For a reaction taking place in three steps at the same temperature,the overall rate constant is $K = \frac{K_1 K_2}{K_3}$. If $E_{a1}$,$E_{a2}$,and $E_{a3}$ are $40 \ kJ/mol$,$50 \ kJ/mol$,and $60 \ kJ/mol$ respectively,the overall activation energy $E_a$ is . . . . . . $kJ/mol$.

For a chemical reaction at $27^{\circ} C$, the activation energy is $600 R$. The ratio of the rate constants at $327^{\circ} C$ to that of at $27^{\circ} C$ will be

The reason for almost doubling the rate of reaction on increasing the temperature of the reaction system by $10 \, ^\circ C$ is

For a chemical reaction,the rate constant,activation energy,and Arrhenius factor at $25 \, ^\circ C$ are $3.0 \times 10^{-4} \, s^{-1}$,$104.4 \, kJ \, mol^{-1}$,and $6.0 \times 10^{14} \, s^{-1}$ respectively. Find the value of the rate constant as $T \rightarrow \infty$.

The specific rate constant of a first-order reaction depends on .......

$A$ 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: $R = 8.3 \; J \; mol^{-1} \; K^{-1}$,$\ln(1.5) = 0.405$)