Notes On Abnormal Molar Masses - CBSE Class 12 Chemistry
When the molecular mass of a substance as determined by studying any of the colligative properties is different than the theoretically expected value, then the substance will have abnormal molecular mass. In order to account for all such abnormalities, Dutch chemist J. H. Van't Hoff, in the year 1880, introduced a factor (i), known as van 't Hoff's factor, which represents the extent of association (or) dissociation of a solute. Van't Hoff's factor (i) is defined as the ratio of the observed colligative property to the calculated colligative property. i = Observed colligative property / Calculated colligative property Observed colligative property ∝ 1/Molar Mass i = Mc/Mo Van't Hoff's factor (i) represents the extent of association (or) dissociation of a solute. i = Total number of moles of particles after association or dissociation / Number of moles of particles before association or disscussion Experimentally determined molar mass is always lower than actual value for dissociation. Molar Mass ∝ 1/Colligative Property If the solute undergoes association in a solution, then the value of van 't Hoff's factor is less than one. If the solute undergoes dissociation then 'i' is greater than one. Ex:                        KCl → K+ + Cl-      1 molecule of KCl furnishes 2 ions in solution i = Total number of moles of particles after dissociation / Number of moles of particles before dissociation  i = 2/1 = 2            2CH3COOH ⇔(CH3COOH)2           Ethanoic acid     Dimer of Ethanoic acid i = Total number of moles of particles after association / Number of moles of particles before association i = 1/2 =  0.5 For substances that undergo neither dissociation nor association (i) is unity. The modified equations for colligative properties using the van 't Hoff factor are: Relative lowering of Vapour pressure of solvent ; (p1° - p1) / p1° = i n2/n1               Elevation of Boiling Point, ΔTb = iKbm            Depression of Freezing Point, ΔTf = iKfm            Osmotic pressure of solution, π = in2RT/V The degree of association of a substance (α) is defined as the fraction of the total substance that exists in the form of associated molecules. Degree of association α = Number of moles associated / Total number of moles taken The degree of dissociation of a substance (α) is defined as the fraction of the total substance that undergoes dissociation. Degree of dissociation α = Number of moles dissociated / Total number of moles taken

#### Summary

When the molecular mass of a substance as determined by studying any of the colligative properties is different than the theoretically expected value, then the substance will have abnormal molecular mass. In order to account for all such abnormalities, Dutch chemist J. H. Van't Hoff, in the year 1880, introduced a factor (i), known as van 't Hoff's factor, which represents the extent of association (or) dissociation of a solute. Van't Hoff's factor (i) is defined as the ratio of the observed colligative property to the calculated colligative property. i = Observed colligative property / Calculated colligative property Observed colligative property ∝ 1/Molar Mass i = Mc/Mo Van't Hoff's factor (i) represents the extent of association (or) dissociation of a solute. i = Total number of moles of particles after association or dissociation / Number of moles of particles before association or disscussion Experimentally determined molar mass is always lower than actual value for dissociation. Molar Mass ∝ 1/Colligative Property If the solute undergoes association in a solution, then the value of van 't Hoff's factor is less than one. If the solute undergoes dissociation then 'i' is greater than one. Ex:                        KCl → K+ + Cl-      1 molecule of KCl furnishes 2 ions in solution i = Total number of moles of particles after dissociation / Number of moles of particles before dissociation  i = 2/1 = 2            2CH3COOH ⇔(CH3COOH)2           Ethanoic acid     Dimer of Ethanoic acid i = Total number of moles of particles after association / Number of moles of particles before association i = 1/2 =  0.5 For substances that undergo neither dissociation nor association (i) is unity. The modified equations for colligative properties using the van 't Hoff factor are: Relative lowering of Vapour pressure of solvent ; (p1° - p1) / p1° = i n2/n1               Elevation of Boiling Point, ΔTb = iKbm            Depression of Freezing Point, ΔTf = iKfm            Osmotic pressure of solution, π = in2RT/V The degree of association of a substance (α) is defined as the fraction of the total substance that exists in the form of associated molecules. Degree of association α = Number of moles associated / Total number of moles taken The degree of dissociation of a substance (α) is defined as the fraction of the total substance that undergoes dissociation. Degree of dissociation α = Number of moles dissociated / Total number of moles taken

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