Question

Derive the expression for integrated rate law for zero order reaction A → Products.

Answer 1

Consider a zero-order reaction, A → Products

The rate of the reaction is, Rate = `(-d[A])/dt`

By rate law,

Rate = k × [A]₀ = k

∴ − 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 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`