Van't Hoff's equation for electrolytes
Van't Hoff observed that the solution of electrolytes (real solutions) showed a wide deviation in the osmotic pressure from the osmotic pressure of free ideal solutions of non-electrolytes.
He attributed this deviation to the ionization of the moles of the solute. Since, colligative properties are the sum of all the types of moles of particles of the solute in the solution, a correction factor was introduced in the standard van't Hoff equation (i) called 'van't Hoff factor'
P = iRTc
The van't Hoff factor can be defined as the total number of particles increased as compared to a solution where there is no ionization at all. Simply put,
P / P0 = i
actual number of particles on ionization/number of particles if no ionization occurred
For example, NaCl would give 2 ions on complete ionization, therefore observed osmotic pressure would be double that of anticipated osmotic pressure if NaCl did not ionize, therefore here, i=2
It was also observed that 'i' approaches to the number of ions into which the solute would ionize on infinite dilution.
Finally, since all colligative properties are the sum of all the particles of the solute in the solution, Van't Hoff factor can be applied to all the colligative properties like lowering of melting point and elevation of boiling point.
Some applications of Van't Hoff and Morse equation:
1. These equations are a preliminary in determining the molecular weight of solutes by taking the colligative properties of the given solutions in different concentrations.
2. By determining the Van't Hoff factor from comparison of the highest concentrations to the highest dilutions, the ionization characteristics of the given solute can be determined.
3. Reverse osmosis is a technique which is essentially the reverse of osmosis. In this method, a pressure equal to and a little greater than that of osmotic pressure is applied across the semi-permeable membrane to reverse the direction of solvent flow.
By determining the osmotic pressure from the Van't Hoff equations, the necessary external pressure to be applied can be estimated. This enables that the membrane used for the technique does not get damaged by high pressures.
There are many applications for reverse osmosis, i.e. desalination of sea water, preparation of pyrogen free water and purification of solutes by removal of the solvent to name a few.
1) Essentials of Physical chemistry; B.S. Bahl, G.D. Tuli, Arun bahl; S. Chand and company; pg: 493. [access date: 10th September, 2010]
2) Physical pharmacy and pharmaceutical sciences,5th edition, Patrick J. Sinko; Lippincott Williams and Wilkins, pgs:147-148 [access date: 10th September, 2010]
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