Description

1 Partial molar concepts
Following is some data on the heat evolved when 1 mole of sulfuric acid (H2SO4) is isothermally mixed with H2O at 298K.
NH2O (mols) 0.25 1.0 1.5 2.33 4.0 5.44 9.0 10.1 19.0 20.0
−∆Hmix (J) 8242 28200 34980 44690 54440 58370 62800 64850 70710 71970

1. Is this mixture ideal? Why?
2. Determine and plot the molar enthalpy of mixing as a function of mole fraction of H2SO4.
3. Estimate the heat evolved when 100g of a 60%(w/w) sulfuric acid solution is mixed with 75g of a 25%(w/w) sulfuric acid solution. Hints: What is the molar composition of the initial solutions? Of the final one?)
4. Estimate the partial molar enthalpies of H2O and H2SO in a 50%(w/w) solution.
5. The mixing enthalpy of a “regular” solution can be written as χ12x1x2. Fit the data to this model to estimate χ12 and to estimate the partial molar enthalpies of H2O and H2SO in a 50%(w/w) solution.
2 Phase diagrams for liquids
Within the regular solution model, the free energy of mixing two liquids is given by
∆gmix = RT {xA lnxA + xB lnxB + χABxAxB}
1. Suppose χAB = 5 at 300 K for some mixture of liquids A and B. You prepare a mixture of 0.3 mol A and 0.7 mol B at this temperature. How many phases are present at equilibrium, what are their compositions, and how much of each phase (if more than one) is present?
2. What are the spinodal compositions at 300 K of the A/B mixture?
3. The binodal and spinodal curves meet at the critical point. The second and third derivatives of the free energy of mixing must vanish at this point. Find the critical composition and temperature of this mixture. Assume that χAB ∝ 1/T.
3 Funny phase diagrams
While χAB ∝ 1/T is the normal behavior, other dependencies are possible.
1. Construct a temperature vs. composition diagram for a system for which χAB is a positive constant independent of temperature.
2. Construct a temperature vs. composition diagram for a system for which χAB ∝ T.

4 Two components, two phases, too much fun!
At 300K, the saturation pressure of A is ten times the saturation pressure of B. A and B mix ideally.
1. Write down an expression for the free energy of a two-component ideal liquid mixture as a function of pressure and composition, gl(P,xB).
2. Write down an expression for the free energy of a two-component ideal gas mixture as a
function of pressure and composition, gv(P,yB).
3. Plot gl and gv vs composition at five pressure from P = Psat,B to P = Psat,A. Identify the important regions on each plot.
5 Vapor-liquid equilibrium.
The partial pressure of CS2 above a CS2/dimethoxymethane (DMM) mixture at 35.2◦C can be fit to the equation:
PCS2 = xCS2(514.5 torr)exp(1.4967x2DMM − 0.68175x3DMM)
1. Use the Gibbs-Duhem relation to determine the partial pressure of DMM as a function of composition. Assume the vapor is ideal.
2. Do CS2 and DMM form a regular solution at these conditions? Hint: Determine the activities of each component and from these the excess free energy of mixing. Is it proportional to x(1 − x)?