Question #44243

A $1.0\text{ molal}$ aqueous solution of a binary electrolyte \ce{AB} is prepared at $300\text{ K}$. The freezing point of this solution is $-3.0^\circ\text{C}$. (Given: $K_f$ of water $= 2.0\text{ K kg mol}^{-1}$, assume the Van't Hoff factor $i$ is independent of temperature).

For the dissolution of \ce{AB(s)}, the standard enthalpy of solution at infinite dilution is $\Delta H_{sol}^{\infty} = +15.0\text{ kJ mol}^{-1}$. At $1.0\text{ m}$ concentration, ion-pairing and non-ideal interactions contribute an excess enthalpy term $\Delta H_{excess} = +4.5\text{ kJ mol}^{-1}$, such that the actual enthalpy of solution is $\Delta H_{sol} = \Delta H_{sol}^{\infty} + \Delta H_{excess}$.

The entropy of dissolution for a hypothetical, fully dissociated ideal solution ($i=2$) is $+80\text{ J K}^{-1}\text{ mol}^{-1}$. Given that the actual entropy of dissolution scales linearly with the Van't Hoff factor ($i$), determine the Gibbs free energy of dissolution ($\Delta G_{sol}$) for $1\text{ mole}$ of \ce{AB} at $300\text{ K}$.