Four colligative properties-
Relative lowering of Vapour Pressure Raoult’s Law
When a non-volatile solute is dissolved in a solvent, the vapour pressure of the solvent is lowered.
According, to Raoult’s law, the partial vapour pressure ‘P’ of a constituent of a liquid solution is equal to the product of its mole fraction ‘X1’ and its vapour pressure in the pure state.
i.e. P = X1Po ….(1)
Where, X1 = Mole fraction of solvent
Po = the vapour pressure of pure solvent
P = the vapour pressure of the solvent above a give solution.
Since X1 in any solution is less than unity, ‘P’ must be less than ‘Po’
The dissolution of a solute in a solvent leads to lowering the vapour pressure of the latter below that of the pure solvent.
ΔP = Po – P
= Po – X1Po
= Po (1 – X1) ….(2)
For a solution X1 + X2 = 1
1 – X1 = X2
ΔP = PoX2
Where, X2 is mole fraction of solute.
Thus, the vapour pressure lowering of the solvent depends both on the vapour pressure of the solvent and the mole fraction of solute in solution.
The relative lowering of vapour pressure is given as,
Thus, the relative lowering of vapour pressure is equal to the mole fraction of the solute in the solution.
The relative lowering of vapour pressure is totally independent of the nature of solvent or solute but depends only on the amount of solute in a solution and hence, a colligative property.
Elevation in boiling point
Thermodynamically relation between the elevation in the boiling point of the solution and the molecular weight of non-volatile solute dissolved.
The boiling point of solvent is the temperature at which the vapour pressure of the solvent becomes equal to 1 atmosphere. When a non-volatile solute is added, the vapour pressure is lowered and the boiling point of the solution is increased. The difference in the boiling point of the solution and pure solvent is known as elevation in boiling point
If external pressure is Po then the solvent boils at To. The solution, however, attains this pressure Po only at temperature T.
The boiling elevation of the solution ΔTb is given as.
ΔTb = T – To (1)
By applying the Clausius Clapeyron equation, we have,
If ‘n1’ is no. of a mole of solvent & ‘n2’ is the number of moles of solute, then the mole fraction of solute is given as,
Where W1 & W2 are weights & M1 & M2 are the molecular weights of solvent & solute respectively.
Molality ‘m’ is the number of moles of solute dissolved in 1000 grams of the solvent.
Since W1 g of solvent contains W2/M2 moles of solute
Therefore 1000g will contain(W2/M2W1) x 1000 moles of solute which is molality,
The relationship between depression in freezing point of the solution and molecular weight of Non- volatile solute dissolved.
The freezing point of the liquid is defined as the temperature at which vapour pressure of the liquid becomes equal to that of solids under one atmospheric pressure.
When a non-volatile solute is dissolved in a solvent the freezing point of the solvent is lowered. The difference between the two-freezing point is known as depression in freezing points.
If we plot a graph of vapour pressure Vs temperature it shows that ‘To’ is the freezing point of pure solvent & ‘T’ is the freezing point of the solution. Then, depression in the freezing point is given as
ΔTf = To – T …. (1)
Let ‘Ps’ correspond to vapour pressure of solid and pure liquid solvent at To and let ‘P’ be the vapour pressure of solid solvent and solution at temperature ‘T’. Let Po be the vapour pressure of the pure, super-cooled liquid at temp ‘T’.
If ‘n1’ is the number of moles of solvent 2 ‘n2’ is the number of moles of solute, then the mole fraction of solute. is given as
Where W1 & W2 are weights & M1 & M2 are molecular weights of solvent & solute respectively.
Substituting for X2 in equation (5) we get.
Osmosis is a phenomenon that refers to the movement or passage of solvent molecules from the pure solvent into a solution or from a dilute solution to a concentrated solution by a semipermeable membrane.
A semipermeable membrane is a membrane that is permeable to solvent molecules, but not to the solute particles
Osmotic pressure (π)
It is the pressure that must be applied to the solution side to stop the inward flow of solvent.
Van’t Hoff equation
Consider the pure solvent in compartment I is at constant T and not subjected to any pressure change of solute addition.
Therefore d (𝓊A) Pure solvent = O (I)
i.e. d (GA) pure solvent = O (II)
𝓊A = chemical potential
G = free energy/mol
The solvent in the solution of compartment (II) is at constant ‘T’ but subject to the addition of a solute and a ‘P’ change. The free energy changes due to of mole fraction ‘XA’ and pressure change ‘dp’ is given as.
dGA = VAdp + RTdℓnXA (III)
XA = mole fraction of solvent
To maintain equilibrium,
dGA = O (IV)
Therefore VAdp = -RTdℓnXA (V)
Integrating eq. (V) between limit XA = 1 to XA pressure Pinitial and Pfinal respectively we get.
VA = (Pfinal – Pinitial) = – RTℓnXA (VI)
The excess of ‘P’ is osmotic pressure ‘π‘ and XA = 1 – XB for dilute solution.
XB << 1
Therefore ℓnXA @ – XB
Substituting in equation (VI)
π = CRT
C = concentration in terms of moles per liter of solution (molarity of solution)
Equation (XI) is valid for dilute solution only.
Molar mass of solute from osmosis
π = CRT
π = n2 /v . RT
n2 = no. of moles of solute
v = volume
n2 = w2/ m2
w2 = weight of solute
m2 = molar mass of solute
π = .w2 /m2v . RT
m2 = w2 RT/ π v
By measuring ‘π’, the molar mass can be calculated.
When two solutions have the same osmotic pressure at a given temperature, they are said to be Isotonic pressure. They are of equimolar concentration.
Vant’s Hoff factor (i)
It is defined as the ratio of the experimental value of the colligative property to the calculated value of the property assuming ideal behaviors.
Ideal behavior = no association and dissociation.
1. i = 1
When solute particles, neither dissociates and associates. E.g. Urea in water.
2. i < 1
When solute particles associate in solution. E.g. Acetic acid in benzene.
3. i > 1 When solute particles dissociate. Eg. NaCl in water
Abnormal Molar masses of solute
The expression of different collective properties is valid for a dilute solution. Hence it is possible to calculate the molecular weight of different solutes by experimentally determining the magnitude of the colligative property for a solution containing a known amount of solute. However, the molecular weight of the solute determined is found to be the same as the expected value for it is an abnormal value. The reason for such abnormality is as follows,
Association in Solution
The same solute like acetic acid, and benzoic acid when dissolving in a solvent like benzene, carbon tetrachloride exists as a dimer in solution. Such association reduces the number of particles in the solution. Thus the value of the colligative property which depends upon the number of particles is found to be less than the theoretical value. As a result molar mass calculated is much higher than expected.
n = no. Of particles produced during associating.
II. Vant’s Hoff factor (i) and degree of dissociation of solute in solution.
Let an electrolyte Axy undergoes dissociation which is represented as-
Z+ and Z- are charged on cation and anion respectively.
Therefore xz+ = yz- for electrical neutrality.
If ‘C’ molar concentration of electrolyte and ‘∝’ degree of dissociation, it follows that at equilibrium.
Concentration of undissociate Axby = (1 – ∝) c.
Concentration of dissociated ions = xc∝ + yc∝
Therefore Total concentration of solute particles = C [(1 – ∝) + x∝ + y∝]
Relation Between Vant’s Hoff factor (i) and degree of association of solute in solution
Let the association reaction of solute ‘A’ can be represented as
What are the types of colligative properties? Or What are the main colligative properties?
There is a total of four colligative properties:
1. Vapour pressure lowering, 2. Boiling point elevation, 3. Freezing point depression, and 4. Osmotic pressure.
Do colligative properties depend on the number of particles?
Yes. Colligative properties depend only on the number of dissolved particles in the solution and not on their identity.