Discussion
If the mixture contains equal masses of A, B and C, then the number average molecular weight, \(\overline{M_{n}}\) will be
Answer: A
The number average molecular weight is \(1.64 \times 10^{4}\) g mol-1.
With equal masses w of each, the number of moles of each is w/M:
\[ \begin{aligned} \overline{M_{n}} &= \frac{\sum w_{i}}{\sum w_{i}/M_{i}} = \frac{3}{\frac{1}{10000} + \frac{1}{20000} + \frac{1}{30000}} \\ &= \frac{3}{1.833 \times 10^{-4}} = 1.64 \times 10^{4} \end{aligned} \]
This is the harmonic mean of the three masses. It is pulled below the simple average of 20000 because, at equal mass, there are more of the light molecules. The larger options do not account for that.
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