Question #44116

A solution of $\ce{Fe^{2+}}$ is titrated with $\ce{K2Cr2O7}$ at $298 \text{ K}$. A redox indicator with a transition potential $E^\circ_{\text{In}} = 0.89 \text{ V}$ is used. The pH of the solution is buffered such that the indicator changes color exactly at the equivalence point. At this equivalence point, the concentration of $\ce{Cr^{3+}}$ is $0.5 \text{ M}$.

Given the equilibrium: $\ce{Cr2O7^{2-} (aq) + H2O (l) \rightleftharpoons 2CrO4^{2-} (aq) + 2H+ (aq)}$, $K_{eq} = 10^{-14}$

Calculate the value of $\log_{10} \left( \frac{[\ce{CrO4^{2-}}]^2}{[\ce{Cr2O7^{2-}}]} \right)$ at the equivalence point.

(Given: $E^\circ_{\ce{Cr2O7^{2-}/Cr^{3+}}} = 1.33 \text{ V}$, $E^\circ_{\ce{Fe^{3+}/Fe^{2+}}} = 0.77 \text{ V}$, $\frac{2.303 RT}{F} = 0.06 \text{ V}$)