At $527 \, ^{\circ}C$ temperature,the activation energy is $54.7 \, kJ/mol$. The value of the Arrhenius factor is $4 \times 10^{10}$. The rate constant will be:

The decomposition of $N_2O$ into $N_2$ and $O_2$ in the presence of argon follows first-order kinetics. If the rate constant is given by $K = 5.0 \times 10^{11} \, e^{-2000/T}$,what is the activation energy of the reaction?

Define the following terms:
$1.$ Effective collision
$2.$ Probability or steric factor $(P)$

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 $R = 8.31 \, J \, K^{-1} \, mol^{-1}]$

Define the following terms:
$(a)$ Activation energy
$(b)$ Activated complex

The energies of activation for forward and reverse reactions for $A_2 + B_2 \rightleftharpoons 2AB$ are $180 \, kJ \, mol^{-1}$ and $200 \, kJ \, mol^{-1}$ respectively. The presence of a catalyst lowers the activation energy of both (forward and reverse) reactions by $100 \, kJ \, mol^{-1}.$ The enthalpy change of the reaction $(A_2 + B_2 \rightarrow 2AB)$ in the presence of a catalyst will be (in $kJ \, mol^{-1}$)