The rate of a reaction at $273 \ K$ is $R_0$. What will be the rate of the reaction at $313 \ K$? (Take the temperature coefficient as $2$)

The decomposition of formic acid on a gold surface follows first-order kinetics. If the rate constant at $300 \ K$ is $1.0 \times 10^{-3} \ s^{-1}$ and the activation energy $E_a = 11.488 \ kJ \ mol^{-1}$,the rate constant at $200 \ K$ is ............ $\times 10^{-5} \ s^{-1}$.
(Round off to the Nearest Integer).
(Given: $R = 8.314 \ J \ mol^{-1} K^{-1}$)

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

Choose the incorrect statement -

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: $R = 8.314 \, J \, K^{-1} \, mol^{-1}$]

The rate constants for the decomposition of acetaldehyde have been measured over the temperature range $700-1000 \ K$. The data has been analysed by plotting a $\ln \ k \ vs \ \frac{10^{3}}{T}$ graph,which gives a slope of $-18.5$. The value of activation energy for the reaction is $...... \ kJ \ mol^{-1}$. (Nearest integer) (Given: $R = 8.31 \ J \ K^{-1} \ mol^{-1}$)