Question

If the number-average degree of polymerization for polystyrene obtained by the bulk polymerization of styrene at 60 (C) is 1000, what would be the number-average degree of polymerization if the polymerization were conducted in a 10% solution in toluene (900 g of toluene per 100 g of styrene) under otherwise identical conditions? The molecular weights of styrene and toluene are 104.12 and 92.15, respectively. State any assumptions that are needed.

Answer 1

Explanation:

Formula to calculate degree of polymerization is as follows.

        Degree of polymerization (DP) = $\frac{\text{Number average molecular weight}}{\text{Average unit molecular weight}}$

         DP = $\frac{\bar{M_{n}}}{m}$

        1000 = $\frac{\bar{M_{n}}}{104.12}$

       $\bar{M_{n}}$ = 104150

Formula to calculate average repeat molecular weight of co-polymer is as follows.

              $\bar{m} = \sum{f_{j}m_{j}}$

where,    $f_{j}$ = mole fraction of each component

Moles of styrene = $\frac{mass}{\text{molar mass}}$              

                            = $\frac{100 g}{104.12 g/mol}$

                            = 0.96 mol

Moles of toulene = $\frac{900 g}{92.15 g/mol}$

                            = 9.77 mol

Therefore, mole fraction will be calculated as follows.

           $f_{1} = \frac{0.96}{0.96 + 9.77}$

                   = 0.0895

           $f_{2} = \frac{9.77}{0.96 + 9.77}$

                   = 0.910

    $\bar{m} = 0.0895 \times 104.12 g/mol + 0.910 \times 92.15 g/mol$

               = 93.22 g/mol

Hence, DP = $\frac{\bar{M_{n}}}{\bar{m}}$

                  = $\frac{104150}{93.22 g/mol}$

                  = 1117

Thus, we can conclude that the number-average degree of polymerization is 1117.