At high temperatures, Chemical $(A{B}_3)$ dissociates into $A_4$ and $B_2$ by the following

reaction:

$4A{B}_3{A}_4+6B_2$

At $800C$ the rate at which $A{B}_3$ dissociates is

$\frac{d{C}_{AB3}}{dt}=-4\mathrm{.}515**{10}^{-6}{C}_{AB3}$

for $t$ in seconds. The reaction occurs in a constant volume, $3-$L vessel, and the initial

concentration of $A{B}_3,A_4,B_{2}is4$kmo$\frac{l}{m^3}.$ Assuming $A{B}_3,A_4,$ and $B_2$ all are gas.

a$.$ If $5$ mol of the $A{B}_3$ reacts, how much $A_4$ and $6B_2$ are produced?

b$.$ Develop expressions for the number of moles of $A{B}_3,A_4,$ and $B_2$ present at any

time, and determine how long it would take for $5$mol of $A{B}_3$ to have reacted.