of association or dissociation of solutes in solution, van’t Hoff introduced a term 'i' which is now called van’t Hoff factor. It is defined as the ratio of the actual molar mass to the abnormal (calculated) molar mass of the solute. Here, the abnormal molar mass is the molar mass calculated using the experimentally determined colligative property. i Normal actual molar mass Observed abnormal molar ma ( ) ( ) ss Observed colligative property Calculated colligative p roperty Unit Unit - - - - The estimated Van’t Hoff factor for acetic acid solution in Benzene is .
and that of sodium chloride solution in water is . The degree of dissociation or association can be related to Van't Hoff factor (i) using the following relationships α dissociation = i– n– (Where n is number ions /species formed by the dissociation of a single molecule) α association = ( –i)n n– (here, n is the number of solute involved in association. The equations relating the four colligative properties with the concentration of the solutes can be rewritten as follows by incorporating the van’t Hoff factor Relative lowering of vapour pressure, p -p p = i n n E solvent solution o solvent o solute solvent levation of boiling point T =iK m Depression in the fre b b ezing point T iK m Osmotic pressure = i w V RT M solute solute ∆ ∆ π f f For a solute that does not dissociate or associate the van’t Hoff factor is equal to (i = ) and the molar mass will be close to the actual molar mass. For the solutes that associate to form higher oligomers in solution the van’t Hoff factor will be less than one (i < ) and the observed molar mass will be greater than the actual molar mass.
For solutes that dissociates into their constituent ions the van’t Hoff factor will be more than one (i > ) and the observed molar mass will be less than the normal molar mass. Example Problem - The depression in freezing point