van't Hoff's equation and Morse equation for non-electrolytic solutions

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Van't Hoff's laws for non-electrolytes

Van't Hoff has observed from Pfeffer's data that there is a similarity in the behaviour of dilute solutions and gases. Thus, he proposed that dilute solutions obey laws similar to the gas laws.

It can be stated as: "a substance in solution behaves exactly like a gas and the osmotic pressure of a dilute solution is equal to the pressure which the solute would exert if it were a gas at the same temperature occupying the same volume as the solution."

According to this theory, it can be derived that 1 mole of any solute dissolved in 22.4 litres would exert 1 atmosphere pressure as osmotic pressure.

Van't Hoff has formulated certain laws pertaining to the process of osmosis based on certain observations, which are:

a) The osmotic pressure of a solution at a given temperature is directly proportional to its concentration.

b) The osmotic pressure of a solution of a given concentration of solution is directly proportional to the absolute temperature.

(1) Boyle-van't Hoff law:

If p is the osmotic pressure and C is the concentration of the solution then, from statement (a) we can write

P?C - (1)

The concentration of a solution C = 1/V, where V is the volume of the solution containing 1 mole of solute.

Therefore, P ? 1/V

(2) Charles'-van't Hoff law:

If T is the absolute temperature, then from statement (b) we can write

P?T - (2)

(3) Van't Hoff equation for solutions:

From eq. (1) and (2) Van't Hoff derived a general relationship

PV = nR'T

From experimental values, the value of R' was found to be close to the gas constant, R.

Since, n/V = c

P = cRT

where, c is the concentration in terms of 'molar concentration' i.e. moles/litre of solution.

(4) Avagadro-Van't Hoff law:

For two different dilute solutions,

P1V1 = n1R1T1

P2V2 = n2R2T2

Where, n1 and n2 are the number of moles of the solute in solutions of volume V1 and V2 respectively.

If P1 = P2 and T1 = T2 then;

n1 / V1 = n2 / V2

When the temperature and osmotic pressure is the same for two dilute solutions, then they are equimolar, i.e., they contain equal number of moles of solute in equal volumes of solution.

Morse equation(2)

The van't Hoff's equation gave results which were a little deviated from the observed experimental results. Morse and other scientists observed that when the concentration was expressed in terms of 'molal concentration (m)' i.e. moles/kg of solvent, the results were more comparable to the experimental results.

P = mRT

Note: Van't Hoff theory holds good only to those solutions in which the solute does not undergo dissociation and association.


1) Essentials of Physical chemistry; B.S. Bahl, G.D. Tuli, Arun bahl; S. Chand and company; pg: 482-486. [access date: 10th September, 2010]

2) Physical pharmacy and pharmaceutical sciences,5th edition, Patrick J. Sinko; Lippincott Williams and Wilkins, pgs:137 [access date: 10th September, 2010]

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Author: Niklesh Rao V

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