Neco Model Questions Vol1 2017 Chemistry Question 42

A random copolymer is prepared from monomer M$_{1}$ (molar mass 100 g mol$^{-1}$, solubility parameter $\delta_{1}=18$ MPa$^{0.5}$) and monomer M$_{2}$ (molar mass 150 g mol$^{-1}$, $\delta_{2}=22$ MPa$^{0.5}$). The polymer contains 70 wt\% of M$_{1}$ and 30 wt\% of M$_{2}$. It is dissolved in a solvent whose solubility parameter is $\delta_{s}=20$ MPa$^{0.5}$. Using the Flory-Huggins approximation $\chi = \frac{V_{1}}{RT}(\delta_{p}-\delta_{s})^{2}$, where $V_{1}=100\,\text{cm}^{3}\,\text{mol}^{-1}$, $R=8.314\,\text{J}\,\text{mol}^{-1}\,\text{K}^{-1}$ and $T=298\,$K, (a) calculate the interaction parameter $\chi$ and state whether the polymer is expected to be soluble (criterion $\chi<0.5$). (b) If the composition is changed to 50 wt\% of each monomer, recalculate $\chi$ and comment on the solubility.