Calculate the mass of a non-volatile solute (molar mass 40 g mol-1) which should be dissolved in 114 g octane to reduce its vapour pressure to 80%.
The mass of non-volatile solute required is 8 g.
Explanation
This question applies Raoult's law for non-volatile solutes. The relative lowering of vapour pressure equals the mole fraction of the solute. Since the vapour pressure is reduced to 80%, the relative lowering is 20% or 0.20. The molar mass of octane (C₈H₁₈) is calculated as 114 g mol⁻¹, which conveniently equals the given mass of octane, simplifying the calculation.
Solution Steps
Step 1: Identify given values: Molar mass of solute (M₂) = 40 g mol⁻¹; Mass of octane (w₁) = 114 g; Vapour pressure reduced to 80% means p₁ = 0.80 × p₁⁰
Step 2: Calculate relative lowering of vapour pressure: (p₁⁰ – p₁)/p₁⁰ = (p₁⁰ – 0.80p₁⁰)/p₁⁰ = 0.20
Step 3: Calculate molar mass of octane (C₈H₁₈): M₁ = () + () = 96 + 18 = 114 g mol⁻¹
Step 4: Apply the formula from context: (p₁⁰ – p₁)/p₁⁰ = (w₂ × M₁)/(M₂ × w₁)
Step 5: Substitute values: 0.20 = (w₂ × 114)/()
Step 6: Solve for w₂: 0.20 = w₂/40; therefore w₂ = = 8 g