CHEMISTRY DEPARTMENT, PORTLAND STATE UNIVERSITY
CHEMISTRY 440/540, PHYSICAL CHEMISTRY.
FALL, 2008
Assignment 1 of 1
This is due 4:30 pm Friday 11/07/08 (three days after the big election!!!!!!!!!!).
Any work not submitted by this time will be graded at a maximum of 50% by
Monday, 11/10/08 and at 0% after that. These assignments can be submitted
through the professor’s mail box in SB2 262 or handed directly to him in his office
(SB2 372). The submission deadline, however, should be religiously observed.
The professor is very unforgiving on the issue of late submission of assignments.
For some of these problems, you may have to read outside the lectures to find the solutions. Our
lectures are not exhaustive, nor are they designed to be. For all problems, students should make
an effort to show all their work so that partial credit can be granted should they not arrive at the
correct solution.
Caveat: While the professor encourages students collaborating, the final submission should
represent a student’s sole efforts. Two scripts that are remarkably similar will both earn a final
score of zero irrespective of who plagiarized whose work.
Question One.
(a)
A perfect gas undergoes isothermal compression which reduces its
volume by 2.20 dm3. The final pressure and volume of the gas are
3.78x103 torr and 4.65 dm3 respectively. Calculate the original
pressure of the gas in mmHg and in atmospheres.
(b)
A Dumas experiment to determine molar volume is conducted in which
a gas sample’s P, V and other parameters are determined. If a 1.08 g
samle of the gas is held in 0.250 dm3 at 303 K at 101.3 kPa; calculate
the sample’s volume at 273.15 K at constant pressure. Calculate,
also, the molar mass of the gas.
(c)
The density of air at 101.325 kPa and 298.15 K is 1.159 g dm -3.
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Assuming air behaves as an ideal gas, calculate its molar mass.
(15 points)
Question Two.
(a)
Suppose that 10.0 mol ethane gas is confined to 4.860 dm 3 at 27 0C.
Predict the pressure exerted by the ethane gas from the perfect gas
and from van der Waals equations of state. In each case, calculate the
compression factor based on your calculations. For ethane, the
VDW’s constants are: a = 5.507 dm6 atm mol-2; b = 0.0651 dm3 mol-1.
(b)
A certain gas obeys the van der Waals equation with a = 0.50 m6 Pa
mol-2. Its volume is found to be 5.00x10-4 m3 mol-1 at 273.15 K and 3.0
MPa. From this information, calculate the VDW’s constant, b. What is
the compression factor for this gas at the prevailing temperature and
pressure?
(c)
Derive an expression for the compression factor of a gas that obeys
the equation of state: p(V-nb) = nRT, where b and R are constants. If
the pressure and temperature are such that Vm = 10b; what is the
numerical value of the compression factor?
(d)
The equation of state of a certain gas is given by p = RT/Vm + (a +
bT)/Vm2; where a, b are constants. Find (δV/δT)p.
(20 points)
Question Three.
(a)
A sample of 70 mmol Kr(g) expands reversibly and isothermally at 373
K from 5.25 mL to 6.29 mL, and the internal energy of the sample is
known to increase by 83.5 J. Use the virial equation of state up to the
second coefficient B = -28.7 mL mol-1 to calculate w, q, and ΔH for this
change of state.
(b)
A sample of 1.00 mol of N2 gas is expanded adiabatically from a
volume of 10.00 dm3 and a temperature of 400 K to a volume of 20.00
dm3. Assume that nitrogen is ideal, with Cv,m = 5R/2. (i) Find the final
temperature if the expansion is carried out reversibly. (ii) Calculate the
final temperature if the expansion is carried out with a constant
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external pressure of 1.00 atm. (iii) Find the final temperature if the gas
expands into a vacuum. (iv) Find ∆U and w for each of the processes
in the three parts, above. (v) For the reversible expansion in (i), show
that the value of w obtained from the integral wrev = -[Integral]Pdv is the
same as the value of w obtained from w = ∆U – q = ∆U.
(20 points)
Question Four.
(a)
Show that the following functions have exact differentials: (a) x2y + 3y2;
(b) x3y2; (c) xcos(xy); (d) t(t+es) + s.
(b)
Starting from the expression for the total differential of enthalpy, H,
express (δH/δP)T in terms of Cp and the Joule-Thompson coefficient.
(c)
A gas obeys the equation of state Vm = RT/P + αT2 and its constant
pressure heat capacity is given by Cp,m = A + BT + CP; where α, A, B,
C are constants independent of T and P. Obtain expressions for (a)
the Joule-Thompson coefficient and (b) its constant volume heat
capacity.
(25 points)
Question Five.
(a)
A gas obeying the van der Waals equation of state undergoes a
reversible isothermal volume change from V1 to V2. Obtain the
expression of the work done, w. Re-evaluate work done after setting a
= b = 0. Next, calculate the work done in the case of 0.500 mol N2,
(while obeying the van der Waals equation of state), expanding
reversibly from 0.400 dm3 to 0.800 dm3 at 300 K. Compare this result
with what you would evaluate if one assumes N2 to be ideal. (VDW’s
constants for N2 can be sourced from the text or elsewhere).
(b)
A certain perfect gas has Cv,m = a + bT where a = 25.0 J mol-1 K-1 and
b = 0.03 J mol-1 K-2. Let 4.00 mol of this gas go from 300 K and 2.00
atm to 500 K and 3.00 atm. Calculate each of the following quantities
for this change of state. If it is impossible to calculate a quantity from
this given information, state this. (a) q; (b) w; (c) ∆U; (d) ∆H. For
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bonus points only; since this homework will be due before we complete
the topic on the second law of thermodynamics: (e) calculate ∆S (3
extra points).
(20 points)
For Bonus Points only. A correct, full response to this question will add 5
points to your score, such that it is possible to obtain a final grade of 108%!
[Indulge!]
Express the work of isothermal reversible expansion of a VDW’s gas in
reduced variables and find a definition of reduced work that makes the overall
expression independent of the identity of the gas. Calculate the work of
isothermal reversible expansion along the critical isotherm from V c to xVc.
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