Determining the Molecular Weight of a Polymer
The polymer polyvinyl chloride (PVC) is soluble in the solvent cyclohexanone. At 25°C it is found that if a solution with 2 g of a specific batch of PVC per liter of solvent is placed in an osmometer, the height h to which the pure cyclohexanone rises is 0.85 cm. Use this information to estimate the molecular weight of the PVC polymer.
Data: Cyclohexanone has a density of 0.98 g / cm ^{3}.
The osmotic pressure corresponding to 0.85 cm of cyclohexanone is
\begin{aligned}\Pi &=\rho g h=0.98 \frac{ g }{ cm ^{3}} \times 0.85 cm \times 10^{4} \frac{ cm ^{2}}{ m ^{2}} \times 9.81 \frac{ m }{ s ^{2}} \times 10^{-3} \frac{ kg }{ g } \\&=81.72 \frac{ kg }{ m s ^{2}}=81.72 \frac{ kg m }{ s ^{2}} \frac{1}{ m ^{2}}=81.72 \frac{ N }{ m ^{2}}=81.72 Pa\end{aligned}
To determine the molecular weight of the polymer, we will use this value of the osmotic pressure and Eq. 11.5-7 and find
m_{\text {solute }}=\frac{R T C_{\text {solute }}}{\Pi} (11.5-7)
m_{\text {solute }}=\frac{8.314 \frac{ Pa m ^{3}}{ mol K } \times 298.15 K \times 2 \frac{ g }{ L } \times 10^{3} \frac{ L }{ m ^{3}}}{81.72 Pa }=60670 \frac{ g }{ mol }=60.67 \frac{ kg }{ mol }
Comment
Osmometry is an important method of determining the molecularweight of macromolecules such as polymers and proteins. The advantages of this method formacromolecules are that membranes permeable to the solvent but not to the macromolecule are easily found, and the osmotic pressure (or height of the solvent) is large and easily measured.