Question

A sample of poly(ethylene terephthalate), PET, was dissolved in a solvent to give a series of solutions of different concentrations (c). A membrane osmometer was used to measure the
corresponding osmotic pressures (pi) at 25 ^oC. Given that a plot by pi/c vs c gave an intercept equivalent to 94.2 J/kg and the point specified by pi/c = 141 J/kg and c = 8.70 x 10^-3 kg/dm³
lies on the plot, evaluate

(i) the second virial coefficient (A2), and

(ii) the average degree of polymerization (DPn) of PET molecule.

(gas constant R = 8.314 J/mol·K).

Answer 1

Information which can be obtained from an osmometer experiment for a polymer.

From the plot of ( Osmotic pressure / Concentration ) v/s   ( concentration ) for the solvents, we can calculate the following information.

1. Calculate the Average Molecular Weight ( Mw ) of the polymer, because polymer solution can have different molecule groups for different degrees of polymerization per molecule or each different molecule.
2. Calculate the virial coefficients to understand the non-ideality of the polymer solution in some solvent.
3. Understand the interaction of the polymer solute with different solvents and calculate the osmotic pressure terms in relation to other physical properties.

Experimental set-up to calculate the osmotic pressure of the polymer, by applying external pressure over the membrane.

Above Equation relates the osmotic pressure of the solution with the concentration of the polymer solution, it is applicable when the plot deviates extensively from the linear curve.

For the case of the linear curve, we will consider only until the second virial coefficient (B) from this above equation, like in this question.

This is the equation that relates the non-ideality of the solutions from the calculation of Pressure with the virial coefficients and the number of molecules in the system.

Ideally, the curve should come as linear relation for the system, but on deviations, we can fit a polynomial equation from virial coefficients.

Degree of polymerization = 137

Second Virial Coefficient (B) = 5.37