A galvanic cell is based on the following half-reactions:
$$\begin{array}{ll}{\mathrm{Fe}^{2+}+2 \mathrm{e}^{-} \longrightarrow
\mathrm{Fe}(s)} & {\mathscr{E}^{\circ}=-0.440 \mathrm{V}} \\ {2
\mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}(g)} &
{\mathscr{E}^{\circ}=0.000 \mathrm{V}}\end{array}$$
where the iron compartment contains an iron electrode and
\(\left[\mathrm{Fe}^{2+}\right]=1.00 \times 10^{-3} M\) and the hydrogen
compartment contains a platinum electrode, $P_{\mathrm{H}_{2}}=1.00
\mathrm{atm},$ and a weak acid, HA, at an initial concentration of 1.00
\(\mathrm{M}\) . If the observed
cell potential is 0.333 \(\mathrm{V}\) at \(25^{\circ} \mathrm{C},\) calculate the
\(K_{\mathrm{a}}\) value for the weak acid HA.