
& {\text{or}}\,\, - \frac{{0.952}}{{0.059}} = \log \,{K_{sp}}\,\,{\text{or}}\,\, - 16.13 = \log \,{K_{sp}} \cr} $$