A galvanic cell is based on the following half-reactions:
$$\begin{array}{ll}
\mathrm{Cu}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Cu}(s) &
\mathscr{E}^{\circ}=0.34 \mathrm{V} \\
\mathrm{V}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{V}(s) &
\mathscr{E}^{\circ}=-1.20 \mathrm{V}
\end{array}$$
In this cell, the copper compartment contains a copper electrode and
\(\left[\mathrm{Cu}^{2+}\right]=1.00 \mathrm{M},\) and the vanadium compartment
contains a vanadium electrode and \(V^{2+}\) at an unknown concentration. The
compartment containing the vanadium \((1.00 \mathrm{L}\) of solution) was
titrated with \(0.0800 M \space \mathrm{H}_{2} \mathrm{EDTA}^{2-},\) resulting
in the reaction
$$\mathrm{H}_{2} \mathrm{EDTA}^{2-}(a q)+\mathrm{V}^{2+}(a q)
\rightleftharpoons \mathrm{VEDTA}^{2-}(a q)+2 \mathrm{H}^{+}(a q) \space
\mathrm{K=?}$$
The potential of the cell was monitored to determine the stoichiometric point
for the process, which occurred at a volume of \(500.0 \mathrm{mL} \space
\mathrm{H}_{2} \mathrm{EDTA}^{2-}\) solution added. At the stoichiometric
point, \(\mathscr{E}_{\text {cell }}\) was observed to be \(1.98 \mathrm{V}\). The
solution was buffered at a pH of \(10.00 .\)
a. Calculate \(\mathscr{E}_{\text {cell }}\) before the titration was carried
out.
b. Calculate the value of the equilibrium constant, \(K,\) for the titration
reaction.
c. Calculate \(\mathscr{E}_{\text {cell }}\) at the halfway point in the
titration.
