1.
The rate of a first order reaction is \[1.5\times {{10}^{-2}}mol\,{{L}^{-1}}{{\min }^{-1}}\] at $$0.5\,M$$ concentration of the reactant. The half life of the reaction is
$$\eqalign{
& {\text{For a first order reaction,}}\,A \to {\text{Products}} \cr
& r = k\left[ A \right]\,{\text{or}}\,k = \frac{1}{{\left[ A \right]}} \cr
& \Rightarrow k = \frac{{1.5 \times {{10}^{ - 2}}}}{{0.5}} = 3 \times {10^{ - 2}} \cr
& {\text{Further}},\,{t_{\frac{1}{2}}} = \frac{{0.693}}{k} = \frac{{0.693}}{{3 \times {{10}^{ - 2}}}} = 23.1 \cr} $$
2.
Consider the following statements :
(i) Increase in concentration of reactant increases the rate of a zero order reaction.
(ii) Rate constant $$k$$ is equal to collision frequency $$A$$ if $${E_a} = 0.$$
(iii) Rate constant $$k$$ is equal to collision frequency $$A$$ if $${E_a} = \infty .$$
(iv) $${\text{ln}}\,k\,\,{\text{vs}}\,\,T$$ is a straight line.
(v) $${\text{In}}\,k\,\,{\text{vs}}\,\,\frac{1}{T}$$ is a straight line.
Correct statements areCorrect statements are
According to Arrhenius equation,
$$\eqalign{
& k = A{e^{ - \,\frac{{Ea}}{{RT}}}} \cr
& \therefore \,\,{\text{when}}\,{E_a} = 0,k = A \cr} $$
Also $${\text{ln}}\,k\,\,{\text{vs}}\,\,\frac{1}{T}$$ is a straight line with slope $$ = - \frac{{{E_a}}}{R}.$$
∴ Statements (ii) and (v) are correct.
3.
Which of the following factors are responsible for the increase in the rate of a surface catalysed reaction?
(i) A catalyst provides proper orientation for the reactant molecules to react.
(ii) Heat of adsorption of reactants on a catalyst helps reactant molecules to overcome activation energy.
(iii) The catalyst increases the activation energy of the reaction.
The catalyst decreases the activation energy of the reaction and thus increases the rate of reaction.
4.
For a first order reaction, the ratio of the time take for $${\frac{7}{8}^{th}}$$ of the reaction to complete to that of half of the reaction to complete is
6.
The reaction $$A \to B$$ follows first order kinetics. The time taken for $$0.8\,mole$$ of $$A$$ to produce $$0.6\,mole$$ of $$B$$ is 1 hour. What is the time taken for conversion of $$0.9\,mole$$ of $$A$$ to produce $$0.675\,mole$$ of $$B?$$
7.
A reaction takes place in various steps. The rate constant for first, second, third and fifth steps are $${k_1},{k_2},{k_3}$$ and $${k_5}$$ respectively. The overall rate constant is given by $$k = \frac{{{k_2}}}{{{k_3}}}{\left( {\frac{{{k_1}}}{{{k_5}}}} \right)^{\frac{1}{2}}}$$ If activation energy are 40, 60, 50 and $$10\,kJ/mol$$ respectively, the overall energy of activation $$\left( {kJ/mol} \right)$$ is :