What will be the effect of temperature on the rate constant?

The rate constant of a reaction at $500 \ K$ and $700 \ K$ are $0.02 \ s^{-1}$ and $0.2 \ s^{-1}$ respectively. The activation energy of the reaction (in $kJ \ mol^{-1}$) is $(R=8.3 \ J \ K^{-1} \ mol^{-1})$

For a reaction,the rate constant is expressed as,$K = A \cdot e^{-40000/T}$. The energy of activation is ....... $cal$.

The first order rate constant $k$ is related to temperature $T$ as $\log \, k = 15.0 - (10^{6} / T)$. Which of the following pairs of values for the Arrhenius factor $A$ and activation energy $E_a$ is correct?

In a multistep reaction such as $A + B$ $\longrightarrow Q$ $\longrightarrow C$,the potential energy diagram is shown below. What is $E_{a}$ for the reaction $Q \longrightarrow C$?

The time taken for half of the initial amount of $N_2O_5$ to decompose is $12 \ min$ at $310 \ K$ and $2 \ hrs$ at $300 \ K$. The activation energy of the reaction in $kJ \ mol^{-1}$ is $\left(R=8.3 \ J \ K^{-1} \ mol^{-1}\right)$