What is zero order reaction? Derive integrated rate law equation for zero order reaction.

Answer:

Zero order reaction: A reaction whose rate does not depend on the concentration of the reactant, i.e. the rate is constant and equal to the rate constant, is called a zero order reaction (e.g. decomposition of NH₃ on a hot platinum surface).

Integrated rate law: For A → products, rate \(= -\dfrac{d[A]}{dt} = k[A]^0 = k\)

\(d[A] = -k\,dt\). Integrating between \(t = 0\), \([A] = [A]_0\) and time \(t\), \([A] = [A]_t\):

\(\displaystyle\int_{[A]_0}^{[A]_t} d[A] = -k\int_0^t dt\)

\([A]_t - [A]_0 = -kt\)

\(\therefore\ k = \dfrac{[A]_0 - [A]_t}{t}\) or \([A]_t = [A]_0 - kt\)

A plot of \([A]_t\) against \(t\) is a straight line with slope \(-k\) and intercept \([A]_0\). The half-life is \(t_{1/2} = \dfrac{[A]_0}{2k}\).