Page 219 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 189

Linearizing the rate expression gives

(
ln Rate) = ln k + n ln P + m ln P (3-275)
2
BH 6 Me CO
2
Equation 3-275 is of the form
=
YC + C X + C X (3-276)
O 1 1 2 2
where the coefficients C = k, C = n, and C = m. The computer
O 1 2
program PROG3 determines the coefficients from the multiple regres-
sion of the independent variables P and P and the dependent
2
2
BH 6 Me CO
variables Rate. The results of the program give the coefficients for
Equation 3-276 as:
• C = 4.67755
O
• C = 0.978166
1
• C = 0.954575
2
• Correlation Coefficient = 0.9930
Therefore, C = k = 4.68, C = n = 0.98, and C = m = 0.95. The
O 1 2
.
.
rate equation is expressed as Rate= 468. P 098 P 0 95 , or as a
2
2
B H 6 Me CO
good approximation,
.
Rate = 47 P P (3-277)
2
2
B H 6 Me CO
The rate constant k can be determined with values of the exponents,
m = n ≅ 1 as follows:
Rate= k P 10 P 10
.
.
2
2
B H 6 Me CO
k = Rate
P P
B H 6 Me CO
2
2
The average rate constant k = 3.85 and the final rate equation is
.
Rate = 385 P P . The computed rate constant from PROG3 is
B H 6 Me CO
2
2
4.68 and the calculated value from Table 3-12 is 3.85. The percentage
deviation between these values is 17.8%. Figure 3-22 shows plots of
partial pressures of B H and Me CO versus the initial rate.
6
2
2