Molecular Weight and Distribution Questions and Answers

Q: The polydispersity index of a polymer is given by the ratio of :

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.

Q: In the study of solution of a polymer, the plot of \(\frac{\pi}{C}\) versus 'C' results into the information of :

The plot gives Mn 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/Mn, 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 Mn to the slope, or call the slope concentration, which is the axis variable, not a result.

Q: The significance of weight average \(\overline{\text{M}}\text{w}\) and number average \(\overline{\text{M}}\text{n}\) molecular weights is that :

The significance is that M̄w is sensitive to high molecular weight and M̄n to low molecular weight species.The number average, M̄n = ΣNiMi/ΣNi, counts every molecule equally, so a large number of small molecules pulls it down. The weight average, M̄w = ΣNiMi2/ΣNiMi, 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.

11.

The polydispersity index of a polymer is given by the ratio of :

A.\(\bar{\mathrm{M}}\mathrm{v} / \bar{\mathrm{M}}\mathrm{w}\)
B.\(\bar{\mathrm{M}}\mathrm{w} / \bar{\mathrm{M}}\mathrm{z}\)
C.\(\bar{\mathrm{M}}\mathrm{w} / \bar{\mathrm{M}}\mathrm{n}\)
D.\(\bar{\mathrm{M}}\mathrm{n} / \bar{\mathrm{M}}\mathrm{w}\)

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

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.

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12.

In the study of solution of a polymer, the plot of \(\frac{\pi}{C}\) versus 'C' results into the information of :

A.\(\overline{\mathrm{Mn}}\) as reciprocal of intercept and polymer-solvent interaction constant as slope
B.\(\overline{\mathrm{Mn}}\) as an intercept and concentration as slope
C.\(\overline{\mathrm{Mn}}\) as the slope and polymer-solvent interaction constant as an intercept
D.Only \(\overline{\mathrm{Mn}}\) as ratio intercept and slope

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

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.

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13.

The significance of weight average \(\overline{\text{M}}\text{w}\) and number average \(\overline{\text{M}}\text{n}\) molecular weights is that :

A.\(\overline{\text{M}}\text{w}\) is sensitive to low molecular weight species
B.\(\overline{\text{M}}\text{n}\) is sensitive to high molecular weight species
C.\(\overline{\text{M}}\text{w}\) is sensitive to high molecular weight and \(\overline{\text{M}}\text{n}\) is sensitive to low molecular weight
D.\(\overline{\text{M}}\text{n}/\overline{\text{M}}\text{w}\) gives information of polydispersivity

Exam Year(s)

MH SET - 2025, SET Exam - 2025,

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.

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