# Chemical kinetics

### Integrated rate law equation for zero order reaction

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

### Integrated rate law equation for first order reaction

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

### Arrhenius equation

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