Q.Give examples for the first order reaction.

Real first-order reactions include every radioactive disintegration, the gas-phase decomposition of $N_2O_5$, and the decomposition of aqueous hydrogen peroxide — all show a rate directly proportional to the concentration of a single reactant.

A reaction is first order when its rate depends on the first power of a single reactant's concentration, $rate=k[A]^1$. (i) Radioactive decay: every natural or artificial radioactive disintegration (e.g. $^{238}_{92}U\rightarrow$ decay products) strictly follows first-order kinetics, which is why radioactive decay is characterised by a constant half-life independent of the amount of substance present.

(ii) Thermal decomposition of dinitrogen pentoxide: $2N_2O_5(g)\rightarrow 4NO_2(g)+O_2(g)$, experimentally found to be first order in $N_2O_5$.

(iii) Decomposition of hydrogen peroxide in aqueous solution (often catalysed, e.g. by $I^-$ or by light): $H_2O_2\rightarrow H_2O+\tfrac{1}{2}O_2$, found experimentally to be first order in $H_2O_2$ concentration. …