Notes On Colligative Properties: Relative Lowering Of Vapour Pressure And Elevation Of Boiling Point - CBSE Class 12 Chemistry
Colligative properties: Colligative properties are defined as properties of the solution that depend only on the total number of solute particles in the solution and are independent of the chemical identity of the solute particles. Colligative properties are properties that depend on the concentration of the solution and not on the nature of its contents. Solutions containing non-volatile solutes exhibit the following Colligative properties: Relative lowering of the vapour pressure of the solvent Depression of its freezing point Elevation of the boiling point Osmotic pressure of the solution. Lowering of the vapour pressure of the solvent: When a non-volatile solute is added to a solvent, the vapour pressure of the solution decreases. According to Raoult's Law, the vapour pressure of a solvent (P1) in a solution containing a non-volatile solute is given by According to Raoult's Law, Vapour pressure of the pure solvent = P1° Vapour pressure of the solvent in solution = P1                           P1 = x1P1°                  ΔP1 = P1° - P1                         = P1° - x1P1°                         = P1° (1 - x1) In a binary solution, 1 - x1 = x2                         ΔP1 = P1° x2                         ΔP1/P1° = (P1° - P1)/P1° = x2 The lowering of vapour pressure relative to the vapour pressure of pure solvent is called relative lowering of vapour pressure. ΔP1/P1° → Relative lowering of Vapour pressure Thus, the relative lowering in vapour pressure depends only on the concentration of solute particles and is independent of their identity. If the solution contains more than one non-volatile solute, then the relative lowering in vapour pressure of a solvent is equal to the sum of the mole fractions of all the non-volatile solutes. If n1 and n2 are respectively the number of moles of the solvent and solute in a binary solution, then the relative lowering in the vapour pressure of the solvent, (P1° - P1)/P1° = x1 + x2 + x3 + ... + xn if n1 and n2 are the number of moles of the solvent and solute, (P1° - P1)/P1° = n2/(n1+n2) For dilute solutions n2 << n1 (P1° - P1)/P1° = n2/n1 n1 = W1/M1 , n2 = W2/M2 (P1° - P1)/P1° = (W2xM1)/(W1xM2)             W1 = Mass of solvent             W2 = Mass of solute             M1  = Molar mass of solvent             M2  = Molar mass of solute Elevaton in Boiling Point: The vapour pressure of a liquid increases with an increase in temperature. When vapour pressure of the liquid becomes equal to the atmospheric pressure (or) external pressure, then liquid starts boiling. The temperature at which the vapour pressure of the liquid is equal to the external pressure is known as its boiling point. At any temperature, the vapour pressure of a solution containing a non-volatile solute is less than that of the pure solvent. The temperatures at which the vapour pressure of the solvent and the solution become equal to the atmospheric pressure are Tb0 and Tb. Tb-Tb0 =∆Tb Thus, it can be seen that the boiling point of a solution is greater than the boiling point of the pure solvent. The boiling point of a solvent changes as the concentration of the solute in the solution changes, but it does not depend on the identity of the solute particles. The elevation of the boiling point depends upon the concentration of the solute in the solution and is directly proportional to molality (m) of the solute in the solution.              ΔTb = Tb - Tb°                 Tb > Tb°           ΔTb ∝ Concentration of solute         ΔTb ∝ m (Molarity)          ΔTb = Kb m Kb = Boiling point elevation constant or molal elevation constant or ebullioscopic constant            Molal elevation constant is defined as the elevation in the boiling point when 1mole of a solute is dissolved in 1kilogram of a solvent. If w2 grams of a solute with M2 molar mass is dissolved in w1gram of a solvent, then molality (m) of the solution is,  m = (W2x1000)/(W1xM2) ΔTb = Kb (W2x1000)/(W1xM2) On Rearranging:         M2 = (KbxW2x1000)/(ΔTb x W1)

#### Summary

Colligative properties: Colligative properties are defined as properties of the solution that depend only on the total number of solute particles in the solution and are independent of the chemical identity of the solute particles. Colligative properties are properties that depend on the concentration of the solution and not on the nature of its contents. Solutions containing non-volatile solutes exhibit the following Colligative properties: Relative lowering of the vapour pressure of the solvent Depression of its freezing point Elevation of the boiling point Osmotic pressure of the solution. Lowering of the vapour pressure of the solvent: When a non-volatile solute is added to a solvent, the vapour pressure of the solution decreases. According to Raoult's Law, the vapour pressure of a solvent (P1) in a solution containing a non-volatile solute is given by According to Raoult's Law, Vapour pressure of the pure solvent = P1° Vapour pressure of the solvent in solution = P1                           P1 = x1P1°                  ΔP1 = P1° - P1                         = P1° - x1P1°                         = P1° (1 - x1) In a binary solution, 1 - x1 = x2                         ΔP1 = P1° x2                         ΔP1/P1° = (P1° - P1)/P1° = x2 The lowering of vapour pressure relative to the vapour pressure of pure solvent is called relative lowering of vapour pressure. ΔP1/P1° → Relative lowering of Vapour pressure Thus, the relative lowering in vapour pressure depends only on the concentration of solute particles and is independent of their identity. If the solution contains more than one non-volatile solute, then the relative lowering in vapour pressure of a solvent is equal to the sum of the mole fractions of all the non-volatile solutes. If n1 and n2 are respectively the number of moles of the solvent and solute in a binary solution, then the relative lowering in the vapour pressure of the solvent, (P1° - P1)/P1° = x1 + x2 + x3 + ... + xn if n1 and n2 are the number of moles of the solvent and solute, (P1° - P1)/P1° = n2/(n1+n2) For dilute solutions n2 << n1 (P1° - P1)/P1° = n2/n1 n1 = W1/M1 , n2 = W2/M2 (P1° - P1)/P1° = (W2xM1)/(W1xM2)             W1 = Mass of solvent             W2 = Mass of solute             M1  = Molar mass of solvent             M2  = Molar mass of solute Elevaton in Boiling Point: The vapour pressure of a liquid increases with an increase in temperature. When vapour pressure of the liquid becomes equal to the atmospheric pressure (or) external pressure, then liquid starts boiling. The temperature at which the vapour pressure of the liquid is equal to the external pressure is known as its boiling point. At any temperature, the vapour pressure of a solution containing a non-volatile solute is less than that of the pure solvent. The temperatures at which the vapour pressure of the solvent and the solution become equal to the atmospheric pressure are Tb0 and Tb. Tb-Tb0 =∆Tb Thus, it can be seen that the boiling point of a solution is greater than the boiling point of the pure solvent. The boiling point of a solvent changes as the concentration of the solute in the solution changes, but it does not depend on the identity of the solute particles. The elevation of the boiling point depends upon the concentration of the solute in the solution and is directly proportional to molality (m) of the solute in the solution.              ΔTb = Tb - Tb°                 Tb > Tb°           ΔTb ∝ Concentration of solute         ΔTb ∝ m (Molarity)          ΔTb = Kb m Kb = Boiling point elevation constant or molal elevation constant or ebullioscopic constant            Molal elevation constant is defined as the elevation in the boiling point when 1mole of a solute is dissolved in 1kilogram of a solvent. If w2 grams of a solute with M2 molar mass is dissolved in w1gram of a solvent, then molality (m) of the solution is,  m = (W2x1000)/(W1xM2) ΔTb = Kb (W2x1000)/(W1xM2) On Rearranging:         M2 = (KbxW2x1000)/(ΔTb x W1)

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