The feed to the batch process consists of a solution of $500$ L of ethanol with $120$ mole of A and $120$ mole of B$.$ If the temperature of the solution is sufficient, A and B will react to form P $($the desired product$)$:

A $($eth$)+$ B $($eth$)->$ P $($s$)$ DHreact $=250$ kJ$/$mol

Note that the product P is sparingly soluble in ethanol, which helps facilitate its removal from the reaction solution. It can be assumed that the reaction rate is first$-$order in both the concentration of A $($cA$)$ and B $($cB$),$ and so second$-$order overall.

i$)$ what is the amount of product per batch knowing that the reaction takes place isothermally at $50\backslash$deg C $(4$ hours, to give conversion of $50\%)?$

ii$)$ since product is sparingly soluble in ethanol, what is the yield of P and what is the amounts dissolved in the by products?