Calculate the Gibbs free energy of mixing for $1g$ poly$($ethylene oxide$)$ with molecular weight $60,000$ in $20g$ of acetone at $20C.$ Take the solubility parameters to be $19\mathrm{.}0MP{a}^{\frac{1}{2}}$ for PEO and $19\mathrm{.}7MP{a}^{\frac{1}{2}}$ for acetone. Would this solution be miscible?

$($Hints: make the assumption that the molar volume of the PEO monomer is the same as the molar volume of acetone, and assume the value of $$ in the Flory Huggins interaction parameter calculation is zero.$)$