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Question
Derive integrated rate law for zero order reaction.
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Solution
Consider a zero-order reaction, \[\ce{A -> Product}\]
The rate of the reaction is:
Rate = `-(d[A])/dt`
By the rate law,
Rate = k × [A]0 = k
On rearranging the equation,
∴ d[A] = k × dt
If [A]0 is the initial concentration of the reactant A at t = 0 and [A]t is the concentration of A present after time t, then by integrating the above equation,
`int_([A]_0)^([A]_t) - d[A] = int_(t = 0)^(t = t) k dt`
`- int_([A]_0)^([A]_t) d [A] = kint_(0)^(t) dt`
`[A]_([A]_0)^([A]_t) = k [t]_0^t`
−([A]t − [A]0) = kt
∴ [A]0 − [A]t = kt
∴ k = `([A]_0 - [A]_t)/t`
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