The rate of a reaction quadruples when temperature changes from $27^{\circ} C$ to $57^{\circ} C$. Calculate the energy of activation.
Given $R=8.314 \ J \ K^{-1} \ mol^{-1}, \log 4=0.6021$

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 decomposition of $A$ into product has a value of $k$ as $4.5 \times 10^{3} \, s^{-1}$ at $10^{\circ} C$ and an energy of activation of $60 \, kJ \, mol^{-1}$. At what temperature would $k$ be $1.5 \times 10^{4} \, s^{-1}$?

The decomposition of a hydrocarbon follows the equation $k = (4.5 \times 10^{11} \ s^{-1}) e^{-28000 \ K / T}$. Calculate the activation energy $E_a$.

Consider $A \xrightarrow{k_1} B$ and $C \xrightarrow{k_2} D$ are two reactions. If the rate constant $(k_1)$ of the $A \rightarrow B$ reaction can be expressed by the following equation $\log_{10} k = 14.34 - \frac{1.5 \times 10^4}{T/K}$ and activation energy of $C \rightarrow D$ reaction $(Ea_2)$ is $\frac{1}{5}$th of the $A \rightarrow B$ reaction $(Ea_1)$, then the value of $(Ea_2)$ is . . . . . . $kJ \ mol^{-1}$. (Nearest Integer)

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?