Neco 2024 Chemistry Question 25

A blend of poly(vinyl chloride) (PVC) and poly(methyl methacrylate) (PMMA) is prepared with weight fractions 0.60 PVC and 0.40 PMMA. The glass‑transition temperatures are \\(T_{g,\text{PVC}} = 80^{\circ}C\\) and \\(T_{g,\text{PMMA}} = 105^{\circ}C\\). Using the Fox equation \\(\frac{1}{T_g}= \frac{w_1}{T_{g1}}+\frac{w_2}{T_{g2}}\\) (temperatures in Kelvin), calculate the glass‑transition temperature of the blend in °C. Both monomers polymerise by step‑growth with extent of reaction \(p = 0.98\). The molar masses of the monomers are 62.5 g mol(^{-1}) for vinyl chloride and 100.1 g mol(^{-1}) for methyl methacrylate, and the initial moles of the two monomers are equal. Determine the number‑average molecular weight (\(M_n\)) of the resulting polymer blend. Give \(T_g\) (°C) to one decimal place and \(M_n\) (g mol(^{-1})) to the nearest integer.