Page 202 - Modeling of Chemical Kinetics and Reactor Design

172 Modeling of Chemical Kinetics and Reactor Design

Consider a mole balance on a constant volume batch reactor repre-
sented by

− dC A = kC C b B (3-227)
a
A
dt
Using the method of initial rates gives

 dC A  a b
−
) = kC
 dt  O =− ( r A O AO C BO (3-228)

Taking the logarithms of both sides of Equation 3-228 gives


+
ln − dC A  = ln ka ln C + b lnC (3-229)
 dt  AO BO
This can be represented in the form

Y = C + C X + C X (3-230)
0 1 1 2 2
where Y = ln (–dC /dt), C = ln k, X = ln C , X = ln C , C = a,
A O 1 AO 2 BO 1
and C = b. If N experimental runs are performed, then for the ith
2
run, Equation 3-230 becomes

Y = C + C X + C X 2,i (3-231)
1,i
i
1
O
2
where X = ln C AOi , with C AOi being the initial concentration of A
1i
for the ith run. Solving for the unknowns C , C , and C for N experi-
1
2
O
mental runs, i = 1, 2, 3 . . . N, gives
N N N
∑ Y = NC + C 1 ∑ X + C 2 ∑ X i 2 (3-232)
i
i 1
O
i=1 i=1 i=1
N N N N
∑ XY = C O ∑ X + C 1∑ X + C 2 ∑ X X i 2 (3-233)
2
i 1
i 1
i 1
i
i 1
=
=
=
=
i 1 i 1 i 1 i 1
N N N N
∑ XY = C O ∑ X i 2 + C 1∑ X X i 2 + C 2 ∑ X 2 i 2 (3-234)
i
i 1
i 2
=
=
=
i 1 i 1 i 1 i 1=