Comments re Chapter 12 Problems:


An exercise in calculating vapor-pressure lowering for a familiar solution.


A T/F problem on the subject of freezing-point depression. Most of the questions (but not (c)) apply to the boiling-point elevation as well.


An exercise involving the practical osmotic coefficient f, which multiplies the molality and accounts for non-ideality (DT = -Kf(m)(fn), where n is the number of ions per formula unit. The coefficient f itself is not so important; what is important is getting n correct for the solute and noticing that the solution is not ideal.  What is the ratio of the measured freezing-point depression to the expected depression?


A problem in which the extent of dimerization of phenol (as measured by an equilibrium constant Kx) is determined from data about a freezing-point depression.


An unusual, but informative, problem involving a freezing-point depression for a solution of two unreactive solutes. Rather than asking for a calculation of DT or molar mass or concentration, Levine asks about the relative amounts of the two solutes.




Exercise in calculating osmotic pressure. In part (b) the calculated and observed osmotic pressures are compared to get a value for the activity coefficient of the solvent.  For this part of the problem it is necessary to go back from the equation PV = nBRT (or, C = nB/V = P/RT) to the earlier equation -ln(gA XA) =  PVA/RT (where VA is the molar volume of A in solution and can be assumed to be the same as the molar volume of pure A).  Note that the density of water is not quite 1.00 g/mL at 20° C.  After getting VA calculate XA and solve for gA.  If gA is not close to 1.00 something is wrong.


Problem involving osmotic pressure and ionic strength.  The equation is PV = nBRT can be arranged to PV = (nB/V)RT = CRT where C is the molarity of the solution.


Very short exercise about the Gibbs Phase Rule.


Please make the requested plot (a P vs. x diagram for the liquid and vapor phases of an ideal binary solution) carefully, maybe using a spreadsheet.  (The word carefully means using either a spreadsheet or a calculator and graph paper).  Draw the tie line that corresponds to a system that has a total pressure of 40.0 torr
(Hint/  Calculate Ptot as a function of Xbenz or Xtol, maybe by calculating Pbenz and Ptol and then adding them together.  Then for that pressure calculate Ybenz (and/or Ytol).  For the plot use one series for Ptot as a function of X and another for Ptot as a function of Y.  The two points for each Ptot won’t be at the same place horizontally, but they will be connected by a tie line).
Optional:  Calculate the ratio of the number of moles of liquid phase to the number of moles of vapor phase using the lever rule if the overall system contains 1 mole each of benzene and toluene and the total pressure is 40.0 torr.
Optional:  Work out the numbers of moles of benzene and of toluene in each of the two phases.  Start by writing the four equations that relate the four unknowns.


A thought problem about two-phase regions and tie lines.


A thought problem that is based on a simple system in which the chemical potential of the solvent differs between two beakers because the solution concentrations are different. Since the liquid solvent is in equilibrium with its vapor, the solvent is constantly vaporizing and condensing. The solvent can therefore migrate from one beaker to the other.


This question can be answered with a single sentence that requires no calculations or equations. Levine provides a slightly longer answer.


Relates the four colligative properties.  The hardest part of the problem is the conversion of molality to mole fraction.  Remember that for water Kb = 0.513 °/m and that Kf = -1.86 °/m.  The needed vapor pressure is given in the problem.




Estimate the eutectic temperature and composition of a solution of benzene and cyclohexane by finding the intersection of the two freezing-point depression curves.  This is a good problem to do with a spreadsheet.  The necessary equation is:

            ln(aA/1) @ ln(XA) @ -(1/R)(DfusH°)[(1/Tfus,A) - (1/Tfus,A°)],
where Tfus,A° is the melting point of the pure solvent.  This equation is the equation for the freezing-point depression but before the last approximations are made and the constants are grouped together to give Kf.


A reasonably simple solid-liquid phase diagram, but partial miscibility (solubility of A in B and B in A) must be considered. Note that neither the temperatures nor the compositions of the eutectics are given so it is just necessary to draw lines that look reasonable.


Another solid-liquid phase diagram.  Several different compounds are present (each one is a line phase) but there are no complications from partial miscibility.


Problem that emphasizes that the solubility of a solid in a liquid should depend only on the freezing point and heat of fusion of the solute.  (The freezing-point depression curve of a liquid-solid phase diagram is also a solubility curve because it gives the composition of the solution that is in equilibrium with the pure substance).  For solutes and solvents that are chemically similar (so that the solutions are reasonably ideal) the solubilities predicted on the basis of the equation given above (see description of 12.44) are surprisingly accurate.



12-46 (not always assigned)

Draw the phase diagram for the water – NaCl system (problem was done in class).

(not always assigned)

A problem that shows that it is possible to get activity coefficients for the liquid components of an azeotrope given the vapor pressures of the pure components and the total pressure of the vapor.  The key is to start from Pi = giliq Xi Pi* = Yi Ptot and then to realize that in an azeotrope Xi = Yi.