Question
The solution of $$CuS{O_4}$$ in which copper rod is immersed is diluted to 10 times. The reduction electrode potential
A.
Increases by $$30\,m\,V$$
B.
Decreases by $$30\,m\,V$$
C.
Increases by $$59\,m\,V$$
D.
Decreases by $$59\,m\,V$$
Answer :
Decreases by $$30\,m\,V$$
Solution :
$$\eqalign{
& {\left( {{E_{C{u^{2 + }}\left| {Cu} \right.}}} \right)_1} = {E^0}_{C{u^{2 + }}\left| {Cu} \right.} + \frac{{0.059}}{2}\log {\left[ {C{u^{2 + }}} \right]_1} \cr
& \left[ {C{u^{2 + }}\left( {aq} \right) + 2{e^ - } \to Cu\left( s \right)} \right]\,{\text{and}} \cr
& {\left( {{E_{C{u^{2 + }}\left| {Cu} \right.}}} \right)_2} = {E^0}_{C{u^{2 + }}\left| {Cu} \right.} + \frac{{0.059}}{2}\log {\left[ {C{u^{2 + }}} \right]_2} \cr
& \Rightarrow \Delta {E_{C{u^{2 + }}\left| {Cu} \right.}} = - \frac{{0.059}}{2}\log \left( {\frac{{{C_2}}}{{{C_1}}}} \right) \cr
& = - \frac{{0.059}}{2}\log 10 \cr
& = - 0.030\,V \cr
& = - 30\,m\,V \cr} $$