What is the slope of the graph plotted between half-life $(t_{1/2})$ and initial concentration $(a)$ for a $1^{st}$ order reaction?

Calculate the rate constant of a first order reaction if the half-life of the reaction is $40 \ minute$.

Mathematical representation for $t_{1/4}$ life for a first-order reaction is given by:

Calculate the rate constant of a first-order reaction if the concentration of the reactant decreases by $90 \%$ in $30 \ minutes$.

If the rate constant for a first order reaction is $k$,the time $(t)$ required for the completion of $99\%$ of the reaction is given by:

The first order decomposition of $H_2O_2$ in an appropriate medium is characterised by a rate constant of $0.2303 \ min^{-1}$. What is the time (in $min$) required to complete $9/10$ fraction of the reaction?