If a reaction follows the Arrhenius equation,the plot $\ln k$ vs $1/(RT)$ gives a straight line with a gradient of $(-y) \ unit$. The energy required to activate the reactant is

Activation energy is given by the formula

In a reaction, for every $10^{\circ} C$ rise of temperature, the rate is doubled. If the temperature is increased from $10^{\circ} C$ to $100^{\circ} C$, the rate of the reaction will become $:-$ (in $\times$)

The rate constant for the decomposition of $N_{2}O_{5}$ at various temperatures is given below:

$T / ^{\circ}C$	$0$	$20$	$40$	$60$	$80$
$10^{5} \times k / s^{-1}$	$0.0787$	$1.70$	$25.7$	$178$	$2140$

Draw a graph between $\ln k$ and $1 / T$ and calculate the values of $A$ and $E_{a}.$ Predict the rate constant at $30^{\circ}C$ and $50^{\circ}C$.

For a reaction,the rate constants $K_1$ and $K_2$ are given by $10^{16} \cdot e^{-2000/T}$ and $10^{15} \cdot e^{-1000/T}$ respectively. At what temperature will $K_1 = K_2$?

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 $\times$)