Question

derive the integrated rate equation for rate constant of a zero order reaction.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{For}\mathrm{a}\mathrm{zero}\mathrm{order}\mathrm{reaction}, \\ \mathrm{Rate}=-\frac{\mathrm{d}[\mathrm{A}{]}^0}{\mathrm{dt}}=\mathrm{k} \\ \mathrm{or},\mathrm{d}\left[\mathrm{A}\right]=-\mathrm{kdt} \\ \mathrm{Integrating}\mathrm{both}\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{equation} \\ {\int }_{[\mathrm{A}{]}_0}^{\left[\mathrm{A}\right]}\mathrm{d}\left[\mathrm{A}\right]=-{\int }_0^{\mathrm{t}}\mathrm{kdt} \\ \mathrm{or},\left[\mathrm{A}\right]-[\mathrm{A}{]}_0=-\mathrm{kt} \\ \mathrm{or},[\mathrm{A}]=[\mathrm{A}{]}_0-\mathrm{kt} \\ \mathrm{This}\mathrm{is}\mathrm{the}\mathrm{integrated}\mathrm{form}\mathrm{of}\mathrm{rate}\mathrm{law}\mathrm{for}\mathrm{zero}\mathrm{order}\mathrm{reaction}. \end{gathered}$$