(a) $\mathit{t}=\frac{2303}{\mathit{k}}\log \frac{{\left[\mathit{A}\right]}_0}{\left[\mathit{A}\right]}$.
(i) $40\min =\frac{2.303}{\mathit{k}}\log \frac{100}{75}$........(i)
(ii) $\mathit{t}=\frac{2.303}{\mathit{k}}\log \frac{100}{20}$ ........(ii)
Dividing (i) by (ii)
$\frac{40}{\mathit{t}}=\frac{2.303}{\mathit{k}}\log \frac{100}{75}∕\frac{2.303}{\mathit{k}}\log \frac{100}{20}$
$\frac{40}{\mathit{t}}=\frac{\frac{2.303}{\mathit{k}}\log \frac{4}{3}}{2.303\log 5}$
$\frac{40}{\mathit{t}}=\frac{0.6021∕4.771}{0.6991}$
$\frac{40}{\mathit{t}}=\frac{0.1250}{0.6991}$
$\mathit{t}=\frac{0.6691\times 40}{0.1250}=223.712\min .$
$\mathit{k}=\frac{2.303}{\mathit{t}}\log \frac{100}{100-0.25}$ $=\frac{2.303}{40}\log \frac{100}{75}$
$=\frac{2.303}{40}\left(\log 4-\log 3\right)$
$=\frac{2.303}{40}\left(0.6021-0.4771\right)$
$=\frac{2.303}{40}\times 0.125=0.007196$
$=7.196\times {10}^{-3}{\min }^{-1}$
(b) Order of reaction: The sum of the coefficients of the reacting species that are involved in the rate equation for the reaction, is called order of reaction.
The condition under which a bimolecular reaction follows first order kinetics is when one of the reactants is taken in large excess that its concentration changes hardly.
OR
(a) At $300\mathrm{K},{\mathit{t}}_{1∕2}=30\min$.

${\mathit{k}}_1=\frac{0.693}{30}=0.0231{\min }^{-1}$
At $320\mathrm{K},{\mathit{t}}_{1∕2}=10\min$

${\mathit{k}}_2=\frac{0.693}{10}=0.0693{\min }^{-1}$
According to Arrhenius equation:
$\log \frac{{\mathit{k}}_2}{{\mathit{k}}_1}=\frac{{\mathit{E}}_{\mathit{a}}}{2.303\mathit{R}}\left[\frac{1}{{\mathit{T}}_1}-\frac{1}{{\mathit{T}}_2}\right]$
$=\log \frac{0.0693}{0.0231}=\frac{{\mathit{E}}_{\mathit{a}}}{2.303\mathit{R}}\left[\frac{{\mathit{T}}_2-{\mathit{T}}_1}{{\mathit{T}}_1{\mathit{T}}_2}\right]$
$=\log \frac{0.0693}{0.0231}=\frac{{\mathit{E}}_{\mathit{a}}}{2.303\times 8.314}$ $\left[\frac{320-300}{300\times 320}\right]$
$\left[\because \mathit{R}=8.314{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}\right]$
$=\log 3=\frac{{\mathit{E}}_{\mathit{a}}\times 20}{2.303\times 8.314\times 300\times 320}$
${\mathit{E}}_{\mathit{a}}=\frac{\log 3\times 2.303\times 8.314\times 300\times 320}{20}$
$=\frac{0.4771\times 2.303\times 8.314\times 300\times 320}{20}$
$=43848.5\mathrm{J}{\mathrm{mol}}^{-1}=43.85\mathrm{kJ}{\mathrm{mol}}^{-1}$
(b) Two conditions for collisions to be effective collision are :
(i) The reactant molecules must have attained sufficient energy to break chemical bonds
(ii) The reactant molecules must have the proper orientation.
(c) The number of the reacting species that collide simultaneously in a chemical reaction is called as molecularity of a reaction. The sum of the coefficients of the reacting species is the order of reaction.
For complex reactions, molecularity has no significance while the order of reaction is applicable.