Q$1)$ The gas$-$phase reaction $A+2BC$ is carried out isothermally in a $20d{m}^3$ constant$-$volume batch reactor. Twenty moles of pure $A$ is initially placed in the reactor. The reactor is well mixed:

$($a$)$ Taking $k=0\mathrm{.}005mo\frac{l}{d}{m}^3.$min, calculate the time required to reduce the number of moles of A in the reactor to $12\mathrm{.}5$mol.

$($b$)$ If the temperature is $127C,$ determine the initial and the final pressure assuming the reaction goes to completion. Take $R=0\mathrm{.}082L*at\frac{m}{m}ol.K$