$1.$ The solubility of a monoclonal antibody $($MW $155,000$ kg kg$-$mole$-1)$ in $1\mathrm{.}5$ kg$-$moles m$-3$ ammonium sulfate solutions is $0\mathrm{.}1$ g L$-1.$ Predict its solubility in an ammonium sulfate$-$free buffer if the salting out constant is $5\mathrm{.}6$ m$3$ kg$-$mole$-1.$ If we increase the ammonium sulfate concentration of $100$ mL of a $0\mathrm{.}5$ g L$-1$ monoclonal antibody solution from zero to

$1\mathrm{.}75$ kg$-$moles m$-3,$ what fraction of the monoclonal antibody will be precipitated?