The decomposition of $xY$ is second order in $xY$ and has a rate constant of $0\mathrm{.}0142M^{-1},$

$s^{-1}$ at a certain temperature.

a$.$ What is the half$-$life for this reaction at an initial concentration of $0\mathrm{.}087M?$

b$.$ How long will it take for the concentration of $xY$ to decrease to $12\%$ of its initial

concentration when the initial concentration is $0\mathrm{.}173M?$

c$.$ If the initial concentration of $xY$ is $0\mathrm{.}215M,$ how long will it take for the concentration

to decrease to $0\mathrm{.}066M?$

d$.$ If the initial concentration of $xY$ is $0\mathrm{.}054M,$ what is the concentration of $xY$ after $45$ s$?$

After $450$ s$?$

This reaction was monitored as a function of time:

$ABA+$BAB$2A+B$

A plot of $\frac{1}{AB}$ versus time yields a straight line with slope $\frac{0\mathrm{.}046}{M}*s.$

a$.$ What is the value of the rate constant, $k,$ for this reaction at this temperature?

b$.$ Write the rate law for the reaction.

c$.$ What is the half$-$lfe when the initial concentration is $0\mathrm{.}22M?$

d$.$ If the initial concentration of $AB$ is $0\mathrm{.}639M,$ and the reaction mixture intially contains

no products, what are the concentrations of A and $B$ after $95$ s$?$