' W ' g of a non-volatile electrolyte solid solute of molar mass ' M ' g mol ⁻¹ when dissolved in 100 mL water, decreases vapour pressure of water from 640 mm Hg to 600 mm Hg. If aqueous solution of the electrolyte boils at 375 K and K _ b for water is 0.52 ~K ~kg ~mol ⁻¹ , then the mole fraction of the electrolyte solute (x₂ ) in the solution can be expressed as (Given : density of water =1 ~g / mL and boiling point

Step-by-step solution

Given the vapour pressure of pure water P^o = 640 mm Hg and vapour pressure of solution P_s = 600 mm Hg. According to Raoult's law for an electrolyte solution, the relative lowering of vapour pressure is given by P^o - P_s P^o = i x₂ , where i is the van't Hoff factor and x₂ is the mole fraction of the solute. Substituting the values: 640 - 600 640 = i x₂ 40 640 = i x₂ i x₂ = 1 16 ... (1) The elevation in boiling point is given by T_b = i K_b m , where m is the molality. Given T_b = 375 K and T_b^o = 373 K, so T_b