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At a given temperature, a nonideal solution of the volatile components \(A\) and \(B\) has a vapor pressure of 795 Torr. For this solution, \(y_{A}=0.375 .\) In addition, \(x_{A}=0.310\), \(P_{A}^{*}=610\) Torr, and \(P_{B}^{*}=495\) Torr. Calculate the activity and activity coefficient of \(A\) and \(B\).

The partial molar volumes of water and ethanol in a solution with \(x_{H_{2}}, o=0.45\) at \(25^{\circ} \mathrm{C}\) are 17.0 and \(57.5 \mathrm{cm}^{3} \mathrm{mol}^{-1},\) respectively. Calculate the volume change upon mixing sufficient ethanol with 3.75 mol of water to give this concentration. The densities of water and ethanol are 0.997 and \(0.7893 \mathrm{g} \mathrm{cm}^{-3}\), respectively, at this temperature.

An ideal solution is made up of the volatile liquids A and \(\mathrm{B}\), for which \(P_{A}^{*}=165\) Torr and \(P_{B}^{*}=85.1\) Torr. As the pressure is reduced, the first vapor is observed at a total pressure of \(110 .\) Torr. Calculate \(x_{\mathrm{A}}\).

Calculate the solubility of \(\mathrm{H}_{2} \mathrm{S}\) in \(1 \mathrm{L}\) of water if its pressure above the solution is 2.75 bar. The density of water at this temperature is \(997 \mathrm{kg} \mathrm{m}^{-3}\).

The densities of pure water and ethanol are 997 and \(789 \mathrm{kg} \mathrm{m}^{-3},\) respectively. For \(x_{\text {ethanol }}=0.35,\) the partial molar volumes of ethanol and water are 55.2 and \(17.8 \times 10^{-3} \mathrm{L} \mathrm{mol}^{-1},\) respectively. Calculate the change in volume relative to the pure components when \(2.50 \mathrm{L}\) of a solution with \(x_{\text {ethanol }}=0.35\) is prepared.

Two liquids, A and B, are immiscible for \(x_{A}=x_{B}\) \(=0.5,\) for \(T < 75.0^{\circ} \mathrm{C}\) and completely miscible for \(T > 75.0^{\circ} \mathrm{C} .\) Sketch the phase diagram, showing as much information as you can from these observations.

An ideal solution is formed by mixing liquids A and \(\mathrm{B}\) at \(298 \mathrm{K} .\) The vapor pressure of pure \(\mathrm{A}\) is 151 Torr and that of pure \(\mathrm{B}\) is 84.3 Torr. If the mole fraction of \(\mathrm{A}\) in the vapor is \(0.610,\) what is the mole fraction of \(A\) in the solution?

A solution is prepared by dissolving 45.2 g of a nonvolatile solute in 119 g of water. The vapor pressure above the solution is 22.51 Torr and the vapor pressure of pure water is 23.76 Torr at this temperature. What is the molecular weight of the solute?