The rate of a reaction doubles when its temperature changes from $300 \, K$ to $310 \, K.$ Activation energy of such a reaction will be .......... $kJ \, mol^{-1}$. $(R= 8.314 \, J \, K^{-1} \, mol^{-1}$ and $\log 2=0.301)$

For reaction $A \rightarrow P$, rate constant $k = 1.5 \times 10^3 \text{ s}^{-1}$ at $27^\circ\text{C}$. If activation energy for the above reaction is $60 \text{ kJ mol}^{-1}$, then the temperature (in $^\circ\text{C}$) at which rate constant $k = 4.5 \times 10^3 \text{ s}^{-1}$ is . . . . . . .

For the decomposition of $N_2O_5,$ the reaction is $2N_2O_{5(g)} \rightarrow 4NO_{2(g)} + O_{2(g)}$ with activation energy $E_a.$ If the reaction is written as $N_2O_{5(g)} \rightarrow 2NO_{2(g)} + 1/2 O_{2(g)}$ with activation energy $E_a',$ what is the relationship between $E_a$ and $E_a'$?

In a bimolecular reaction,the steric factor $P$ was experimentally determined to be $4.5$. The correct option$(s)$ among the following is(are)
$[A]$ The activation energy of the reaction is unaffected by the value of the steric factor
$[B]$ Experimentally determined value of frequency factor is higher than that predicted by Arrhenius equation
$[C]$ Since $P=4.5$,the reaction will not proceed unless an effective catalyst is used
$[D]$ The value of frequency factor predicted by Arrhenius equation is higher than that determined experimentally

The decomposition of a hydrocarbon follows the equation $K = (4.5 \times 10^{11} \, s^{-1}) e^{-28000 \, K/T}$. What will be the value of activation energy in $KJ \, mol^{-1}$?

Based on the provided energy profile diagram,how many steps are in the mechanism of the reaction?