Example 1.2: A number of experiments were conducted to
study the decomposition reaction of acetic anhydride (first order). Find the energy of activation and frequency
factor if the following data apply:
|
T/°C |
310 |
320 |
330 |
340 |
350 |
|
k/s-1 |
0.1177 |
0.1945 |
0.3159 |
0.5052 |
0.7957 |
Solution
·
Plot ln(k) versus 1/T and draw a straight line.
Alternately, use
method of least squares to obtain slope and intercept. The values of X, Y, XY, X2, SY, SXY, SX2 are presented.
|
t/°C |
k/s-1 |
X
= 1/T |
Y = ln(k) |
XY |
X2 |
|
310 |
0.1177 |
1.71 ´
10-3 |
-2.139 |
-3.67 ´
10-3 |
2.94 ´
10-6 |
|
320 |
0.1945 |
1.69 ´
10-3 |
-1.638 |
-2.76 ´
10-3 |
2.84 ´
10-6 |
|
330 |
0.3159 |
1.66 ´
10-3 |
-1.152 |
-1.91 ´
10-3 |
2.75 ´
10-6 |
|
340 |
0.5052 |
1.63 ´
10-3 |
-0.683 |
-1.11 ´
10-3 |
2.66 ´
10-6 |
|
350 |
0.7957 |
1.60 ´
10-3 |
-0.229 |
-3.67 ´
10-4 |
2.58 ´
10-6 |
|
S |
|
8.29 ´
10-3 |
-5.841 |
-9.82 ´
10-3 |
1.38 ´
10-5 |
·
Slope, m (Equation 1.2):
|
|
·
Energy of activation, E = -Rm = 1.9872 ´
(-1.736´104)
= 3.45 ´
104 cal/mol
·
Intercept, I (Equation 1.3):
|
|
·
Frequency factor, A = exp(I)
= exp(27.631) = 1.0 ´ 1012 s-1.