Colligative Properties - Osmotic Pressure

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The excess pressure that must be applied to the solution/conc.solution to prevent osmosis.

fig 3.11 - Principle of measuring osmotic pressure

fig 3.12

If two solutions of identical composition but different concentration are separated by a semi permeable membrane (one that permits only the solvent to pass through it), the direction of flow will be from the more dilute to the more concentrated solution (left to right in the illustration). This flow will continue until the hydrostatic pressure is developed at the concentrated solution front. This pressure prevents the further movement of solvent molecules. This pressure is called osmotic pressure.

Or

Osmosis is defined as the passage of solvent from pure solvent or from solution of lower concentration into solution of higher concentration through a semi-permeable membrane.

The osmotic pressure of a solution at a particular temperature may be defined as the excess hydraulic pressure that builds up when the solution/conc.solution is separated from the solvent/dil solution by a semi permeable membrane.

Vant Hoff 's Laws of Osmotic Pressure

Vant Hoff, analyzing the available data on osmotic pressure of solutions concluded that osmotic pressure of dilute solutions varied with their concentration and temperature in the same way as pressure of the gas.

He enunciated some laws for solutions which are parallel to those relating to gases.

Vant Hoff Boyles law

Osmotic pressure (p) of a solution at a constant temperature is directly proportional to its concentration C (i.e., moles per liter)

where n is the number of moles of solute present in volume V liters of solution.

Vant Hoff Charless Law

For a solution of fixed concentration the osmotic pressure (p) of a solution is directly proportional to its absolute temperature (T).

Combining both the laws,

The constant of proportionality also turns out to be the same as gas

Measurement of osmotic pressure by the Berkeley and Hartley's apparatus

fig 3.13 - Berkley and Hartley's apparatus

The apparatus consists of a strong steel vessel into which a porous pot is fitted. The walls of the porous pot are coated with copper ferrocyanide. Due to osmosis water moves into the steel vessel from the porous pot. The water level falls in the indicator tube. This can be stopped by applying pressure using the plunger. The pressure applied is equal to the osmotic pressure. This can be recorded using a pressure gauge.

Osmotic Pressure as a Colligative Property

For a given solvent the osmotic pressure depends only upon the molar concentration of solute but does not depend on its nature.

The following relation relates osmotic pressure to number of moles of solute:

pV=nRT Van't Hoff 's solution equation (p = Osmotic pressure)

or

but,

Therefore,

p = CRT

where C = Concentration of solution in moles per liter

R = Gas constant

T = Temperature

n = Number of moles of solute

v = Volume of solution in liters

Determination of Molecular Mass from Osmotic Pressure

In order to determine the molecular mass of unknown non volatile compound, a known mass (say w g) of the compound is dissolved to prepare a known volume (say v liters) of solution. The osmotic pressure of the solution is determined and the molar mass is calculated as follows:

where n_B is the number of moles of the solute and is given by W_B/M_B.

Hence W_B is the mass of the solute in gms and M_B is the molecular mass of the solute.

Thus,

This method is exceptionally suitable for the determination of molecular masses of macromolecules such as proteins and polymers. This is due to the reason that for these substances the values of other colligative properties such as elevation in boiling point or depression in freezing point are too small to be measured. On the other hand, osmotic pressure of such substances are measurable.