VAN’T HOFF THEORY OF DILUTE SOLUTIONS  

van’t Hoff realized that an analogy exists between gases and solutions provided osmotic pressure of solutions is used in place of ordinary gas pressure. He showed that for dilute solutions of non-electrolysis the following laws hold good.  

1. Boyle-van’t Hoff law:  

The osmotic pressure (P or α) of a solution is directly proportional to its concentration (C) when the temperature is kept constant. The concentration of the solution containing one gram mole in V litres is equal to 1/V (C = 1/V)

Thus P ∝ C                 (when temperature is constant)  

or P ∝ 1/V

or PV = constant             or     πV = constant  

van’t Hoff presumed that the osmotic pressure is due to the bombardment of solute molecules against the semipermeable membrane as the gas pressure is due to hits recorded by gas molecules against the walls of its container.  

2. Pressure-Temperature law (Gay-Lussac-van’t Hoff law):  

Concentration remaining same; the osmotic pressure of a dilute solution is directly proportional to its absolute temperature (T), i.e.,  

P ∝ T  

or P/T = constant       or            μ/T constant  

Combining the two laws, i.e., when concentration and temperature both are changing, the osmotic pressure will be given by:  

P ∝ CT  

or P = kCT  

or P = k.1/V.T           (since C = 1/V)

or PV = ST or πV = ST  

S is called molar solution constant.  

Here V is the volume of solution containing one gram mole of the solute. The value of 5 comes out to 0.082 lit atm K−1 mol−1 which is in agreement with the value of R, the molar gas constant. In case the solution contains n gram moles in V litres, the general equation would become  

          PV = nST  or     πV = ST  

3. Third law:  

Equimolecular solutions of different solutes exert equal osmotic pressure under identical conditions of temperature. Such solutions which have the same osmotic pressure are termed isotonic or iso-osmotic. When two isotonic solutions are separated by a semipermeable membrane, no flow of solvent molecules is observed on either side.  

The law is similar to Avogadro’s hypothesis. It can be stated as, “Equal volumes of dilute solutions of different solutes, having the same temperature and osmotic pressure, contain equal number of molecules.”  

For solution I,             PV = n1ST  

For solution II,            PV = n2ST  

Thus, n1 must be equal to n2 when P, V and T are same.  

The analogy of dilute solutions with gases is this perfect.  

This led van’t Hoff to suggest that a solute in dissolved state (i.e., in solution) behaves as a gas and the osmotic pressure of the solution is equal to the pressure which the solute would exert if it were a gas at the same temperature and occupying the same volume as that of the solution. This statement is known as van’t Hoff.

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