Page 211 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 181

Y = Ae BX (3-253)

Linearizing Equation 3-253 gives

ln Y = ln A + BX (3-254)

where ln Y = ln k T
ln A = ln k O
B = –E/R
X = 1/T
The computer program PROG1 determines the values of constants
A and B. Table 3-9 gives the results of the program and the con-
stants A and B
The constants for the equation are:

• A = 78728 × 10 15
• B = –0.94869 × 10 4
• Correlation Coefficient = 0.99966

4
14
The slope B = –E/R = –0.9487 × 10 and A = k = 7.873 × 10 .
O
4
The activation energy E = R • B = 8.314 × 10 (J/mol) and E = 78.9
–1
14
3
× 10 J/mol. The pre-exponential factor is k = 7.87 × 10 sec .
O
Figure 3-20 gives a plot of ln k against 1/T.
T
Example 3-3
R. T. Dillon (1932) studied the reaction between ethylene bromide
and potassium iodide in 99% methanol with the following data:

Table 3-9
Actual Estimated
–1
–1
1/T ln k(sec ) ln k(sec )
0.00353 0.732 0.795
0.00346 1.520 1.456
0.00339 2.109 2.103
0.00333 2.760 2.745
0.00326 3.346 3.332
0.00321 3.831 3.859
0.00314 4.538 4.546