$ \mathrm{t}_{1 / 2}=\frac{0.693}{\mathrm{~K}} $
$ \mathrm{~K}=\frac{0.693}{36}=0.01925 \mathrm{hr}^{-1} $
$1^{\text {st }}$ order rxn kinetic equation
$ t=\frac{2.303}{K} \log \frac{a}{a-x} $
$ \log \frac{a}{a-x}=\frac{t \times K}{2.303} \quad(t=1 \text { day }=24 \mathrm{hr}) $
$ \log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=\frac{24 \mathrm{hr} \times 0.01925 \mathrm{hr}^{-1}}{2.303} $
$ \log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=0.2006 $
$ \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=\operatorname{anti} \log (0.2006) $
$ \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=1.587 $
$ \text { If } \mathrm{a}=1 $
$ \frac{1}{1-\mathrm{x}}=1.587 \Rightarrow 1-\mathrm{x}=0.6301=\text { Fraction remain } $ after one day
$[A] (mol\,L^{-1})$ | $[B] (mol\,L^{-1})$ | પ્રક્રિયાનો પ્રારંભિક વેગ $(mol\, L^{-1}\,s^{-1} )$ |
$0.05$ | $0.05$ | $0.045$ |
$0.10$ | $0.05$ | $0.090$ |
$0.20$ | $0.10$ | $0.72$ |
$\left( {{\rm{R}} = 8.3\;{\rm{Jmo}}{{\rm{l}}^{ - 1}}{{\rm{K}}^{ - 1}},\ln \left( {\frac{2}{3}} \right) = 0.4,\left. {{e^{ - 3}} = 4.0} \right)} \right.$