Question

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

Answer 1

The rate of a zero-order reaction is independent of the concentration of the reactant.

For a zero-order reaction:

A → P

The differential rate law is given by:

`-(d[A])/dt = k[A]^0 = k`

Rearranging Equation (i):

`(d[A])/dt = -k => d[A] = -k  dt ("since" [A]^0 = 1)`

`int` Integrating Between the Limits:

Let: 

[A]₀ be the concentration at t = 0

[A]_t​ be the concentration at time t

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

[A]_t​ − [A]₀ ​= −kt ⇒ [A]₀ ​− [A]_t ​= kt

`k = ([A]_0 - [A]t)/t`

Let concentration be in mol dm⁻³ and time in seconds (s):

`k = ("mol dm"^-3)/("time")` = mol dm⁻³ t⁻¹

If time is in seconds:

k = mol dm⁻³ s⁻¹