Question #44730

An aqueous solution is prepared by dissolving $0.10 \text{ mol}$ of a primary amine \ce{RNH2} and $0.10 \text{ mol}$ of an aldehyde \ce{R'CHO} in $1.0 \text{ kg}$ of water. The solution is maintained at a constant pH of 10.0 using a polymeric buffer that contributes negligibly to the freezing point depression. The $pK_a$ of the conjugate acid \ce{RNH3+} is 10.0. The unprotonated amine reacts with the aldehyde to form a Schiff base (imine) according to the following equilibrium: $\ce{RNH2(aq) + R'CHO(aq) <=> R'CH=NR(aq) + H2O(l)}$ The equilibrium constant for this reaction is $K = 40 \text{ kg mol}^{-1}$. Assuming ideal behavior and that the mass of the solvent remains exactly $1.0 \text{ kg}$, what is the freezing point depression ($\Delta T_f$) of the solution? (Given: $K_f$ for water is $1.86 \text{ K kg mol}^{-1}$)