 # Van't Hoff Factor and Modified Colligative Properties

Abnormal colligative properties:-
When solute particle associated or dissociated in solvent.
(a) i = Vant Hoff factor = \tt \frac{Actual \ moles \ of \ solute}{Moles \ of \ solute \ without \ dissociation \ or \ association}
(b) \tt i = \frac{observed \ (or) \ experimental \ colligative \ properties}{Theoretical \ (or) \ calculated \ colligative \ properties}
(c) Relative lowering of vapour pressure \tt \frac{P^{0} - P}{P^{0}} = \frac{i.n_{solute}}{i.n_{solute} + n_{solvent}}
(d) Elevation of boiling point ΔTb = i·kb m
(e) Depression of freezing point ΔTf = i·kf m
(f) Osmotic pressure π = i.CRT
(g) For dissociation i = 1 + (n − 1) α
(h) For association \tt i = 1 + \left(\frac{1}{n} - 1\right)\alpha
(i) Degree of dissociation \tt \alpha = \frac{i - 1}{n - 1}
(j) Degree of association \tt \alpha = \frac{1 - i}{1 - \frac{1}{n}}
where n is number of particle formed on product side after dissociation (or) number of particles undergoing association.

Trick:
Raoult's law for solution containing non volatile solid solute
\tt P = P_{A}^{0}X_{A}
P = Vapour pressure of solution containing non volatile solute
XA = mole fraction of solvent
\tt P_{A}^{0} = Vapour pressure of pure solvent

### View the Topic in this Video from 0:08 to 19:35

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1. Van't Hoff factor, \tt i=\frac{Colligative\ effect\ produced\ by\ a\ given\ concentration\ of\ an\ electrolytic\ solution}{Colligative\ effect\ produced\ by\ the\ same\ concentration\ of\ a\ non \ electrolytic\ solution}
Thus, we can write i = \frac{-\Delta T_{f}}{(-\Delta T_{f})_{0}} = \frac{\Delta T_{b}}{(\Delta T_{b})_{0}} = \frac{\prod}{(\prod)_{0}} = \frac{\Delta p}{(\Delta p)_{0}}

2. Degree of dissociation of a Weak Electrolyte and van't Hoff Factor
\tt \alpha = \frac{i-1}{v-1}

where v = sum of stoichiometric numbers of cation and anion in a molecule of electrolyte.