Page 224 - Modeling of Chemical Kinetics and Reactor Design

194 Modeling of Chemical Kinetics and Reactor Design

Determine the order of the reaction and the rate constant.

Solution

If the reaction is second order, the rate equation is:

− ( r A )=− dC A = kC 2 A (3-283)
dt

Rearranging Equation 3-283 and integrating with the boundary
conditions, at t = 0, C = C AO and at t = t, C = C , gives
A
A
A
C A dC t
∫
− ∫ A = kdt
C 2 A (3-284)
C AO 0

1 1
− = kt (3-285)
C A C AO

A plot of 1/C versus t gives a straight line with the slope = k =
A
0.06661/gmol•s. The computer program PROG1 determines the rate
constant for a second order reaction. Equation 3-285 is of the form
1/Y = A + BX where the slope B is the rate constant k. The results
of the computer program are shown in Table 3-14.
The constants for the equation are:

• A = 0.496 × 10 2
• B = 0.0666
• Correlation Coefficient = 0.9992

Table 3-14
Actual Estimated
Time, sec 1/C NOCl , gmol/l 1/C NOCl , gmol/l
0 50 49.6
200 62.5 62.9
300 68.97 69.5
500 83.3 82.8