1. Molecular Weight Distribution
Summary

2. Colligative Properties and Mn
For an ideal solution (dilute):
DV = 0 and DH = 0
Mole fraction of i.
Standard chemical potential of pure
component i.
For the solvent in a polymer solution:
Thus:
Also:
Molar volume of solvent.
Molecular weight of solute.

3. So for ideal solutions (DV=0 and DH=0):
This is known as a virial equation and the
property (m1-m1o) relates to the colligative
properties osmotic pressure, boiling point
elevation, freezing point depression and
pressure lowering.
For osmotic pressure, it can be shown that:
where P is the osmotic pressure.
So,

4. For real solutions (DV and DH not 0):
where A2 and A3 are second and third
virial coefficients.
These equations are also written as:
Or:

5. Colligative Properties and Mn
Osmotic Pressure:
Boiling Point Elevation:
Freezing Point Depression:
Vapor Pressure Lowering:

6. semi-permeable membrane!
Membrane Osmometry
(pp in Shaw) P
semi-permeable membrane!
watch your units!!
Recall...
Assume A2, A3 … are equal to 0.
Q: What would be the osmotic pressure for a10 g/L solution of Polystyrene of 200,000 g/mol in toluene at 25C?

7. Answer:
At 25C: RT ~ 23 L x atm
C ~ 10 g/L x 1 mol/200,000 g = 5 x 10-5 M
P ~ 10-3 atm
P ~ 14 mm toluene
Modern osmometers can measure with accuracy of ~ 0.2 mm so the error here is ~ 0.15%. For this same sample:
DTb ~ 1 x 10-4 C
DP ~ 2 x 10-4 mm Hg (2.7 x 10-3 Pa)
Neither which can be measured with great accuracy!

8. slope of A2 c
Practical considerations:
Solvent
low viscosity, equilibrates fast
Membrane
strength (i.e. 1M NaCl P=0.42 atm)
no leakage or attack by solvent
does it pass what you want? mechanism?
possible membranes
cellophane
animal membranes
polyurethane

9. Measurement
Capillary effects
Temperature effects
Impurities
Depends on number of particles,
high MW sample can be contaminated
by relatively (by mass) small amounts
of low MW impurity.
Practical limits-- M=
Two types of osmometers available:
(1) Static -

10. (2) Dynamic – Pressure is adjusted on one side of membrane to cancel the solvent flow. (1 transparency from the Web)
Raw osmometry data are in cm (mm) of solvent:
P = r g h
Recall:
So called Flory-Huggins parameter

11. What kind of results are possible?
P/c2 c2
better solvent
so called theta (Q) solvent
Is this possible?
P/c2 c2
lower molecular weight in the same solvent

12. In Summary:
Upper limit depends on smallest pressure that can be measured.
Lower limit depends on permeability of the membrane.

13. Donnan Equilibria
Problems occur when a solution of diffusible and non-diffusible ions are introduced in an osmometer (say in the case of measuring on proteins).
Unrealistically low molecular weights are determined due to the excess of diffusible ions on the side of the macromolecule.
Working with moderately low protein concentrations and moderately high salt concentrations will solve this difficulty.

14. Donnan Equilibria 1 2 Na+ = a Na+ = b Before Pr- = a Cl- = b Equb’m
1 2
Na+ = a
Pr- = a
Na+ = a + x
Cl- = x
Before
Equb’m At
Na+ = b
Cl- = b
Na+ = b - x
Cl- = b - x
Excess of ions in compartment 1 over
compartment 2 (text)

15. Reverse Osmosis - Desalination 2270 m3/day, at P = 400 psi P>P
Note: P is not transmitted through membrane!