The decomposition of $xY$ is second order in $xY$ and has a rate constant of $7\mathrm{.}02{10}^{-3}{M}^{-1}*s^{-1}$ at a certain temperature.

a$.$ What is the half$-$life for this reaction at an initial concentration of $0\mathrm{.}100M?$

b$.$ How long will it take for the concentration of $xY$ to decrease to $12\mathrm{.}5\%$ of its initial concentration when the initial concentration is $0\mathrm{.}100M?$ When the initial concentration is $0\mathrm{.}200M?$

c$.$ If the initial concentration of $xY$ is $0\mathrm{.}150M,$ how long will it take for the concentration to decrease to $0\mathrm{.}062M?$

d$.$ If the initial concentration of $xY$ is $0\mathrm{.}050M,$ what is the concentration of XY after $5\mathrm{.}0{10}^{1}s?$ After $5\mathrm{.}50{10}^{2}s?$