The rate constant for the decomposition of a hydrocarbon is given as $K = (4.5 \times 10^{11} \ s^{-1}) e^{-(28000 \ K) / T}$. The activation energy of the reaction (in $J/mol$) is:

For the reaction $A_2 + B_2 \rightleftharpoons 2 AB$,the activation energies $(E_a)$ for the forward and backward reactions are $180 \ kJ \ mol^{-1}$ and $200 \ kJ \ mol^{-1}$ respectively. If a catalyst lowers the $E_a$ for both reactions by $100 \ kJ \ mol^{-1}$,which of the following statements is correct?

For a first-order reaction,the time taken to complete $10\%$ at $298\, K$ is equal to the time taken to complete $25\%$ at $308\, K$. The activation energy of the reaction is ................ $kJ/mol$.

$A \rightarrow B$. The molecule $A$ changes into its isomeric form $B$ following first-order kinetics at a temperature of $1000 \ K$. If the energy barrier with respect to reactant energy for such isomeric transformation is $191.48 \ kJ \ mol^{-1}$ and the frequency factor is $10^{20} \ s^{-1}$,the time required for $50 \%$ of molecules of $A$ to become $B$ is $..............$ picoseconds (nearest integer). $[R = 8.314 \ J \ K^{-1} \ mol^{-1}]$

The rate of a reaction quadruples when temperature changes from $27^{\circ} C$ to $57^{\circ} C$. Calculate the energy of activation.
Given $R=8.314 \ J \ K^{-1} \ mol^{-1}, \log 4=0.6021$

If $R = k[NO]^2[O_2]$,the rate constant can be increased by: