Abnormal Molecular Weight & Van’t Hoff Factor

Since colligative properties depend upon the number of particles of the solute, in some cases where the solute associates or dissociates in solution, abnormal results for molecular masses are obtained.

Van’t Hoff Factor:

Van’t Hoff, in order to account for all abnormal cases introduced a factor i known as the Van’t Hoff factor, such that

$\large i = \frac{observed \; colligative \; property (actual)}{Theoretical \; colligative \; property (expected)}$

$\large = \frac{No. \; of \; molecules \; actually \; present}{No. \; of \; molecules \; expected \; to \; be \; present}$

Association:

There are many organic solutes which in non-aqueous solutions undergo association, that is, two or more molecules of the solute associate to form a bigger molecule.

Thus, the number of effective molecules decreases and, consequently the osmotic pressure, the elevation of boiling point or depression of freezing point, is less than that calculated on the basis of a single molecule.
Two examples are : acetic acid in benzene and chloroacetic acid in naphthalene.

Association of Acetic acid in benzene through hydrogen bonding

Degree of Association:

The fraction of the total number of molecules which combine to form bigger molecule. Consider one mole of solute dissolved in a given volume of solvent.

Suppose n simple molecules combine to form an associated molecule,

i.e. nA <—> (A)n

Let α be the degree of association, then,

The number of unassociated moles = 1 − α

The number of associated moles = α/n

Total number of effective moles = 1 − α + α/n

$\large i = \frac{1-\alpha + \alpha/n}{1}$

i = 1 − α (1 − 1/n)

Obviously, i < 1

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