The specific rate constant of a first-order reaction depends on .......

Consider the following plots of rate constant versus $\frac{1}{T}$ for four different reactions. Which of the following orders is correct for the activation energies of these reactions?

Reactant $(A)$ produces two products. If $Ea_2 = 2 Ea_1$,then $K_1$ and $K_2$ are related as:
$A \xrightarrow{K_1} B$,activation energy: $Ea_1$
$A \xrightarrow{K_2} C$,activation energy: $Ea_2$

Fill in the blanks:
$(a)$ $A$ catalyst ......... the change of equilibrium in reaction.
$(b)$ Boltzmann and Maxwell used ......... to explain the rate of reaction.

The value of the rate constant for the reaction $A + B \to \text{products}$ depends on:

The rate constant of a reaction depends on