For the reaction $2$P $+$ Q $->$ R in the gas phase, it is known that it is elemental and has a rate constant of $8\mathrm{.}2$ mol$2$dm$-6$hr$-1$ at $477$ oK and $14\mathrm{.}9$ atm. We will work in a variable volume BATCH reactor at these pressure and temperature conditions to reach $85\%$ conversion. Neglecting pressure changes and assuming that the gases behave as ideal, calculate the time IN HOURS necessary to achieve the desired conversion if you have a feed with a $20\%$ stoichiometric excess of Q$.$