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Question
Derive the integrated rate equation for the rate constant of a zero order reaction.
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Solution
Consider a zero order reaction A→ products.
The rate law is rate =−d[A]dt=k[A]0=k
Rearrange above equation
d[A]=−kdt
Integrate between limits [A]=[A]0 at t=0 and [A]=[A]t at t=t
∫[A][A]0d[A]=−k∫t0dt
Hence, [A][A]t[A]0=−k(t)t0
[A]t−[A]0=−kt
[A]t=−kt+[A]0
k=[A]0−[A]tt
The rate law is rate =−d[A]dt=k[A]0=k
Rearrange above equation
d[A]=−kdt
Integrate between limits [A]=[A]0 at t=0 and [A]=[A]t at t=t
∫[A][A]0d[A]=−k∫t0dt
Hence, [A][A]t[A]0=−k(t)t0
[A]t−[A]0=−kt
[A]t=−kt+[A]0
k=[A]0−[A]tt
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