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-
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
Similarly,
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
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
Case-1
When k2[A]o <<< k1
then, [A] = [A]oe − k1t
Case-2
When k2[A]o >>> k1
then, 1/[A] = 1/[A]oe + k2t
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