A solution of two components containing n₁ moles of the 1ˢᵗ component and n₂ moles of the 2ⁿᵈ component is prepared. M₁ and M₂ are the molecular weights of component 1 and 2 respectively. If d is the density of the solution in g mL –1 , C₂ is the molarity and x₂ is the mole fraction of the 2ⁿᵈ component, then C₂ can be expressed as :

Solution

Chemistry ma’am · 4 steps

Take one mole of solution in total: then x₂ is the moles of solute, and the density turns mass into volume.

1. Pick a convenient amount. Molarity does not depend on how much solution you take, so take n₁ + n₂ = 1 mol in total. Then component 2 is x₂ mol and component 1 is 1 - x₂ mol.
2. Mass of solution. Mass = (1 - x₂)M₁ + x₂ M₂ = M₁ + x₂(M₂ - M₁) grams.
3. Volume in litres. Volume in mL is mass divided by d. Divide by 1000 more to get litres, so V = (M₁ + x₂(M₂ - M₁))/1000d L.

   C₂ = x₂/V = (1000 d x₂)/(M₁ + x₂(M₂ - M₁))

4. So. The expression matches option (b).

The idea to keep. To change mole fraction into molarity, take 1 mol of solution in total. Find its mass from the molar masses, use the density to get its volume, and convert mL to litres with the factor 1000.

Answer from the NTA final answer key. Solution by PrepWiser.