What is the value of the slope of the plot $\ln K$ versus $\frac{1}{T}$ for a reaction having $E_{a} = 33.256 \ J \ mol^{-1}$?

When the temperature changes from $293 \ K$ to $313 \ K$,the rate of a certain reaction becomes four times. Find the activation energy of the reaction in $kJ \ mol^{-1}$. $(R = 8.314 \ J \ K^{-1} \ mol^{-1})$

For a particular reaction,the rate constant becomes double on increasing temperature from $27^{\circ} C$ to $37^{\circ} C$. Calculate the approximate activation energy (in $kcal \ mol^{-1}$,$R=2 \ cal \ mol^{-1} \ K^{-1}$).

The rate of a reaction doubles when its temperature changes from $300 \ K$ to $310 \ K$. The activation energy of such a reaction will be ........ $kJ/mol$.

The activation energy for the reaction $2 HI_{(g)} \rightarrow H_{2(g)} + I_{2(g)}$ is $209.5 \ kJ \ mol^{-1}$ at $581 \ K$. Calculate the fraction of molecules of reactants having energy equal to or greater than activation energy?

$A$ reaction rate constant is given by $k = 1.2 \times 10^{14} \, e^{-25000/RT} \, sec^{-1}$. It means