Question #44889

A $0.025 \text{ mol kg}^{-1}$ aqueous solution of potassium dichromate (\ce{K2Cr2O7}) is prepared at $298 \text{ K}$. In aqueous solution, the dichromate ion undergoes hydrolysis according to the equilibrium: $\ce{Cr2O7^{2-}(aq) + H2O(l) <=> 2HCrO4^{-}(aq)}$ The thermodynamic equilibrium constant for this reaction is $K_{eq} = 0.1152$. At this concentration, the activity coefficients for the ions are $\gamma_{\ce{HCrO4^-}} = 0.80$ and $\gamma_{\ce{Cr2O7^{2-}}} = 0.50$. Assuming the activity of neutral water is unity, \ce{K2Cr2O7} acts as a strong electrolyte before hydrolysis, and the solution behaves ideally with respect to colligative properties once equilibrium is established (osmotic coefficient $\phi = 1$), what is the apparent Van't Hoff factor ($i$) for \ce{K2Cr2O7} in this solution?