Isomerisation of gaseous cyclobutene to butadiene is a first order reaction. At $T \ K$,the rate constant of the reaction is $3.3 \times 10^{-4} \ s^{-1}$. What is the time required (in $min$) to complete $90 \%$ of this reaction at the same temperature? $(\log 2 = 0.3)$

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

$A$ first order reaction is $75\%$ completed in $100 \ min$. How long will it take for its $87.5\%$ completion? (in $\min$)

Half-life for a first order reaction is $6.93 \ hour$. What is the time required for $80 \%$ completion of the reaction (in $hours$)?

The decomposition of the smog component peroxyacetyl nitrate $(PAN)$ follows a first-order reaction into peroxyacetyl radical and $NO_{2(g)}$,with a half-life of $32 \ min$.
$CH_3COONO_2 \to CH_3COO^{\bullet} + NO_2$
If the initial concentration of $PAN$ in an air sample is $5.0 \times 10^{14} \ molecules/L$,what will be the concentration after $1.5 \ hr$?

What is a first-order reaction? Determine the integrated rate equation for a first-order reaction $R \to P$.