What is the value of the slope in the graph of $\log_{10} K$ against $\frac{1}{T}$?

When the temperature changes from $293 \ K$ to $313 \ K$,the rate of a certain reaction becomes four times. Find the activation energy of the reaction in $kJ \ mol^{-1}$. $(R = 8.314 \ J \ K^{-1} \ mol^{-1})$

How much faster would a reaction proceed at $25\,^{\circ}C$ than at $0\,^{\circ}C$ if the activation energy is $65\,kJ/mol$?

Find True $(T)$ and False $(F)$ statements in the following:
$1.$ Effective collision depends on rate.
$2.$ When the reactant converts into product,the bonds in the reactant break and new bonds form.
$3.$ The breaking of old bonds and the formation of new bonds take place simultaneously.

$A$ reaction is catalysed by $X$. Here $X$:

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 $700 \ K$.