91Ó°ÊÓ

A galvanic cell is based on the following half-reactions: $$\mathrm{Cu}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Cu}(s) \quad \mathscr{E}^{\circ}=0.34 \mathrm{V}$$ $$\mathrm{V}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{V}(s) \quad \mathscr{E}^{\circ}=-1.20 \mathrm{V}$$ In this cell, the copper compartment contains a copper electrode and \(\left[\mathrm{Cu}^{2+}\right]=1.00 M,\) and the vanadium compartment contains a vanadium electrode and \(\mathrm{V}^{2+}\) at an unknown concentration. The compartment containing the vanadium \((1.00 \mathrm{L}\) of solution) was titrated with 0.0800\(M \mathrm{H}_{2} \mathrm{EDTA}^{2-}\) , resulting in the reaction $$\mathrm{H}_{2} \mathrm{EDTA}^{2-}(a q)+\mathrm{V}^{2+}(a q) \rightleftharpoons \mathrm{VEDTA}^{2-}(a q)+2 \mathrm{H}^{+}(a q)$$ $$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad K=?$$ The potential of the cell was monitored to determine the stoichiometric point for the process, which occurred at a volume of 500.0 \(\mathrm{mL} \mathrm{H}_{2} \mathrm{EDTA}^{2-}\) 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.