The rate constant of a reaction is given by $k = P Z e^{-E_{a} / R T}$ under standard notation. In order to speed up the reaction,which of the following factors has to be decreased?

For an endothermic reaction $X \rightarrow Y$,the activation energies for the forward and backward reactions are $E_f$ and $E_b$ respectively. Then,in general:

For a reaction taking place in three steps at the same temperature,the overall rate constant is $K = \frac{K_1 K_2}{K_3}$. If $E_{a1}$,$E_{a2}$,and $E_{a3}$ are $40 \ kJ/mol$,$50 \ kJ/mol$,and $60 \ kJ/mol$ respectively,the overall activation energy $E_a$ is . . . . . . $kJ/mol$.

If for two reactions $E_{a_1} > E_{a_2}$ and $\mu_1$ and $\mu_2$ are their respective temperature coefficients,then which of the following is correct?

In the presence of a catalyst,the heat evolved or absorbed during the reaction . . . . . . .

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