The rate constant of a first-order reaction is $1.5 \times 10^7 \text{ s}^{-1}$ at $300 \text{ K}$ and $3.0 \times 10^7 \text{ s}^{-1}$ at $330 \text{ K}$. What is the activation energy $(E_a)$ for the reaction? $[R \times 2.303 = 19.15 \text{ J K}^{-1} \text{mol}^{-1}]$

The velocity of the chemical reaction doubles every $10^\circ C$ rise of temperature. If the temperature is raised by $50^\circ C$,the velocity of the reaction increases to about .......... times.

Consider the given energy profile diagram for a reaction and choose the correct option:

For an exothermic reaction $A \to B$,the activation energy is $65 \ kJ \ mol^{-1}$ and the heat of reaction is $-42 \ kJ \ mol^{-1}$. The activation energy for the reverse reaction $B \to A$ would be....... $kJ \ mol^{-1}$

The specific rate constant of decomposition of a compound is given by $\ln k = 5.0 - \frac{12000}{T}$. The activation energy of decomposition for this compound at $300 \ K$ is

In a bimolecular reaction,the steric factor $P$ was experimentally determined to be $4.5$. The correct option$(s)$ among the following is(are)
$[A]$ The activation energy of the reaction is unaffected by the value of the steric factor
$[B]$ Experimentally determined value of frequency factor is higher than that predicted by Arrhenius equation
$[C]$ Since $P=4.5$,the reaction will not proceed unless an effective catalyst is used
$[D]$ The value of frequency factor predicted by Arrhenius equation is higher than that determined experimentally