The half-life period for a first order reaction is $693 \ sec$. The rate constant for this reaction would be: (in $sec^{-1}$)

Time required for completion of $99.9 \%$ of a First order reaction is . . . . . . times of half life $(t_{1/2})$ of the reaction.

$A$ first order reaction is found to have a rate constant,$k = 5.5 \times 10^{-14} \ s^{-1}$. The half life of reaction is . . . . . . .

For a first order reaction at $27^{\circ} C$,the ratio of time required for $75 \%$ completion to $25 \%$ completion of reaction is

In a first order decomposition reaction,the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are $t_1$ and $t_2 \ s$,respectively. The ratio $t_1 / t_2$ will be:

In a first order reaction,the ratio $\frac{a}{a-x}$ was found to be $8$ after $10 \, \text{min}$. The rate constant is: