Problem 26
A sample of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) of mass \(13.2 \mathrm{g}\) is placed in a test tube of radius \(1.25 \mathrm{cm} .\) The bottom of the test tube is a membrane that is semipermeable to water. The tube is partially immersed in a beaker of water at \(298 \mathrm{K}\) so that the bottom of the test tube is only slightly below the level of the water in the beaker. The density of water at this temperature is \(997 \mathrm{kg} \mathrm{m}^{-3}\). After equilibrium is reached, how high is the water level of the water in the tube above that in the beaker? What is the value of the osmotic pressure? You may find the approximation \(\ln (1 /(1+x)) \approx-x\) useful.
Problem 28
The vapor pressures of 1 -bromobutane and 1-chlorobutane can be expressed in the form \\[\ln \frac{P_{\text {bromo }}}{\mathrm{Pa}}=17.076-\frac{1584.8}{\frac{T}{\mathrm{K}}-111.88}\\] and \\[\ln \frac{P_{\text {chloro }}}{\mathrm{Pa}}=20.612-\frac{2688.1}{\frac{T}{\mathrm{K}}-55.725}\\] Assuming ideal solution behavior, calculate \(x_{\text {bromo}}\) and \(y_{\text {bromo}}\) at \(305 \mathrm{K}\) and a total pressure of \(9750 .\) Pa.
Problem 30
Assume that 1-bromobutane and 1-chlorobutane form an ideal solution. At \(273 \mathrm{K}, P_{\text {chloro }}^{*}=3790 \mathrm{Pa}\) and \(P_{\text {bromo}}^{*}=1394\) Pa. When only a trace of liquid is present at \(273 \mathrm{K}, y_{\text {chloro}}=0.750\). a. Calculate the total pressure above the solution. b. Calculate the mole fraction of 1 -chlorobutane in the solution. c. What value would \(Z_{\text {chloro}}\) have in order for there to be 4.86 mol of liquid and 3.21 mol of gas at a total pressure equal to that in part (a)? [Note: This composition is different from that of part (a).]
Problem 33
The dissolution of 7.75 g of a substance in 825 g of benzene at \(298 \mathrm{K}\) raises the boiling point by \(0.575^{\circ} \mathrm{C}\). Note that \(K_{f}=5.12 \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1}, K_{b}=2.53 \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1},\) and the density of benzene is \(876.6 \mathrm{kg} \mathrm{m}^{-3} .\) Calculate the freezing point depression, the ratio of the vapor pressure above the solution to that of the pure solvent, the osmotic pressure, and the molecular weight of the solute. \(P_{\text {benzene }}^{*}=103\) Torr at \(298 \mathrm{K}\).
