Physical Chemistry Third Edition

466 10 Transport Processes

EXAMPLE10.14

Calculate the viscosity coefficient of O 2 gas at 292 K from its hard-sphere diameter. Compare

your result with the value in Table A.18 in the appendix.

Solution

m

0 .03200 kg mol−^1

6. 02214 ×1023 mol−^1

 5. 3137 × 10 −^26 kg

η

5

16

1

(3. 58 × 10 −^10 m)^2

(

(5. 3137 × 10 −^26 kg)(1. 3807 × 10 −^23 JK−^1 )(292 K)

π

) 1 / 2

 2. 013 × 10 −^5 kg m−^1 s−^1

The value in Table A.18 is 2.018 g× 10 −^5 kg m−^1 s−^1. This relatively close agreement is not

surprising since the effective hard-sphere diameters are presumably obtained from viscosity

data, probably using a somewhat more accurate formula than Eq. (10.3-12).

Exercise 10.13

Calculate the hard-sphere diameter of water molecules at 100◦C from the coefficient of viscosity

in Table A.18. Compare your result with the hard-sphere diameter in Table A.15.

Exercise 10.14

Certain useful dimensionless ratios of physical constants are calleddimensionless groups. Show

that for a monatomic hard-sphere gas each of the following ratios equals a dimensionless constant

and find each constant:

η

mND

,

cVη

κm

,

DcVN

κ

PROBLEMS

Section 10.3: The Gas Kinetic Theory of Transport

Processes in Hard-Sphere Gases

10.22a. Calculate the self-diffusion coefficient of helium gas
at STP (273.15 K, 1.000 atm) from the hard-sphere
diameter.
b. Calculate the self-diffusion coefficient of argon gas at
STP from the hard-sphere diameter.
c.Calculate the self-diffusion coefficient of argon gas at
0.100 atm and 273.15 K from the hard-sphere diameter.
Comment on the comparison with the result of part b.
d.Calculate and compare the rms distances traveled
in one direction in 60.0 minutes by He and

Ar atoms diffusing at STP in self-diffusion

experiments.

10.23a. Calculate the self-diffusion coefficient of carbon

dioxide gas at 1.000 bar and 298.15 K from the

hard-sphere diameter.

b. Calculate the self-diffusion coefficient of O 2 gas

at 1.000 bar and 373.15 K from the hard-sphere

diameter.

10.24Calculate the effective hard-sphere diameter of argon

atoms from the value of its self-diffusion coefficient at

273 K in Table A.19. Compare it with the value from

Table A.15.