Physical Chemistry , 1st ed.

most important measure of the nonideality of a real gas. Table 1.3 lists values

of the second virial coefficient of several gases.

Virial equations of state in terms of pressure instead of volume are often

written not in terms of compressibility, but in terms of the ideal gas law itself:

pVRTB pC p^2 D p^3    (1.18)

where the primed virial coefficients do nothave the same values as the virial

coefficients in equation 1.17. However, if we rewrite equation 1.18 in terms of

compressibility, we get

Z

p

R

V

T

 1 

B

R

T

p



C

R

p

T

2



D

R

T

p^3

   (1.19)

At the limit of low pressures, it can be shown that BB. The second virial

coefficient is typically the largest nonideal term in a virial equation, and many

lists of virial coefficients give only Bor B.

Example 1.4

Using equations 1.17 and 1.19, show that Band B have the same units.

Solution

Equation 1.17 implies that the compressibility is unitless, so the second vir-

ial coefficient must cancel out the unit in the denominator of the second

term. Since volume is in the denominator,Bmust have units of volume. In

equation 1.19, compressibility is again unitless, so the unit for B must can-

cel out the collective units ofp/RT.But p/RThas units of (volume)^1 ; that is,

units of volume are in the denominator. Therefore,B must provide units of

volume in the numerator, so B must also have units of volume.

12 CHAPTER 1 Gases and the Zeroth Law of Thermodynamics

2.5

2.0

1.5

1.0

0.5

(a)

0

0

p (atm)

200 400 600 800 1000 1200

Z

^

pV

/RT

2.00

CO N 2

O 2

CH 4

H 2

CO 2

NH 3

 50 °C

0 °C

100 °C

300 °C

1.80

1.60

1.40

1.20

1.00

(b)

0.80

0

p (bar)

200 400 600 800 1000

Compressibility factor

Figure 1.8 (a) Compressibilities of various gases at different pressures. (b) Compressibilities

of nitrogen at different temperatures. Note that in both graphs, the compressibilities approach 1

at the limit of low pressure. (Sources:(a) J. P. Bromberg,Physical Chemistry,2nd ed., Allyn &

Bacon, Boston, 1980. Reprinted with permission of Pearson Education, Inc. Upper Saddle River,

N.J. (b) R. A. Alberty,Physical Chemistry,7th ed., Wiley, New York, 1987.)

Table 1.3 Second virial coefficients B

for various gases (in cm^3 /mol,

at 300 K)

Gas B

Ammonia, NH 3  265

Argon, Ar  16

Carbon dioxide, CO 2  126

Chlorine, Cl 2  299

Ethylene, C 2 H 2  139

Hydrogen, H 2 15

Methane, CH 4  43

Nitrogen, N 2  4

Oxygen, O 2  16 a

Sulfur hexafluoride, SF 6  275

Wa t e r, H 2 O  1126

Source:D. R. Lide, ed.,CRC Handbook of Chemistry and

Physics,a 82nd ed., CRC Press, Boca Raton, Fla., 2001.

Extrapolated