The rate of a chemical reaction doubles for every $10^\circ \text{C}$ rise in temperature. If the temperature is increased by $50^\circ \text{C}$,the rate of reaction will increase by a factor of ........

According to the Arrhenius equation,the slope of the $\log k$ vs. $\frac{1}{T}$ plot is . . . . . . .

If the activation energy of a reaction is $80.9 \, kJ \, mol^{-1}$,the fraction of molecules at $700 \, K$,having enough energy to react to form products is $e^{-x}$. The value of $x$ is ....... . (Rounded off to the nearest integer) $[$Use $R = 8.31 \, J \, K^{-1} \, mol^{-1}]$

The rate constant of a reaction at temperature $200 \ K$ is $10$ times less than the rate constant at $400 \ K.$ What is the activation energy $({E_a})$ of the reaction ($R = $ gas constant) (in $R$)?

Among the following,the $INCORRECT$ statement regarding the collision theory of chemical reaction is:

Correct statements regarding Arrhenius equation among the following are:
$(A)$ Factor $e^{-Ea/RT}$ corresponds to fraction of molecules having kinetic energy less than $Ea$.
$(B)$ At a given temperature, lower the $Ea$, faster is the reaction.
$(C)$ Increase in temperature by about $10^{\circ}C$ doubles the rate of reaction.
$(D)$ Plot of $\log k$ vs $\frac{1}{T}$ gives a straight line with $slope = -\frac{Ea}{2.303R}$.
Choose the correct answer from the options given below: