PHYSICAL CHEMISTRY II
Spring, 2016
Second Hour Exam
Total value of exam: 100 points
Name:__________________________________
(20 points)
1. a) Maintaining equality of chemical potential across the solid-liquid phase boundary during
preparation of a solution leads to freezing point depression.
⎛ µ1sol ⎞
⎛ µ1liq ⎞
Using the Gibbs-Helmholtz equation, show that requiring d ⎜
= d⎜
⎝ T ⎟⎠
⎝ T ⎟⎠
for an ideal solution yields : ln X1 =
ΔH fus, m ⎛ 1
1⎞
−
R ⎜⎝ T f* T f ⎟⎠
(15 points)
1. b) Lead (Pb) has a freezing point of 600.65 K and a molar heat of fusion ΔH fus, m of 4.81 kJ/mol.
Tin (Sn) has a freezing point of 505.12 K and a molar heat of fusion ΔH fus, m of 7.21 kJ/mol.
Certain mixtures of lead and tin form a eutectic composition.
Estimate the temperature and mole fraction at the eutectic point by forcing intersection of
1
Tf
from each of the freezing point depression equations for lead and for tin from Problem 1a.
HINT*: After you force the intersection of the two equations use trial and error values of mole
fraction X to estimate the Xeutectic . Using this Xeutectic , find Teutectic .
(10 points)
c)
Sketch the solid-liquid phase diagram (T vs. XPb) for Pb/Sn, labeling all sections and points
on the diagram.
2.
liq
X acet
0
0.0821
0.2003
0.3365
0.4188
0.5061
0.6034
0.709
0.8147
0.9397
1
vap
X acet
0
0.05
0.1434
0.3171
0.4368
0.5625
0.6868
0.8062
0.8961
0.9715
1
ptotal (torr )
pacet (torr )
pchl (torr )
293
279
262
249
248
255
267
286
307
332
344
0
13.95
37.5708
78.9579
108.3264
143.4375
183.3756
230.5732
275.1027
322.538
344
293
265.05
224.4292
170.0421
139.6736
111.5625
83.6244
55.4268
31.8973
9.462
0
(15 points)
a) From the acetone-chloroform data at 35 °C provided above calculate the Raoult’s law and
Henry’s law activity coefficients ( γ R and γ H ) for both acetone and chloroform at
liq
= 0.709. Assume the vapor phase is ideal.
X acet
2. (cont.) (10 points)
b) Calculate ΔGmix for a solution containing 0.709 moles of acetone and 0.291 moles
chloroform at 35 °C.
(10 points)
c) Sketch the accompanying temperature vs. X(acetone) phase diagram for acetonechloroform near ptotal = 249 torr. Qualitatively label all regions and points on the
diagram.
(5 points)
d) Identify the composition of the distillate and residue fractions of a multiple-plate
(fractional) distillation of an acetone-chloroform mixture whose starting composition
was Xliq(acetone) = 0.709.
(15 points)
3.
Rank in order of decreasing chemical potential of glucose (µglucose).
a) Pure glucose at 25 °C.
b) An ideal solution at 146 °C of 1 mole of sucrose and 9 moles of glucose.
c) A super-saturated solution of glucose in benzene at 25 °C.
d) Liquid glucose at its melting point of 146 °C.
USEFUL INFORMATION
⎛ µ⎞
−H
d ⎜ ⎟ = 2 dT
⎝T⎠
T
Gibbs-Helmholtz equation
a1R =
p1
= X 1liqγ R
p1 *
Raoult’s law activity (ideal vapor)
a1H =
p1
= X 1liqγ H
p1 °
Henry’s law activity (ideal vapor)
µ1 = µ1 * + RT ln X 1liq
µ1 = µ1 ° + RT ln
f1
= µ1 ° + RT ln a1
f1 °
ideal solution
real solution
ΔGmix = nA ( µ A − µ A *) + nB ( µ B − µ B *)
free energy of mixing
R = 8.314 J mol-1 K-1
gas constant