Among the following graphs showing the variation of rate constant $(k)$ with temperature $(T)$ for a reaction,the one that exhibits Arrhenius behaviour over the entire temperature range is:

The rate constant for the decomposition of hydrocarbons is $2.418 \times 10^{-5} \, s^{-1}$ at $546 \, K$. If the energy of activation is $179.9 \, kJ / mol$,what will be the value of the pre-exponential factor?

The temperature coefficient of a reaction is $2$. When the temperature is increased from $30^{\circ} C$ to $90^{\circ} C$,the rate of reaction is increased by: (in $times$)

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 a first-order reaction,if the rate constant is $k_1$ at temperature $T_1$ and $k_2$ at temperature $T_2$,which of the following relations is correct? ($E_a$ = activation energy)

The differential form of the Arrhenius equation is: