Properties of solution that depend on the ratio of no: of solute particles to the total no: of particles in the solution.
1. Relative lowering of vapour pressure:
⇒ Vapour pressure of solvent in solution is less than that of pure solvent.
According to Raoult’s law
PA = XA x P°A
⇒ So the reduction in vapour pressure is given as
Δ PA = P°A – PA
i.e., Δ PA = P°A (1 – XA) = P°AXB
\(\frac{\Delta {{P}_{A}}}{{{P}_{A}}}={{X}_{B}}=\frac{{{n}_{2}}}{{{n}_{1}}+{{n}_{2}}}\)i.e., therefore, relative lowering of vapour pressure Δ PA/PA is equal to mole fraction of solute XB.
⇒ If two or more non-volatile solutes are present then it is equal to sum of the mole fraction of the solutes
\(\frac{\Delta {{P}_{A}}}{{{P}_{A}}}={{X}_{B}}+{{X}_{C}}+………+{{X}_{N}}\)For dilute solutions:
\(\frac{\Delta {{P}_{A}}}{{{P}_{A}}}={{X}_{B}}=\frac{{{n}_{2}}}{{{n}_{1}}}\) (As n₂ << n₁)
\(\frac{\Delta {{P}_{A}}}{{{P}_{A}}}=\frac{{{w}_{B}}\times {{M}_{A}}}{{{M}_{B}}\times {{w}_{A}}}\)Where, wA = mass of solvent
MA = Molar mass of solvent
WB = mass of solute
MB = Molar mass of solute
2. Elevation of boiling point:
⇒ A liquid boils at a temperature where its vapour pressure becomes equal to atmospheric pressure.
⇒ Since in a solution the vapour pressure of solvent is reduced, the temperature needs to be raised to increase the vapour pressure to atmospheric pressure.
⇒ Therefore, the boiling point of solution is always higher than that of pure solvent.
ΔTb = Tb – T°b
= elevation in boiling point
Tb= boiling point of solution
Tb0 = boiling point of pure solvent
For dilute solutions:
Tb α m
Δ Tb = Kb x m
m = molality
Kb = molal elevation constant (Ebullioscopic Constant). Units: K kg mol-1
\({{K}_{b}}=\frac{R\times {{M}_{1}}\times {{T}_{b}}^{2}}{1000\times {{\Delta }_{vap}}H}\)R = gas constant
M1 = molar mass of solvent
ΔvapH = enthalpy of vaporization
3. Depression of freezing point
⇒ A solution freezes when its vapour pressure becomes equal to the vapour pressure of pure solid solvent.
⇒ As the vapour pressure of a solvent decreases when a non-volatile solute is added, the freezing point of solvent decreases.
ΔTf = T°f – Tf
ΔTf = depression in freezing point
T°f = freezing point of pure solvent
Tf = freezing point of solution
For dilute solution:
Δ Tf α m
Δ Tf = Kf x m
Kf = Molal depression constant (Cryoscopic constant). Units: K kg mol¯¹
\({{K}_{f}}=\frac{R\times {{M}_{1}}\times {{T}_{f}}^{2}}{1000\times {{\Delta }_{fus}}H}\)R = gas constant
M1= molar mass of solvent
ΔfusH = enthalpy of fusion