Assuming that the volume of the system is constant, derive the expression for the average rate of the system R$\to$P in terms of R and P. (time = t sec, R = reactant, P = products).

If $\left[\mathrm{R}{]}_1\text{ and }\right[\mathrm{P}{]}_1$ are the concentrations of R and P respectively at time ${\mathrm{t}}_1\text{ and }\left[\mathrm{R}{]}_2\text{ and }\right[\mathrm{P}{]}_2$ are their concentrations at time ${\mathrm{t}}_2\text{ then, }\mathrm{\Delta t}={\mathrm{t}}_2-{\mathrm{t}}_1$
$\mathrm{\Delta }\left[\mathrm{R}\right]=[\mathrm{R}{]}_2-[\mathrm{R}{]}_1;\mathrm{\Delta }\left[\mathrm{P}\right]=[\mathrm{P}{]}_2-[\mathrm{P}{]}_1$
The square brackets in the above expressions are used to express molar conencentration.
Average rate of reaction w.r.t. R =  $\frac{\text{ decrease in concentration of }\mathrm{R}}{\text{ Time taken for the decrease }}=\frac{-\mathrm{\Delta }\left[\mathrm{R}\right]}{\mathrm{\Delta t}}$
Average rate of reaction w.r.t. P = $\frac{\text{ increase in concentration of }\mathrm{P}}{\text{ Time taken for the increase }}=\frac{+\mathrm{\Delta }\left[\mathrm{P}\right]}{\mathrm{\Delta t}}$