The rate of a chemical reaction doubles for every $10\,^{\circ}C$ rise of temperature. If the temperature is raised by $50\,^{\circ}C,$ the rate of the reaction increases by about ......... times.

Assertion $(A)$ : $A$ catalyst increases the rate of a reaction.
Reason $(R)$ : In presence of a catalyst,the activation energy of the reaction increases.
The correct answer is

The first order rate constant for the decomposition of ethyl iodide by the reaction $C_{2}H_{5}I_{(g)} \rightarrow C_{2}H_{4(g)} + HI_{(g)}$ at $600 \ K$ is $1.60 \times 10^{-5} \ s^{-1}$. Its energy of activation is $209 \ kJ/mol$. Calculate the rate constant of the reaction at $700 \ K$.

$A$ reaction takes place in three steps with individual rate constant and activation energy as follows:

$Step$	$Rate \ constant$	$Activation \ energy$
$Step-1$	$k_1$	$E_{a1} = 180 \ kJ/mol$
$Step-2$	$k_2$	$E_{a2} = 80 \ kJ/mol$
$Step-3$	$k_3$	$E_{a3} = 50 \ kJ/mol$

If overall rate constant,$k = (\frac{k_1 k_2}{k_3})^{2/3}$,then overall activation energy of the reaction will be .......... $kJ/mol$.

$A$ graph plotted between $\log \,K$ vs $\frac{1}{T}$ for calculating activation energy is shown by:

The reaction between $H_{2(g)}$ and $O_{2(g)}$ is highly feasible,yet allowing the gases to stand at room temperature in the same vessel does not lead to the formation of water. Explain.