### Chemical kinetics

Integrated rate law equation for zero order reaction
$$\text {(a) k } = \frac{[R]_{\,o}–[R] }{t}$$ Where k is rate constant and [R]o is initial molar concentration and [R] is final concentration at time t. $$\text {(b) } t_{\, \frac{1}{2}} = \frac{[R]_{\,o}}{2k}$$ t1/2 is half life period of zero order reaction.

Integrated rate law equation for first order reaction
$$\text {(a) k } = \frac{2.303}{t} \log \frac{[R]_{\,o} }{[R]}$$ Where k is rate constant and [R]o is initial molar concentration and [R] is final concentration at time t. $$\text {(b) } t_{\, \frac{1}{2}} = \frac{0.693}{k}$$ t1/2 is half life period of first order reaction.

Arrhenius equation
$$\text {(a) k } = Ae ^{-Ea/RT}$$ Where A is frequency factor, Ea is the energy of activation, R is universal gas contant and T is absolute temperature.- Ea/RT gives the fraction of collisions having energy equal to or greater than Ea. $$\text {(b) } \log \frac{k _{\,2}}{k _{\,1}} = \frac{E _{\,a}}{2.303 R} ( \frac{T_{\,2} - T_{\,1}}{T_{\,1} T_{\,2}})$$ Where k1 is rate constant at temperature T1 and k2 is rate constant at temperature T2 .