Page 148 - Introduction to chemical reaction engineering and kinetics

130 Chapter 6: Fundamentals of Reaction Rates

where p is the reduced molecular mass defined by:

P = mAmd(mA + 5) (6.4-6)

The collision frequency of like molecules, Z,, can be obtained similarly, but the
collision cross-section is cr = rdi, the reduced mass is Al. = m,/2, and we must divide
by 2 to avoid counting collisions twice:

z,, = (1/2)oz+;)2 (6.4-7)

(a) Calculate the rate of collision (2,s) of molecules of N, (A) and 0, (B) in air (21
mol % O,, 78 mol % N2) at 1 bar and 300 K, if dA = 3.8 X lo-lo m and dB =
3.6 X lo-lo m
(b) Calculate the rate of collision (2,) of molecules of N, (A) with each other in air.

SOLUTION

(a) From equations 6.4-4 and -5, with u = rdi,,

Z,, = d&$,c;(8n-kBTIp)1” (6.4-4a)

with

dAB = (3.8 + 3.6) X lo-“/2 = 3.7 X-lo m
From equation 4.2-3a,

CL = NAVcA = N,,p,IRT = 6.022 X 1023(0.78)105/8.314(300)
= 1.88 X 1O25 molecules mP3

Similarly,

CL = 0.507 X 102’ molecules me3
p = mAmBl(m, + m,) = 28.0(32.0)/(28.0 + 32.0)(6.022 X 1023)1000
= 2.48 x 1O-26 kg
z, = (3.7 x lo-lo 2 ) (1.88 x 1025)(0.507 x 1025)[8~(1.381 x 10-23)300/2.48 x 10-26]“2
= 2.7 X 1034m-3s-1

(b) From equation 6.4-7, together with 6.4-5 and -6 (giving /.L = m,/2), and with (T =
n-d;,

Zu = 2d~(c~)2(?rkBTlm,)“2 (6.4-7a)