Molecular Weight and Distribution Questions and Answers

Answer: C

The polydispersity index is M̄w / M̄n, the weight-average over the number-average molecular weight.

The number average weights every chain equally, while the weight average gives heavier chains more weight. For any sample with a spread of chain lengths M̄w is larger than M̄n, so the ratio is at least 1, and the larger it is the broader the distribution. A perfectly uniform polymer has a ratio of exactly 1; a typical condensation polymer is near 2.

M̄n / M̄w is the inverse and would always be 1 or less. M̄w / M̄z and M̄v / M̄w use the z-average and the viscosity average, which are real averages but are not the ones that define the polydispersity index.

Answer: A

The plot gives M_n as reciprocal of intercept and polymer-solvent interaction constant as slope.

For a dilute polymer solution, the osmotic pressure follows a virial equation:

\[ \begin{aligned} \frac{\pi}{C} &= RT \\ &\times \left(\frac{1}{\overline{M}_{n}} + A_{2}C + \cdots\right) \end{aligned} \]

A plot of π/C against C is a straight line at low concentration. Its intercept at C = 0 is RT/M_n, so the number-average molar mass is found from the reciprocal of the intercept. Its slope is RTA₂, where the second virial coefficient A₂ measures polymer-solvent interaction (positive in a good solvent, zero at the theta temperature).

The other options assign M_n to the slope, or call the slope concentration, which is the axis variable, not a result.

Answer: C

The significance is that M̄w is sensitive to high molecular weight and M̄n to low molecular weight species.

The number average, M̄n = ΣN_iM_i/ΣN_i, counts every molecule equally, so a large number of small molecules pulls it down. The weight average, M̄w = ΣN_iM_i²/ΣN_iM_i, weights each molecule by its mass, so a few very large molecules raise it markedly.

The first two options state the sensitivities the wrong way round. The polydispersity index is M̄w/M̄n (always 1 or more), not M̄n/M̄w as the last option writes it.