Question

Derive the integrated rate law for the zeroth order reaction. 

Answer 1

For zero-order reaction, A → P

the differential rate law is given by

rate = \[\mathrm{rate}=-\frac{\mathrm{d}[\mathrm{A}]}{[\mathrm{A}]}=k [\mathrm{A}]^0=k\]   ...(i)

Rearrangement of Eq. (i) gives

d[A] = −k dt   

Integration between the limits

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

\[\int\limits_{\left[\mathrm{A}\right]_0}^{[\mathrm{A}]^\mathrm{t}}\mathrm{d}[\mathrm{A}]=-\mathrm{k}\int\limits_0^\mathrm{t}\mathrm{dt}\]

or [A]_{t −} [A]₀ = −kt

Hence, kt = [A]₀ − [A]_t   ...(ii)