Question

A galvanic cell is constructed with $A{g}^{+}/Ag$ and $F{e}^{3+}/F{e}^{2+}$ electrodes. The concentrations of $A{g}^{+}$ at which the e.m.f. of the cell is zero at equimolar concentration of $F{e}^{2+}$ and $F{e}^{3+}$. Write answer as nearest integer after multiplying it with $10$.
Given $E_{A{g}^{+}/Ag}^o=0.80V$ and $E_{F{e}^{3+}/F{e}^{2+}}^o=0.77V$

Answer 1

For equimolar concentrations of $F{e}^{2+}$ and $F{e}^{3+}$, $E_{F{e}^{3+}|F{e}^{2+}}=E_{F{e}^{3+}|F{e}^{2+}}^0=0.77V$
The expression for the potential of the half electrodes.
$E_{A{g}^{+}|Ag}=E_{A{g}^{+}|Ag}^0-\frac{0.0592}{n}log\left[A{g}^{+}\right]$
Substitute values in the above expression.
$0.77=0.80-\frac{0.0592}{1}log\left[A{g}^{+}\right]$
$log\left[A{g}^{+}\right]=-\frac{0.80-0.77}{0.0592}=-0.5067$
$\left[A{g}^{+}\right]=0.31$, the concentrations of $A{g}^{+}$ at which the e.m.f. of the cell is zero at equimolar concentration of $F{e}^{2+}$ and $F{e}^{3+}$.