Neco Model Questions Vol1 2020 Chemistry Question 3

At 25 °C a saturated solution of calcium fluoride, \(\text{CaF}_2\), has a solubility \(s_1 = 1.5 \times 10^{-4}\ \text{mol\,L}^{-1}\). The dissolution is endothermic with \(\Delta H^\circ = +15\ \text{kJ\,mol}^{-1}\). A student adds \(0.001\ \text{mol}\) of sodium fluoride, NaF, to 1.0 L of this saturated solution at 25 °C. (a) State whether \(\text{CaF}_2\) will precipitate under these conditions. (b) Assuming the solution can be heated, calculate the temperature (in °C) to which it must be raised so that the added fluoride just remains in solution (i.e., the ion product equals the solubility product). Use the van't Hoff relation \(\ln(K_2/K_1) = -\Delta H^\circ/R\,(1/T_2 - 1/T_1)\) with \(R = 8.314\ \text{J\,mol}^{-1}\text{K}^{-1}\) and \(T_1 = 298\ \text{K}\).