For \( \mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}+14 \mathrm{H}^{+}+6 e^{-} \rightarrow 2 \mathrm{Cr}^{3+}+7 \mathrm{H}_{2} \mathrm{O} ; \mathrm{E}^{\circ}=1.33 \mathrm{~V} \mathrm{At}\left[\mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}\right]=4.5 \)
millimole, \( \left[\mathrm{Cr}^{3+}\right]=15 \) millimole, \( \mathrm{E}^{\circ} \) is \( 1.067 \mathrm{~V} \). The \( \mathrm{pH} \) of the solution is nearly equal to

\( \mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}+16 \mathrm{H}^{+}+6 e^{-} \rightarrow 2 \mathrm{Cr}^{3+}+7 \mathrm{H}_{2} \mathrm{O} \)
\( E_{\text {cell }}=E_{\text {cell }}^{\circ}+\frac{0.0591}{6} \log \frac{\left[\mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}\right]\left[\mathrm{H}^{+}\right]^{4}}{\left[\mathrm{Cr}^{+3}\right]^{2}} \)
\( 1.067=1.33+\frac{0.0591}{6}\left(\log \frac{\left[\mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}\right]}{\left[\mathrm{Cr}^{3+}\right]^{2}+\log \left[\mathrm{H}^{+}\right]^{14}}\right) \)
\( 1.067-1.33=\frac{0.0591}{6}-\left(-\log \frac{\left[\mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}\right]}{\left[\mathrm{Cr}^{+3}\right]^{2}}-\log \left[\mathrm{H}^{+}\right]^{14}\right) \)
\( -0.263=\frac{-1}{100}\left(-\log \frac{\left(4.5 \times 10^{-3}\right)}{\left(15 \times 10^{-3}\right)^{2}}+14 p H\right) \)
\( 26.3=\log \frac{1}{20}+14 p H \)
\( 26.3=-1.3010+14 p H \)
\( 27.6=14 p H p H \approx 2 \)