Physical Chemistry , 1st ed.

Figure 4.7 shows such a plot for neon at 150 K. The fugacity of neon at any

pressure is the area under this curve from zero to that pressure.

Example 4.13

Calculate the fugacity of 100. atm of argon gas at 600. K assuming its com-

pressibility is adequately represented by the truncated virial equation Z

1 Bp/RT.Bfor Ar at 600 K is 0.012 L/mol (from Table 1.4). Comment on

the answer.

Solution

Using equation 4.61:

ln 

100 atm

0

dp

100 atm

0

dp

100 atm

0



R

B

T



dp



B

R



T

p



0

100 atm



B(10

R

0

T

atm)



By substituting B0.012 L/mol,R0.08205 L atm/mol K and T

600 K, we have

ln  0.024

Therefore, ln 0.024, so 1.024. Since fp, this means that f

102. atm. This argon gas acts as if it had a slightly larger pressure than it ac-
     tually does. This should be considered approximate, since the virial coeffi-
     cient Bshould be applicable to conditions of 100. atm and 600. K.

To illustrate how fugacity varies with pressure, Table 4.1 lists the fugacities

of nitrogen gas. Note how the fugacity almost equals the pressure at p1 atm,

but by the time p1000 atm, the fugacity is almost twice the pressure.

(0.012 mLol)(100 atm)



(0.08205 mL^ oatlm K)(600 K)

BRTp



p

1 BRTp 1



p

4.9 Fugacity 113

0.0009

0.0008

0.0007

0.0006

0.0005

0.0004

0.0003

0.0002

0

p (bar)

100 200 300 400 500 600

Z 

1

p

(bar

^1

)

Figure 4.7 On a plot of (Z1)/pversus pressure for a real gas, the area under the curve be-

tween 0 and some pressure pgives the logarithm of the fugacity coefficient for the gas at that

pressure. The data plotted here are for neon at 150 K.

Table 4.1 Fugacities of nitrogen gas at 0°C
P(atm) Fugacity (atm)
1 0.99955
10 9.956
50 49.06
100 97.03
150 145.1
200 194.4
300 301.7
400 424.8
600 743.4
800 1196
1000 1839
Source: G. N. Lewis, M. Randall.Thermodynamics,revised by
K. S. Pitzer and L. Brewer, McGraw-Hill, New York, 1961.