Degree of dissociation–vanthoff factor formula

Introduction of the Van't Hoff factor modifies the equations for the colligative properties as follows :

Relative lowering of vapour pressure = = iXB
Elevation of boiling point, ΔTb = ikbm
Depression in freezing point, ΔTf = iKfm
Osmotic pressure, π = ; π = iCRT
From the value of 'i', it is possible to calculate degree of dissociation or degree of association of substance.

Degree of dissociation(αd) :

It is defined as the fraction of total molecules which dissociate into simpler molecules or ions.
αd = ; m = Number of particles in solution

Degree of association (αa) :

It is defined as the total number of molecules which associate or combine together resulting in the formation of a bigger molecules.
αa= ; m = Number of particles in solution

Nernst Distribution law :

A solute distributes itself between two immiscible solvents in such a way that the ratio of the concentrations of the solute in the two solvents is constant at constant temperature provided that the solute does not undergo any dissociation or association in any of the solvents. Mathematically C1 / C2 = K, called distribution coefficient or partition coefficient
Calculation of the boiling point of liquid at a given pressure when boiling point at some other pressure is given (using clausius–clapeyorn equation)
T1 is the boiling point of the liquid at pressure p1
T2 is the boiling point of the liquid at pressure p2
ΔHV is the enthalpy of vaporization of the liquid.
R is gas constant( = 8.314 Jk–1mol–1

Ostwald's dilution law :

The degree of ionization or dissociation (α) of week electrolyte increases with dilution and law of mass action can be applied to them.

Application of Ostwald's dilution law

(i) It is useful in the calculation of the dissociation constant (K) of the weak acids and weak base, by determining the degree of dissociation (α) from conductance measurements ( λV/λ∞ at any concentration (C).
(ii) Knowing the value of K which is constant for a particular temperature, the degree of dissociation (α) of the week acid or week base can be calculated at any concentration
Isotonic, hypertonic and hypotonic solutions

Based on the osmatic pressure, the solutions are classified into three major types, isotonic, hypertonic and hypotonic solutions.

i. Isotonic solutions :

When two solutions made of different solutes have same osmotic pressure, they are said to be isotonic or iso-osmotic solutions.
The solution is represented as π1 = π2 where, π1 and π2 represents osmotic pressures of solutions.

Example:Solutions of urea and glucose (that do not dissociate in water); have same concentration (c1 = c2) besides osmotic pressure.

Note: Recall the relation among osmotic pressure and concentration (in molarity) as given below.

Osmotic pressure (π) = cRT
where c = concentration measured in molarity and is given by
As concentration is also related to the mole (n) and volume (v) as c = n / v;
for isotonic solutions, c1 = c2
⇒ [n1] / v1 = [n2] / v2
Since, mole is the ratio of weight(w) of substance to its molecular weight (m),
therefore, w1 / m1 × v1 = w2 / m2 × v2
There are isotonic solutions like urea + NaCl and urea + benzoic acid that have π1 = π2 but c1 ≠ c2

ii. Hypertonic and hypotonic solutions

In a mixture, the solution that has more osomotic pressure is said to be hypertonic and the one with lower is called hypo tonic. In other words, hyper tonic solution has high concentration of solute. When the mixture is placed in a membrane tank, flow of solvent is always observed from the hypotonic.

Example: Mixture of 1 N H2SO4 and 1 N HCl having osmotic pressures π1 and π2 respectively. Ionization of H2SO4:

Total no of particles = 3
No of H+ particles = 2
Therefore, c = 3/2 = 1.5 and π1 = 1.5 RT
Ionization of HCl:
Total no of particles = 2
No of H+ particles = 1
Therefore, c= 2/1 = 2 and π2 = 2 RT
Therefore, π1 <π2
As the osmotic pressure is more for HCl, it is hypertonic

In the solution, size of solvent (water) is smaller than solute (acids: HCl,H2SO4). This makes water move from hypertonic solution (HCl) to less concentrated H2SO4solution by means of membrane.
Ex 1:

In certain solvent, phenol dimerises to the extent of 60%. Its observed molecular mass in the solvent should be

Sol:

i = 1 –
Observed =
Ex 2:

A solution containing 8.6 g urea in one litre was found to be isotonic with a 5% (wt./vol.) solution of an organic non – volatile solute. The molecular weight of latter is

Sol:

For isotonic solution
⇒ M = 348.9
Ex 3:

Osmotic pressure of blood is 7.55 atm at 310 K. An aqueous solution of glucose that will be isotonic with blood is...........wt/vol

Sol:

For isotonic solution p1 = p2
7.65 = × 0.0821 × 310
7.65 = × 0.0821 × 310
= 54.1 g/lt = 5.41%M
Ex 4:

The relationship between the values of osmotic pressures of 0.1 M solutions of KN03(P1) and CH3COOH (P2) is

Sol:

For equimolar solution, osmotic pressure depends on the value of Vant Hoff s factor (i)
∴ Osmotic pressure ∴ i
KNO3, being strong electrolyte, completing ionizes, i1 = 2
But for CH3COOH, i2 = 1 + ∝
∴ i1 > i2 But P1 < i1
P2 < i2
∴ P1 > P2
Ex 2:

The mol. weight of NaCl determined by studying freezing point depression of its 0.5% aqueous solution is 30. The apparent degree of dissociation of NaCl is

Sol:

⇒ α = 0.95.