For a reaction,the temperature coefficient is $2$. Calculate the activation energy $(E_a)$ in $kJ/mol$. (Assume the temperature range is $25^{\circ}C$ to $35^{\circ}C$)

For the reaction,$aA + bB \rightarrow cC + dD$,the plot of $\log k$ vs $\frac{1}{T}$ is given below. The temperature at which the rate constant of the reaction is $10^{-4} \ s^{-1}$ is ............... $K$. (Rounded-off to the nearest integer) [Given: The rate constant of the reaction is $10^{-5} \ s^{-1}$ at $500 \ K$.]

Which of the following would give a linear plot?
($k$ is the rate constant of an elementary reaction and $T$ is temperature in absolute scale)

Write the Arrhenius equation representing the relationship between the rate constants $k_1$ and $k_2$ at two different temperatures $T_1$ and $T_2$.

The first order rate constant for the decomposition of ethyl iodide by the reaction $C_{2}H_{5}I_{(g)} \rightarrow C_{2}H_{4(g)} + HI_{(g)}$ at $600 \ K$ is $1.60 \times 10^{-5} \ s^{-1}$. Its energy of activation is $209 \ kJ/mol$. Calculate the rate constant of the reaction at $700 \ K$.

For the reaction $A \rightarrow B$,the rate constant $k$ (in $s^{-1}$) is given by $\log_{10} k = 20.35 - \frac{2.47 \times 10^{3}}{T}$. The energy of activation in $kJ \, mol^{-1}$ is ..... . (Nearest integer) [Given: $R = 8.314 \, J \, K^{-1} \, mol^{-1}$]