Problem $2(35$ points$).200$ liters of a solution containing $10\frac{g}{?}$ liter of and antibody and $5\frac{g}{?}$ liter of a

second protein are to be treated with ammonium sulfate. The objective is to recover $90\%$ of the

antibody in the precipitate. The following solubility data is available

The solubility of the impurity is not affected by $p{H}_H$

a$)$ What is the intrinsic solubility of the antibody at $pH5$ and at $pH8?$

b$)$ Assuming that coprecipitation is negligible, at what $pH$ would you perform the precipitation and

what will be the purity of the antibody in the precipitate?