Liquid Solution : Elevation in boiling point

Elevation in boiling point of the solvent (Ebullioscopy)                        

Boiling point of a liquid may be defined as the temperature at which its vapour pressure becomes equal to atmospheric pressure, i.e., 760 mm. Since the addition of a non-volatile solute lowers the vapour pressure of the solvent, solution always has lower vapour pressure than the solvent and hence it must be heated to a higher temperature to make its vapour pressure equal to atmospheric pressure with the result the solution boils at a higher temperature than the pure solvent. Thus sea water boils at a higher temperature than distilled water. If Tb is the boiling point of the solvent and T is the boiling point of the solution, the difference in the boiling point (ΔT or ΔTb) is called the elevation of boiling point.

                   T – Tb = ΔTb or ΔT

Elevation in boiling point is determined by Landsberger’s method and Cottrell’s method. Study of elevation in boiling point of a liquid in which a non-volatile solute is dissolved is called as ebullioscopy.

Important relations concerning elevation in boiling point

(i)      The elevation of boiling point is directly proportional to the lowering of vapour pressure, i.e.,

          ΔTb  ∝ po − p

(ii)     ΔTb = Kb × m

where Kb = molal elevation constant or ebullioscopic constant of the solvent;  m = Molality of the solution, i.e., number of moles of solute per 1000g of the solvent;  ΔTb = Elevation in boiling point

(iii)   \[\Delta {{T}_{b}}=\frac{1000\times {{K}_{b}}\times w}{m\times W}  or  \[m=\frac{1000\times {{K}_{b}}\times w}{\Delta {{T}_{b}}\times W}

where, Kb is molal elevation constant and defined as the elevation in b.p. produced when 1 mole of the solute is dissolved in 1 kg of the solvent. Sometimes the value of Kb is given per 0.1 kg (100 g), in such case the expression becomes

\[m=\frac{100\times {{K}_{b}}\times w}{\Delta {{T}_{b}}\times W}

Where w and w are the weights of solute and solvent and  is the molecular weight of the solute.

(iv)   \[{{K}_{b}}=\frac{0.002{{({{T}_{0}})}^{2}}}{{{l}_{V}}}

Where T0 = Normal boiling point of the pure solvent; lv =Latent heat of evaporation in cal/g of pure solvent; Kb for water is 0.52 deg – kg mol−1

 

Depression in freezing point of the solvent (Cryoscopy)

Freezing point is the temperature at which the liquid and the solid states of a substance are in equilibrium with each other or it may be defined as the temperature at which the liquid and the solid states of a substance have the same vapour pressure. It is observed that the freezing point of a solution is always less than the freezing point of the pure solvent. Thus the freezing point of sea water is low than that of pure water. The depression in freezing point (ΔT or ΔTf) of a solvent is the difference in the freezing point of the pure solvent (Ts) and the solution (Tsol).

                   Ts – Tsol = ΔTf  or ΔT

NaCl or CaCl2 (anhydrous) are used to clear snow on roads. They depress the freezing point of water and thus reduce the temperature of the formation of ice.

Depression in freezing point is determined by Beckmann’s method and Rast’s camphor method. Study of depression in freezing point of a liquid in which a non-volatile solute is dissolved in it is called as cryoscopy.

Important relations concerning depression in freezing point.

(i)      Depression in freezing point is directly proportional to the lowering of vapour pressure.

          ΔTf  ∝ p0 − p

(ii)     ΔTf = Kf × m

where Kf = molal depression constant or cryoscopic constant; m = Molality of the solution (i.e., no. of moles of solute per 1000g of the solvent);  ΔTf = Depression in freezing point

(iii)   \[\Delta {{T}_{f}}=\frac{1000\times {{K}_{f}}\times w}{m\times W}  or  \[m=\frac{1000\times {{K}_{f}}\times w}{\Delta {{T}_{f}}\times W}

Where Kf is molal depression constant and defined as the depression in freezing point produced when 1 mole of the solute is dissolved in 1 kg of the solvent. Sometimes the value of Kf is given per , in such case the expression becomes

\[m=\frac{100\times {{K}_{f}}\times w}{\Delta {{T}_{f}}\times W}                  

where w and w are the weights of solute and solvent and m is the molecular weight of the solute.

(iv)   \[{{K}_{f}}=\frac{R{{({{T}_{0}})}^{2}}}{{{l}_{f}}1000}=\frac{0.002{{({{T}_{0}})}^{2}}}{{{l}_{f}}}

where T0 = Normal freezing point of the solvent; lf = Latent heat of fusion/g of solvent ; Kf for water is 1.86 deg – kg mol−1 Relative lowering of vapour pressure, elevation in boiling point and depression in freezing point are directly proportional to osmotic pressure.

 

Colligative properties of electrolytes  

The colligative properties of solutions, viz. lowering of vapour pressure, osmotic pressure, elevation in b.p. and depression in freezing point, depend solely on the total number of solute particles present in solution. Since the electrolytes ionise and give more than one particle per formula unit in solution, the colligative effect of an electrolyte solution is always greater than that of a non-electrolyte of the same molar concentration. All colligative properties are used for calculating molecular masses of non-volatile solutes. However osmotic pressure is the best colligative property for determining molecular mass of a non-volatile substance.

Points to remember

(i)      Colligative properties ∞ Number of particles

∞ Number of molecules (in case of non-electrolytes)

∞ Number of ions (In case of electrolytes)

∞ Number of moles of solute

∞ Mole fraction of solute

(ii)     For different solutes of same molar concentration, the magnitude of the colligative properties is more for that solution which gives more number of particles on ionisation.

(iii)    For different solutions of same molar concentration of different non-electrolyte solutes, the magnitude of the colligative properties will be same for all.

(iv)    For different molar concentrations of the same solute, the magnitude of colligative properties is more for the more concentrated solution.

(v)     For solutions of different solutes but of same percent strength, the magnitude of colligative property is more for the solute with least molecular weight.

(vi)    For solutions of different solutes of the same percent strength, the magnitude of colligative property is more for that solute which gives more number of particles, which can be known by the knowledge of molecular weight and its ionisation behavior.