Discussion
For any polydispersed system, which of the following statements is true ?
Answer: B
For a polydisperse system the number average molar mass is less than the mass average.
The two averages are
\[ \bar{M}_{n} = \frac{\sum n_{i}M_{i}}{\sum n_{i}} \]
\[ \bar{M}_{w} = \frac{\sum n_{i}M_{i}^{2}}{\sum n_{i}M_{i}} \]
The mass average weights each molecule by its mass, so the heavier chains count for more, and whenever the molecules differ in size it exceeds the number average. Their ratio, the polydispersity index Mw/Mn, is therefore greater than 1. The two coincide (option C) only for a monodisperse sample, and option A has the inequality the wrong way round.
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