Ammonium sulfate is being used to precipitate a humanized monoclonal

antibody $($Mw$=156$ kDa$)$ from $10$ litres of cell culture media, the initial concentration of

the antibody in this liquid being $0\mathrm{.}5$ mg$/$ml$.$ Solid ammonium sulfate is added to the

liquid such that the concentration of the salt is $1\mathrm{.}5$ M$.$ This results in the precipitation of

$90\%$ of the antibody. When the ammonium sulfate concentration of the mixture is raised

to $1\mathrm{.}75$ M$,$ a further $76\mathrm{.}5\%$ of the remaining antibody is precipitated.

a$)$ Predict the ammonium sulfate concentration needed for total antibody precipitation.

b$)$ What is the solubility of the antibody in ammonium sulfate free aqueous medium?