The second order homogeneous reaction in the gas phase:

A $->$ R $+$ S occurs in a batch reactor at constant volume and an initial pressure is $1$atm. Experiments performed at $791$ K found a $50\%$ conversion of A after $197$s of reaction. It is desired to produce $2000$ kg$/$day of reaction mixture with a conversion of $85\%$ A to $791$ K$.$

a$)$ How many batches are produced per day and what is the charge of each batch?

$($The average specific mass of the mixture is $30$ kg $/$m$3.$

Charging time,unloading and cleaning $=30$ min

Production Day $=8$ hours$).$ Answer:A: a$)$ number of batches $=9$