Question

(20 pts.) Consider two competing reactions: In this case, A decomposes to give B and C via two competing paths. Assuming each path is irreversible and that each reaction is first-order: (a) Write the rate law for the overall reaction. (b) Derive the integrated rate expression for [A]

Answer 1

Part a

For the Reaction

?A - - - - > B

Rate of reaction = - k1[A]

Negative Sign shows the decomposition of A

For the Reaction

?A - - - - > C

Rate of reaction = - k2[A]

Overall rate of reaction = - k1[A] - k2[A]

Part b

d[A] /dt = - k1[A] - k2[A]

- d[A] /[A] = (k1 + k2) dt

?Integrate the above equation

-
Part a For the Reaction ?A B Rate of reaction = -k1[A] Negative Sign shows the decomposition of A For the Reaction ?A C Rate of reaction = -k2[A] Overall rate of reaction = -k1[A] - k2[A] Part b d[A] /dt = -k1[A] - k2[A] - d[A] /[A] = (k1 + k2) dt ?Integrate the above equation integral_{[A0]}^{[A]} d[A] /[A] = (k1 + k2) integral_{0}^{t} dt At t = 0, [A] = [A0] ?At t = t, [A] = [A] - ln [A]/[A0] = (k1 + k2) t [A] = [A0] exp [-(k1 + k2) t]
d[A] /[A] = (k1 + k2) $\int_{0}^{t}$ dt

At t = 0, [A] = [A0]

?At t = t, [A] = [A]

- ln [A]/[A0] = (k1 + k2) t

[A] = [A0] exp [-(k1+k2) t]