$($a$)$ A lab worker has left unintentionally an open beaker containing $1\mathrm{.}8$ liters of $1,3$ butadiene

$(C_4{H}_6)$ on the desk in his lab office at the end of the workday, and he closed his office door when

he left. To save energy, the company turns off the office ventilation system at the end of the

workday. If the $C_4{H}_6$ evaporates, it might form a flammable mixture in air, and an explosion

might result if the worker turns the light switch on in the morning. The temperature is $30C$ and

the ambient pressure is $1\mathrm{.}0$atm. The floor area of the room is $4\mathrm{.}0m$ by $2\mathrm{.}5m,$ and the ceiling

height is $3\mathrm{.}0m.$

$($i$)$ Estimate the resulting concentration of $C_4{H}_6$ in the room, in volume $\%.$ Make comments by

compare to the flammability limit$.$

$($ii$)$ Estimate the equivalent amount of TNT from the vapor. Make sure you clearly state any

assumptions.

$($iii$)$ If the vapor explodes, at what distance in the $3$ psi overpressure found.

Physical property data for $C_4{H}_6$ at $30C$ :

Vapor pressure: $,0\mathrm{.}568$atm

Liquid density: $,614\mathrm{.}9k\frac{g}{m^3}$

Molecular weight: $,0\mathrm{.}05409k\frac{g}{m}ol$

Normal boiling point: $-4\mathrm{.}4C$

Heat of Combustion $H_c=3800\mathrm{.}2k\frac{J}{m}ol$

$R_g=8\mathrm{.}205{10}^{-5}{m}^{3}at\frac{m}{m}olK$

Flammability limit: LFL $2\%$

UFL $,11\mathrm{.}5\%$