An irreversible gas phase reaction is conducted in an isothermal batch reactor. The overall reaction may be represented by A $->2$B

The reactor is filled with a mixture of $70$ mol$\%$ A and $30$ mol$\%$ inert gas. The initial pressure is $90$ kPa and the temperature is $400$ K$.$ The rate expression is $2$nd order and the rate constant have a value of k $=0\mathrm{.}75$ m$3/$mol$-$h at $400$ K$.$ Assume ideal gases.

$($a$)$ Calculate the time required to achieve $60\%$ conversion of A in a constant volume batch reactor.

$($b$)$ Calculate the time required to achieve $60\%$ conversion of A in a constant pressure batch reactor