### 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.
$$ \text {(b) } t_{\, \frac{1}{2}} = \frac{[R]_{\,o}}{2k} $$
t_{1/2} 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.
$$ \text {(b) } t_{\, \frac{1}{2}} = \frac{0.693}{k} $$
t_{1/2} 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 k_{1 }is rate constant at temperature T_{1 } and k_{2 } is rate constant
at temperature T_{2 }.