PHYSICAL CHEMISTRY OF MILK

Module 6. Colligative properties

Lesson 12
COLLIGATIVE PROPERTIES OF DILUTE SOLUTIONS - 2

12.1 Introduction

Osmosis is one of the most important colligative properties of liquids. Osmosis is influenced by the pressure exerted by the liquid on the membrane. It is helpful in isolating some of the constituents of milk.

12.2 Definition

Osmosis is the movement of solvent molecules through a selectively permeable membrane into a region of higher solute concentration, aiming to equalize the solute concentrations on the two sides.

When a solution and the pure solvent used in making that solution are placed on either side of a semi permeable membrane, it is found that more solvent molecules flow out of the pure solvent side of the membrane than solvent flows into the pure solvent from the solution side of the membrane. That flow of solvent from the pure solvent side makes the volume of the solution rise. When the height difference between the two sides becomes large enough, the net flow through the membrane ceases due to the extra pressure exerted by the excess height of the solution chamber. Converting that height of solvent into units of pressure gives a measure of the osmotic pressure exerted on the solution by the pure solvent. ‘P’ stands for ‘pressure, ‘r’ is the density of the solution, and ‘h’ is the height of the solution.

More solvent molecules are at the membrane interface on the solvent side of the membrane than on the solution side. Therefore, it is more likely that a solvent molecule will pass from the solvent side to the solution side than vice versa. That difference in flow rate causes the solution volume to rise. As the solution rises, by the pressure depth equation, it exerts a larger pressure on the membrane's surface. As that pressure rises, it forces more solvent molecules to flow from the solution side to the solvent side. When the flow from both sides of the membrane is equal, the solution height stops rising and remains at a height reflecting the osmotic pressure of the solution.

The equation relating the osmotic pressure of a solution to its concentration has a form quite similar to the ideal gas law: PV= inRT

This form of the equation has been derived by realizing that n / V gives the concentration of the solute in units of molarity, M.P = iMRT

12.3 Raoult's Law

The French chemist Francois Henricus Raoult discovered a law to determine the vapor pressure of a solution when a solute has been added to it. Raoult’s law states that the vapor pressure of an ideal solution is dependent on the vapor pressure of each chemical component and the mole fraction of the component present in the solution.

12.3.1 Vapor pressure

When a nonvolatile solute is added to a liquid to form a solution, the vapor pressure above that solution decreases. To understand why that might occur, let's analyze the vaporization process of the pure solvent then do the same for a solution. Liquid molecules at the surface of a liquid can escape to the gas phase when they have a sufficient amount of energy to break free of the liquid's intermolecular forces. That vaporization process is reversible. Gaseous molecules coming into contact with the surface of a liquid can be trapped by intermolecular forces in the liquid. Eventually the rate of escape will equal the rate of capture to establish a constant, equilibrium vapor pressure above the pure liquid.

If we add a nonvolatile solute to that liquid, the amount of surface area available for the escaping solvent molecules is reduced because some of that area is occupied by solute particles. Therefore, the solvent molecules will have a lower probability to escape the solution than the pure solvent. That fact is reflected in the lower vapor pressure for a solution relative to the pure solvent. That statement is only true if the solvent is nonvolatile. If the solute has its own vapor pressure, then the vapor pressure of the solution may be greater than the vapor pressure of the solvent.

Fig. 12.1 Differentiation of vapor pressure

Note that we need not identify the nature of the solvent or the solute (except for its lack of volatility) to derive that the vapor pressure should be lower for a solution relative to the pure solvent. That is what makes vapor pressure lowering a colligative property it only depends on the number of dissolved solute particles.

On the surface of the pure solvent (shown on the left) there are more solvent molecules at the surface than in the right-hand solution flask. Therefore, it is more likely that solvent molecules escape into the gas phase on the left than on the right. Therefore, the solution should have a lower vapor pressure than the pure solvent.

12.3.2 Raoult's law

The law that mathematically describes the vapor pressure lowering phenomenon.

Raoult's law is given in:

P = c_solvent P^o

P - vapor pressure of a solution

c_solvent - Vapour pressure of the solvent above a solution

P^o - vapor pressure of the pure solvent

12.4 Lowering of Vapour Pressure

The vapour Pressure of a given solution is lower than that of the pure solvent. This fact is being explained by using the Raoult’s as explained below.

Raoult's law states that the vapor pressure of a solution, P, equals the mole fraction of the solvent, C_solvent, multiplied by the vapor pressure of the pure solvent, P^o. While that "law" is approximately obeyed by most solutions, some show deviations from the expected behavior. Deviations from Raoult's law can either be positive or negative. A positive deviation means that there is a higher than expected vapor pressure above the solution. A negative deviation, conversely, means that we find a lower than expected vapor pressure for the solution.

The reason for the deviation stems from a defect in our consideration of the vapor pressure lowering event--we assumed that the solute did not interact with the solvent at all. That, of course, is not true most of the time. If the solute is strongly held by the solvent, then the solution will show a negative deviation from Raoult's law because the solvent will find it more difficult to escape from solution. If the solute and solvent are not as tightly bound to each other as they are to themselves, then the solution will show a positive deviation from Raoult's law because the solvent molecules will find it easier to escape from solution into the gas phase.

Solutions that obey Raoult's law are called ideal solutions because they behave exactly as we would predict. Solutions that show a deviation from Raoult's law are called non-ideal solutions because they deviate from the expected behavior. Very few solutions actually approach ideality, but Raoult's law for the ideal solution is a good enough approximation for the non- ideal solutions that we will continue to use Raoult's law.