Short Answer Questions

Answer any four of the following questions (8 pts each)

1. Crystalline sulfur can exist in two stable forms identified by their symmetry, namely monoclinic and rhombic. The P-T phase diagram for pure sulfur thus exhibits three triple points, as shown at right. At the triple point where liquid and gaseous sulfur are present, the solid form is monoclinic. Label the P-T phase diagram with the appropriate phases.

2.
Sketch on the following plots of chemical potential vs. T the effect of an increase of pressure on the m_solid and m_liquid curves for both benzene and water (note that these substances differ in the relative densities of solid and liquid at their standard melting points). Show in each case the effect of pressure on the melting point.

3.
Sketch the qualitative appearance of a DSC scan (i.e., the constant-pressure heat capacity of a substance as a function of T) for a second-order phase transition according to the Ehrenfest classification.

4. Which of the following pairs of compounds would you expect to exhibit markedly nonideal mixing, and which should exhibit more nearly ideal mixing?
(a) H₂O and n-propanol, CH₃(CH₂)₃CH₂OH
(b) toluene (methyl benzene) and ethyl benzene
(c) solid D-alanine, CH₃CH(NH₂)COOH, and its stereoisomer, L-alanine
(d) acetone and carbon tetrachloride
(e) ethanol and methanol

5. n-heptane and n-hexane form an ideal solution. Does there exist a composition for which the entropy of mixing is greatest? If not, state why not. If so, what are the proportions of the two liquids at that composition?

Problems (20 points each)

Do any three of the following four problems. Be sure to show your work! Partial credit will be awarded for the correct approach even if your answer is wrong. Use the back of these sheets if necessary.

1. The volume of an aqueous solution of NaCl at 25°C was measured for a series of molalities m, and found to fit the expression
V/cm³ = 1003 + 16.62 b + 1.77 b^3/2 + 0.12 b²
where V is the volume of a solution formed from 1.000 kg of water, and b is the numerical value of the molality, i.e. b = m / m°, with m° º1 molal.
Find
(a) the total volume of a 0.0100 m solution of NaCl
(b) the partial molar volume of NaCl at this concentration
(c) the partial molar volume of water at this concentration

(You may take the molecular weight of water to be 18.00 g mol^-1)

2. Partial pressure data as a function of composition for a solution of acetone and chloroform are given in the table below and also plotted at right.

xC	PC/Torr	PA/Torr	Ptot/Torr
0	0	347	347
0.2	35	270	305
0.4	82	185	267
0.6	142	102	244
0.8	219	37	256
1	293	0	293

Use this information to obtain
(a) The Raoult’s Law activities and activity coefficients of acetone and chloroform at 0.6 mole fraction of chloroform
(b) The Henry’s Law activities and activity coefficients of acetone and chloroform at this composition [Hint: If all else fails, try a graphical solution]

3. If the chemical potential of each component in a binary mixture is expressed as

where a_i = g_i x_i, show that the Gibbs-Duhem equation for the chemical potentials,

leads to the following (Gibbs-Duhem) equation for the chemical activity coefficients:

4. For D₂O (where D º ²H), the normal freezing point is 3.82°C and DH_m,fus = 6.23 kJ mol^-1.
(a) Find the molal freezing point depression constant for D₂O.
(b) Find the freezing point of a solution of 0.954 g of CH₃COCH₃ in 100 g of D₂O (at. wts: H = 1.008, ²H = 2.014, C=12.01, O = 16.00).
(c) Explain why your answer is approximate.

Bonus (15 pts)

Some liquid crystals exhibit what are known as re-entrant phases, as shown on the diagram below. At certain temperatures as the pressure increases, one observes a transition from phase b to phase a followed by a transition back to the b phase, as shown by the dashed line. Suggest an explanation for this behavior in terms of the Clapeyron equation [Hint: Why is the phase boundary curved?]

Physical Constants:

L = 6.022´10²³ mol^-1; R = 8.315 J^-1 K^-1 mol^-1 = 0.08206 atm dm³ K^-1 mol^-1

1 torr = 1 mm Hg = 133.322 Pa; 1 atm = 1.01325´10⁵ Pa = 760 torr

Partial Molar Quantities: ; for Y = G, V, H, A, U, S...

Gibbs-Duhem Equation: for Y = G, V, H, A, U, S,...

Molality:

Ideal Gas	mA = mA°+RT ln P/P°	xA,vap = PA/Ptot	P°= 1 bar
Ideal Solution	mA = mA*+RT ln xA,soln	xA,soln = PA/PA*	pure substance
Ideal-Dilute Solution	mB = mB°+RT ln xB,soln	xB,soln = PB/KB*	behavior at xB®0 extrapolated to xB=1
Nonideal Solution	mA = mA°+RT ln aA,soln	aA,soln = PA/PA* OR aB,soln = PB/KB	pure substance, OR behavior at xB®0 extrapolated to xB=1

Some Useful Derivative Relations:

Chemical Potential:

Condition for Phase Equilibrium: for substance i between phases a and b

Clapeyron Equation:

Clausius-Clapeyron Equation:

Quantities of mixing:

Entropy of mixing in ideal solutions:

Freezing Point Depression Constant: