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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

Answer: A

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.

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