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Question
Derive integrated rate law for a zero-order reaction \[\ce{A -> Product}\].
Solution
The integrated rate law for zero order reaction:
For zero order reaction,
A →P
The differential rate law is given by,
Rate = d[A] = k[A]0 = k .............(i)
Rearrangement of Eq. (i) gives,
d[A] = -kdt
Integration between the limits.
[A] = [A]0 at t = 0 and [A] = [A]t at t = t gives,
`int_{[A]_0}^{[A]^t}d[A] = -kint_0^t dt`
or [A]t - [A]0 = -kt
Hence, kt = [A]0 - [A]t
k = `([A]_0 - [A]_t)/t`
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