$A$ sample of milk splits after $60 \; min.$ at $300 \; K$ and after $40 \; min.$ at $400 \; K$ when the population of $Lactobacillus \; acidophilus$ in it doubles. The activation energy (in $kJ / mol$) for this process is closest to ............. $kJ / mol$.
(Given: $R = 8.3 \; J \; mol^{-1} \; K^{-1}$,$\ln(1.5) = 0.405$)

The decomposition of formic acid on a gold surface follows first-order kinetics. If the rate constant at $300 \ K$ is $1.0 \times 10^{-3} \ s^{-1}$ and the activation energy $E_a = 11.488 \ kJ \ mol^{-1}$,the rate constant at $200 \ K$ is ............ $\times 10^{-5} \ s^{-1}$.
(Round off to the Nearest Integer).
(Given: $R = 8.314 \ J \ mol^{-1} K^{-1}$)

For a first-order reaction $A \to P$,the rate constant equation is given by $\log K = -2000 \, (1/T) + 6.0$. The pre-exponential factor $A$ and the activation energy $E_a$ are,respectively:

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 graph for the process $R \rightarrow P$ is given below. Determine the activation energy $(E_a)$ for the forward reaction if the energy of the reactant is $50 \ kJ$ and the energy of the transition state is $170 \ kJ$. (in $kJ$)

The first order rate constant for the decomposition of $CaCO_3$ at $700 \ K$ is $6.36 \times 10^{-3} \ s^{-1}$ and activation energy is $209 \ kJ \ mol^{-1}$. Its rate constant (in $s^{-1}$) at $500 \ K$ is $x \times 10^{-6}$. The value of $x$ is ..... (Nearest integer)
Given $R=8.31 \ J \ K^{-1} \ mol^{-1} ; \log(6.36 \times 10^{-3})=-2.19 ; [10^{-4.79}=1.62 \times 10^{-5}]$