X$->2$Y$+$Z

$6.$ The decomposition of gas X to produce gases Y and Z is represented by the equation above. In a certain experiment, the reaction took place in a $5\mathrm{.}00$ L flask at $428$ K$.$ Data from this experiment were used to produce the information in the table below, which is plotted in the graphs that follow.

Time $($minutes$)$

$1[$X$]($mol L $)$

ln $[$X$]$

$[$X$]1($L mol$1)$

$0$

$0\mathrm{.}00633$

$5\mathrm{.}062$

$158$

$10.$

$0\mathrm{.}00520$

$5\mathrm{.}259$

$192$

$20.$

$0\mathrm{.}00427$

$5\mathrm{.}456$

$234$

$30.$

$0\mathrm{.}00349$

$5\mathrm{.}658$

$287$

$50.$

$0\mathrm{.}00236$

$6\mathrm{.}049$

$424$

$70.$

$0\mathrm{.}00160$

$6\mathrm{.}438$

$625$

$100.$

$0\mathrm{.}000900$

$7\mathrm{.}013$

$1,110$

a$.$ How many moles of X were initially in the flask?

b$.$ How many molecules of Y were produced in the first $50$ minutes of the reaction?

c$.$ What is the order of this reaction with respect to X$?$ Justify your answer. d$.$ Write the rate law for this reaction.

e$.$ Calculate the specific rate constant for this reaction. Specify units.

f$.$ Calculate the concentration of X in the flask after a total of $110.$ minutes of reaction.