Kinetics of Parallel Reactions

Kinetics of Parallel Reactions

Kinetics of Parallel Reactions

Parallel Reactions

Reactions in which initial species react to give multiple products simultaneously.
Let's consider a reactant 'A' reacts to form product 'B' and 'C' simultaneously is given below-
Consecutive Reactions
Where k1 and k2 are the rate contents.

If the initial concentration of 'A' is'[A]o' and that of 'B' and 'C' be zero. After time 't', the concentration of A, B and C be [A], [B,] and [C] respectively.
If we assume that both the reactions are first order, then both the rates R1 and R2 can be given as-
Rate R1 = −d[A]/dt = d[B]/dt = k1[A]1     ---Eq.-1
Rate R1 = −d[A]/dt = d[C]/dt = k2[A]1     ---Eq.-2
Now total rate of reaction-
−d[A]/dt = R1 + R2     ---Eq.-3
or, −d[A]/dt = k1[A] + k2[A]     ---Eq.-4
or, −d[A]/dt− = (k1 + k2)[A]     ---Eq.-5
or, d[A]/dt = −(k1 + k2)[A]     ---Eq.-6
on integrating the above equation with respect to 't', we get the following equation-

[A] = [A]o e−(k1 + k2)t      ---Eq.-6

d[B]/dt = k1[A] = k1[A]oe−(k1 + k2)t      ---Eq.-7
[B] = − k1[A]o/(k1 + k2)(e−(k1 + k2)t) + C      ---Eq.-8
When 't' = 0, [B] = 0
Putting the value of 't' and [B] in Eq.-8 we get-
C = k1[A]o/(k1 + k2)      ---Eq.-9
Now putting the value of 'C' in Eq.-8 we get-

[B] = k1[A]o/(k1 + k2)(1 − e−(k1 + k2)t)      ---Eq.-10

Likewise [B]-

[C] = k2[A]o/(k1 + k2)(1 − e−(k1 + k2)t)      ---Eq.-11

Now the ratio of [B] to [C]-
[B]/[C] = k1/k2      ---Eq.-12
Percentage Yield of [B] = k1/(k1 + k2) x 100      ---Eq.-13
Percentage Yield of [C] = k2/(k1 + k2) x 100      ---Eq.-14
Consecutive Reactions

If we assume that one is 1st order and other is 2nd order reactions, then-
d[B] = k1[A]1
d[C] = k2[A]2
So, − d[A]/dt = k1[A] + k2[A]2
or, [A] = k1/ek1t(k1 + k2[A]o) − k2[A]o
When k2[A]o <<< k1
then, [A] = [A]oe − k1t
When k2[A]o >>> k1
then, 1/[A] = 1/[A]oe + k2t