The rate of reaction is tripled for a $10^\circ C$ rise in temperature. The increase in the reaction rate if the temperature is increased by $60^\circ C$ is $............$ times.

When the temperature of a reaction is increased from $300 \ K$ to $310 \ K$,the rate of the reaction increases by $2.5$ times. If the rate constant of the reaction at $300 \ K$ is $K$,what will be the rate constant at $310 \ K$?

For the reaction,following data is given,
$A \rightarrow B$; $K_1 = 10^{15} \exp \left( \frac{-2000}{T} \right)$
$C \rightarrow D$; $K_2 = 10^{14} \exp \left( \frac{-1000}{T} \right)$
The temperature at which $K_1 = K_2$ is ........... $K$ $(exp. = e)$

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 $(A_2 + B_2 \to 2AB)$ in the presence of catalyst will be (in $kJ \ mol^{-1}$)

The number of molecules with energy greater than the threshold energy for a reaction increases five-fold by a rise of temperature from $27^{\circ} C$ to $42^{\circ} C$. Its energy of activation in $J \ mol^{-1}$ is.............. (Take $\ln 5 = 1.6094$; $R = 8.314 \ J \ mol^{-1} K^{-1}$)

For the reaction $A_2 + B_2 \rightleftarrows 2AB$,the activation energy for the forward and backward reactions are $180 \ kJ \ mol^{-1}$ and $200 \ kJ \ mol^{-1}$,respectively. If a catalyst lowers the activation energy of both forward and backward reactions by $100 \ kJ \ mol^{-1}$,what will be the enthalpy change $(\Delta H)$ for the reaction $A_2 + B_2 \rightarrow 2AB$ in the presence of the catalyst?