Question

What is zeroth order reaction? Derive its integrated rate Law. What are the units of rate constant?

Answer 1

The rate of zero order reaction is independent of the reactant concentration. For zero-order reaction, A → P the differential rate law is given by rate 

`= - (d[A])/dt = k[A]_0 = k`   ...(i)

Rearrangement of Eq. (i) gives

d[A] = - k dt             ...(∵ [A]⁰ = 1)

Integrating between the Limits

[A] = [A]₀ at t = 0 and [A] = [A]t at t = t gives

`int_[[A]_0]^[[A]_t] d[A] = - k int_0^t dt`    or

 [A]_t - [A]₀ = - kt

Hence, kt = [A]₀ - [A]_t      ... (ii)

Units of rate constant of zero order reactions

`k = ([A]_0 - [A]_t)/t = "mole"^(-1)/t`

= mole dm^-3 r^-1 

The units of rate constant of zero order reaction are the same as the rate.