An aqueous acetic acid solution containing $6kg-$moles of acid per $m^3$ is to be extracted with chloroform at $25C$ to recover the acid from chloroform$-$insoluble impurities present in the water. The water and chloroform are essentially immiscible. If $10m^3$ of solution are to be extracted at $25C,$ calculate the percent recovery of acid obtained with $10m^3$ of chloroform under the following conditions.

$($a$)$ Using the entire quantity of solvent in a single batch extraction.

$($b$)$ Using three batch extractions with one third of the total solvent used in each batch.

$($c$)$ Using three batch extractions with $5m^3$ of solvent in the first, $3m^3$ in the second and $2m^3$ in the third batch.