Discussion
The weight average molar mass (\(\overline{\mathrm{M}}\)w) of a polymer having 50 and 75 molecules with corresponding molecular mass of 5000 and 6000 g/mol respectively is :
Answer: B
The weight-average molar mass is 5,642 g/mol.
\[ \bar{M}_{w} = \frac{\sum N_{i} M_{i}^{2}}{\sum N_{i} M_{i}} \]
\[ \begin{aligned} \sum N_{i} M_{i}^{2} &= 50(5000)^{2} + 75(6000)^{2} \\ &= 1.25 \times 10^{9} + 2.70 \times 10^{9} \\ \sum N_{i} M_{i} &= 2.5 \times 10^{5} + 4.5 \times 10^{5} \\ \bar{M}_{w} &= 3.95 \times 10^{9} / 7.0 \times 10^{5} \\ &= 5642.9 \end{aligned} \]
The key's 5,642 is this value without rounding. The number average would be 7.0 × 105/125 = 5,600, and 5,800, 6,800 and 10,000 fit neither average.
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