For a first order reaction, the graph between $\log \frac{a}{(a-x)}$ (on $y$-axis) and time (in min, on $x$-axis) gave a straight line passing through origin. The slope is $2 \times 10^{-3} \mathrm{~min}^{-1}$. What is the rate constant (in $\mathrm{min}^{-1}$ )?

The decomposition of benzene diazonium chloride is a first order reaction. The time taken for its decomposition to $\frac{1}{4}$ and $\frac{1}{10}$ of its initial concentration are $t_{\frac{1}{4}}$ and $t_{\frac{1}{4}}^{10}$ respectively. The value of $\frac{t_{\frac{1}{4}}^4}{t_1} \times 100$ is (Give: $\log 2=0.3$ )

Consider the gaseous reaction, $$ A_2+B_2 \longrightarrow 2 A B $$ The following data was obtained for the above reaction.

[A₂]₀	[B₂]₀	Initial rate of formation of AB (mol L⁻¹ s⁻¹)
0.1 M	0.1 M	2.5 × 10⁻⁴
0.2 M	0.1 M	5.0 × 10⁻⁴
0.2 M	0.1 M	1.0 × 10⁻³

The value of rate constant for the above reaction is

For a first order reaction, a plot of $\ln k\left(Y\right.$-axis) and $\frac{1}{T}$ $(X$-axis) gave the straight line with slope equal to $-10^3 \mathrm{~K}$ and intercept equal to 2.303 ( on $Y$-axis). What is the activation energy ( $E_a$ in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) of the reaction? (Given, $R=8314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ )