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