Page 278 - Physical Chemistry

lev38627_ch08.qxd 3/14/08 12:54 PM Page 259

259
8.10 SUMMARY Problems
The compression factor of a gas is defined by Z PV /RT and measures the devia-
m
tion from ideal-gas P-V-T behavior. In the van der Waals equation of state for gases,
2
2
(P a/V )(V b) RT, the a/V term represents intermolecular attractions and b
m
m
m
represents the volume excluded by intermolecular repulsions. The Redlich–Kwong
equation is an accurate two-parameter equation of state for gases. The parameters in
these equations of state are evaluated from critical-point data. The virial equation, de-
rived from statistical mechanics, expresses Z as a power series in 1/V , where the ex-
m
pansion coefficients are related to intermolecular forces.
Important kinds of calculations dealt with in this chapter include:
• Use of nonideal equations of state such as the van der Waals, the Redlich–Kwong,
and the virial equations to calculate P or V of a pure gas or a gas mixture.
• Calculation of constants in the van der Waals equation from critical-point data.
• Calculation of differences between real-gas and ideal-gas thermodynamic proper-
ties using an equation of state.
• Use of an equation of state to calculate vapor pressures and saturated liquid and
vapor molar volumes.

FURTHER READING AND DATA SOURCES

Poling, Prausnitz, and O’Connell, chaps. 3 and 4; Van Ness and Abbott, chap. 4;
McGlashan, chap. 12.
Compression factors: Landolt-Börnstein, 6th ed., vol. II, pt. 1, pp. 72–270.
Critical constants: A. P. Kudchadker et al., Chem. Rev., 68, 659 (1968) (organic
compounds); J. F. Mathews, Chem. Rev., 72, 71 (1972) (inorganic compounds);
Poling, Prausnitz, and O’Connell, Appendix A; Landolt-Börnstein, 6th ed., vol. II,
pt. 1, pp. 331–356; K. H. Simmrock, R. Janowsky, and A. Ohnsorge, Critical Data of
Pure Substances, DECHEMA, 1986; Lide and Kehiaian, Table 2.1.1; NIST Chemistry
Webbook at webbook.nist.gov/.
Virial coefficients: J. H. Dymond and E. B. Smith, The Virial Coefficients of Pure
Gases and Mixtures, Oxford University Press, 1980.

PROBLEMS

Section 8.2 right side of (8.5), and compare the coefficient of each power of
8.1 Give the SI units of (a) a and b in the van der Waals equa- 1/V with that in (8.4).
m
tion; (b) a and b in the Redlich–Kwong equation; (c) B(T ) in 8.5 Use Eq. (8.7) and data in Sec. 8.2 to find V of Ar(g) at
the virial equation. 200 K and 1 atm. m
3
8.2 Verify that the van der Waals, the virial, and the 8.6 At 25°C, B 42 cm /mol for CH and B 732
4
3
Redlich–Kwong equations all reduce to PV nRT in the limit cm /mol for n-C H . For a mixture of 0.0300 mol of CH and
4
10
4
of zero density. 0.0700 mol of n-C H 10 at 25°C in a 1.000-L vessel, calculate
4
the pressure using the virial equation and (a) the approximation
3
8.3 For C H at 25°C, B 186 cm /mol and C 1.06
2 6 1
4
2
6
2
12
10 cm /mol . (a) Use the virial equation (8.4) to calculate the B (B B ); (b) the fact that for this mixture, B 180
2
1
12
3
3
pressure of 28.8 g of C H (g) in a 999-cm container at 25°C. cm /mol. Compare the results with the ideal-gas-equation
2 6
Compare with the ideal-gas result. (b) Use the virial equation result.
(8.5) to calculate the volume of 28.8 g of C H at 16.0 atm and
2 6 Section 8.4
25°C. Compare with the ideal-gas result.
8.7 For ethane, P 48.2 atm and T 305.4 K. Calculate the
c
c
3
8.4 Use the following method to verify Eq. (8.6) for the virial pressure exerted by 74.8 g of C H in a 200-cm vessel at 37.5°C
2
6
coefficients. Solve Eq. (8.4) for P, substitute the result into the using (a) the ideal-gas law; (b) the van der Waals equation;