Page 168 - Essentials of physical chemistry

130 Essentials of Physical Chemistry

q ffiffiffiffiffiffi
2
(10) 4. Derive the expressions for V and V of a gas molecule using the Boltzmann principle.
(Answer in Chapter 3, how fast can you do the derivation?)
(10) 5. Compute DH 0 298 for the reaction: C 6 H 6 þ 3H 2(g) ! C 6 H 12 given the data
DH comb (C 6 H 6 ) ¼ 782:3kcal=mol, DH comb (C 6 H 12 ) ¼ 937:8kcal=mol, and DH comb (H 2 ) ¼
68:3kcal=mol. (DH 0 298 ¼ 49.4 kcal, use Hess’s rule of summation)
(15) 6. Calculate the temperature of air compressed adiabatically in a one-cylinder diesel engine
3 3
from 1035 cm at 258Cto35cm . Given C V ¼ (5=2)R, compute moles of air, Q, W, DU, and
DH for this compression if the initial pressure is 1 atm.
(T 2 ¼ 11558K, P 2 ¼ 114.61 atm, mol ¼ 0.0423, Q ¼ 0, W ¼ DU ¼þ180 cal, DH ¼þ252 cal)

qU
(15) 7. Derive the expression for of a van der Waals gas and use it to compute DU for the
qT
T
isothermal expansion of 7 mol of Ne gas from 50 to 500 L at constant 258C given

qP
2
2
‘‘a’’ ¼ 0.21 L atm=mol . (Hint: Use dU ¼ T P)
qT
V
!
500 L dV 1
ð 500 L
2
2
DU ¼ n a ¼ n a ¼þ4:485 cal ¼þ18:765 J, note sign
V 2 V
50 L 50 L
(5) 8. Show that (C P C V ) ¼ R for an ideal gas. (Answer in Chapter 4, how fast can you do it?)
(5) 9. Calculate V for He gas in mph at 258C(He ) 4:002602 g=mol)
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
!
r ffiffiffiffiffiffiffiffiffi
7
8RT 8(8:314 10 erg=K mol)(298 K) 3600 s=h

¼ 2809:4 mph
V ¼ ¼ 5
pM p(4:002602) 1:6093 10 cm=mile
BIBLIOGRAPHY
Hill, T. L., An Introduction to Statistical Thermodynamics, Addison-Wesley, Reading, MA, 1960, p. 186.
REFERENCES
1. Lide, D. R., CRC Handbook of Chemistry and Physics, 90th Edn., CRC Press, Boca Raton, FL,
2009–2010, pp. 6–72.
2. Maron, S. H. and Prutton, C. F., Principles of Physical Chemistry, The Macmillan Co., New York, 1958,
p. 91.
3. Petersen, S. L., S. L. Naccarato, and G. John, December 2007=January 2008, Forensic Magazine. See the
article at http:==www.csigizmos.com=products=latentdevelopment=enhancinglatent.html
4. Lide, D. R., CRC Handbook of Chemistry and Physics, 87th Edn., CRC Press, Boca Raton, FL, 2007,
p. 9–48.
5. Kier, L. B. and C.-K. Cheng, A cellular automata model of water, J. Chem. Inf. Compu. Sci., 34, 647
(1994).
6. Lewis, G. N. and Randall, M.: Revised by Pitzer, K.S. and L. Brewer (1961), Thermodynamics, 2nd
Edn., McGraw-Hill, New York, 1961.
7. Barrow, G. A., Physical Chemistry, 6th Edn., The McGraw-Hill Companies, Inc., New York, 1996, p. 305.
8. Bukowski, R., K. Szalewicz, G. C. Groenenboom, and Ad van der Avoird, Predictions of the properties
of water from first principles, Science, 315, 1249 (2007).
9. Lide, D. R., CRC Handbook of Chemistry and Physics, 90th Edn., CRC Press, Boca Raton, FL,
2009–2010, p. 9–52.
10. Wall,F.T.,ChemicalThermodynamics, 3rdEdn.,W.H.FreemanandCo.,SanFrancisco,CA,1974,p.463.
11. Goodman, J. M., Chemical Applications of Molecular Modeling, The Royal Society of Chemistry,
Cambridge, U.K., 1998.
12. Kier, L. B., A cellular automata model of bulk water, Chem. Biodivers., 4, 2540 (2007).