# Specific Applications of Raoult's Law in Osmotic Pressure Determinations

1. ## Background

Osmosis is the movement or diffusion of substances from regions of high concentration to regions of lower concentrations in order to eliminate the concentration differences.

2. Osmosis may be seen as the following sequence of events.

1. The addition of the nonvolatile solute to the solvent forms a solution in which the vapour pressure of the solvent is reduced.
2. The pure solvent is now placed adjacent to the solution but separated from it by a semipermiable membrane, solvent molecules will passs through the membrane into the solution in an attempt to dilute out the solute and raise the vapour pressure back to its original value (namely that of the original solvent).
3. The osmotic pressure that is set up as a result of this passage of solvent molecules may be determined either by measuring the hydrostatic head appearing in the solution or by applying a known pressure that just balances the osmotic pressure and prevents any net movement of solvent moelcules into the solution. The latter is the preferred technique. The osmotic pressure thus obtained is proportional to the reduction in vapour pressure brought about by the concentration of solute present.
3. ## Diffusion of Water

Specifically, we consider the diffusion of water molecules through a semi-permeable membrane in order to equalize the osmotic pressure of the solutions on each side of the membrane. The relationship of this diffusion to solute concentration, and more precisely number of solute molecules, can be justified as follows.

1. The diffsion of water molecules out of the solution with the lower concentration can be looked upon as a function of the escaping tendency of water molecules from that solution. Given the relationship of escaping tendency to vapour pressure and then through Raoult's Law to mole fraction (hence number of molecules) osmotic pressure can be seen to be related to the number of solute molecules in a solution.

Consider Raoult's Law in detail for a mixture of two components, A and B.

Pa+b = Pa + Pb

Where PA+B is the total vapour pressure over the mixture and Pa and Pb are the partial vapour pressures of A and B and

Pa = Pao * Xa
Pb = Pbo * Xb

Where Po represents the vapour pressure of the pure component and X represents the mole fraction of that component in the mixture.

If A is a pure solvent, its vapour pressure (Pa) would be:

Pa = Pao since Xa = 1

If a non-volatile solute, B, is dissolved in A, the total vapour pressure becomes

Pa+b = Pa + Pb

But if B is non-volatile, its vapour pressure, Pbo = 0, therefore Pb = 0 and therefore

Pa+b = Pa = Pao * Ma / (Ma + Mb)

Where Ma and Mb are the number of moles of A and B in the solution.

Since Ma / (Ma + Mb) < 1

Therefore Pa+b < Pa

The vapour pressure over the solution is less than the vapour pressure of the pure solvent.

Considering the phase diagram of water, the lowering of the vapour pressure from Pa to Pa+b must produce both a lowering of the freezing point and an elevation of the boiling point a the Triple Point moves along the sublimation curve to establish an equilibrium at the lower pressure.

Measurement of osmotic pressure can also be used (with limitations) in molecular weight determinations. Through the van't Hoff Equation:

pV = n R T

where p = osmotic pressure
V = volume of solution
n = number of moles (hence number of molecules) = Weight of solute / MW
R = gas constant
T = absolute temperature

Therefore, the relationship of osmotic pressure to solute weight can be used to calculate molecular weight of the solute.

4. ## Applications in Pharmaceutical Dosage Forms

1. Ophthalmic Solutions Reduction of irritation caused by hypo- or hyper-osmotic solutions.
2. Parenteral Solutions Injection of solutions which are not iso-osmotic can cause problems which begin with irritation and pain at the injection site and potentially result in severe toxicity due to osmotic differences and electrolyte imbalance.