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:

The slope of the Arrhenius plot $(\ln k \, vs \, \frac{1}{T})$ of a first-order reaction is $-5 \times 10^{3} \, K$. The value of $E_{a}$ of the reaction is: (in $kJ \, mol^{-1}$)
$[\text{Given } R = 8.314 \, J \, K^{-1} \, mol^{-1}]$

The number of given statement/s which is/are correct is $.....$.
$(A)$ The stronger the temperature dependence of the rate constant,the higher is the activation energy.
$(B)$ If a reaction has zero activation energy,its rate is independent of temperature.
$(C)$ The stronger the temperature dependence of the rate constant,the smaller is the activation energy.
$(D)$ If there is no correlation between the temperature and the rate constant then it means that the reaction has negative activation energy.

Activation energy for the acid catalysed hydration of sucrose is $6.22 \ kJ \ mol^{-1}$,while the activation energy is only $2.15 \ kJ \ mol^{-1}$ when hydrolysis is catalysed by the enzyme sucrase. Explain.

When a biochemical reaction is carried out in a laboratory without the presence of enzymes,the rate of reaction is $10^{-6}$ times slower. What will be the activation energy $(E_a)$ in the presence of enzymes?

In most cases,for a rise of $10 \ K$ temperature,the rate constant is doubled or tripled. This is due to the reason that