The temperature dependence of the rate constant $(k)$ of a chemical reaction is expressed by the Arrhenius equation,$k = A \cdot e^{-E^*/RT}$. The activation energy $(E^*)$ of the reaction can be calculated by plotting:

The rate constant,the activation energy and the Arrhenius parameter of a chemical reaction at $25\,^oC$ are $3.0 \times 10^{-4}\,s^{-1}$,$104.4\,kJ\,mol^{-1}$ and $6.0 \times 10^{14}\,s^{-1}$ respectively. The value of the rate constant as $T \to \infty$ is

For a first order chemical reaction,

Consider a complex reaction taking place in three steps with rate constants $k_1$,$k_2$,and $k_3$ respectively. The overall rate constant $k$ is given by the expression $k = \sqrt{\frac{k_1 k_3}{k_2}}$. If the activation energies of the three steps are $60$,$30$,and $10 \ kJ \ mol^{-1}$ respectively,then the overall energy of activation in $kJ \ mol^{-1}$ is $..........$ $(Nearest \ integer)$

The relation between the rate constant and temperature according to the Arrhenius equation is:

The half-life of a first order reaction varies with temperature according to