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]

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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

- \int_{[A0]}^{[A]} 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]

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