Chemical Engineering 160/260 Polymer Science and Engineering Lecture 4 - Direct Measures of Lecture 4 - Direct Measures of Molecular Weight: Molecular Weight: Osmometry Osmometry and and Light Scattering Light Scattering January 24, 2001 January 24, 2001
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Chemical Engineering 160/260Polymer Science and Engineering
Lecture 4 - Direct Measures ofLecture 4 - Direct Measures ofMolecular Weight: Molecular Weight: OsmometryOsmometry and and
Light ScatteringLight Scattering
January 24, 2001January 24, 2001
Outline
!! Chemical potential of dilute solutionsChemical potential of dilute solutions
!! Raoult’s Raoult’s LawLaw
!! Osmotic pressureOsmotic pressure
!! Van’t Hoff Van’t Hoff EquationEquation
!! Virial Virial expansionexpansion
!! Light scatteringLight scattering
Experimental Approaches
!! DirectDirect measures of molecular weight may bemeasures of molecular weight may beobtained from obtained from osmometryosmometry, light scattering, and, light scattering, andultracentrifugationultracentrifugation..
!! IndirectIndirect measures of molecular weight, such as measures of molecular weight, such asviscometry viscometry and gel permeation chromatography,and gel permeation chromatography,yield relative estimates that must be calibrated.yield relative estimates that must be calibrated.
Chemical Potential of Dilute Solutions
The chemical potential of a solvent in a solution is
µ µs so s
soRT
P
P= + ln
= chemical potential for pure solvent at T
= vapor pressure above the solution at T
= vapor pressure above the pure solvent at T
µ µs so
sRT a= + ln
µso
sa
P
P
s
so
= activity of solvent
If the solvent vapor obeys the ideal gas law, we have
P Ps so
s so
<
<µ µ
Raoult’s Law
In general, the activity is related to vapor pressure by
aP
Pss
so=
If the solution is sufficiently dilute, Raoult’s Lawwill be obeyed
a xP
Ps ss
so= =
= mole fraction of solvent in solutionxs
µ µs so
sRT x= + ln
Osmotic Pressure
Semipermeable membrane
Po + π
Solution Pure solvent
Po
The osmotic pressure π is the additional pressure thatmust be imposed to keep solvent and solution sectionsat the same level. This static method requires a long time to reach equilibrium.
Semipermeable Membrane Construction
!! Membranes for different solventsMembranes for different solvents
"" Organic - cellulose, gel cellophaneOrganic - cellulose, gel cellophane