Calculate the mass of a non-volatile solute (molar mass 40 g) which should be dissolved in 114 g octane to reduce its vapour pressure to 80%.

Given:

Molar mass of non-volatile solute = 40g

Let no. of moles of solute be n.

Mass of octane = 114g

Molar mass of octane(C₈H₁₈) = 12 × 8 + 1 × 18 = 114g/mol

Moles of octane = given mass/molar mass

⇒ n = 114/114 moles

⇒ n = 1 mole

Molar fraction of solute,

⇒ x₂ = n/n + 1

Let the vapour pressure of original solvent(without solute) be p₁^⁰

Accordingly after addition of solute vapour pressure of solution reduces to 80% i.e. 0.8 p₁^⁰ = p₁

Applying the formula:

⇒

⇒ n/n + 1 = 0.2

⇒ 0.2n + 0.2 = n

⇒ n = 0.25 moles

Hence, mass of solute is:

moles = given mass/molar mass

⇒ 0.25moles = mass/40g

⇒ mass = 10g.