Question

A 5.25% solution of a substance is isotonic with a 1.5% solution of urea (molar mass = 60 g mol⁻¹) in the same solvent. If the densities of both the solutions are assumed to be equal to 1.0 g cm⁻³, molar mass of the substance will be ______.

Options

• 90.0 g mol⁻¹

• 115.0 g mol⁻¹

• 105.0 g mol⁻¹

• 210.0 g mol⁻¹

Answer 1

A 5.25% solution of a substance is isotonic with a 1.5% solution of urea (molar mass = 60 g mol⁻¹) in the same solvent. If the densities of both the solutions are assumed to be equal to 1.0 g cm⁻³, molar mass of the substance will be 210.0 g mol⁻¹.

Explanation:

Given: 5.25% solution of unknown substance is isotonic with 1.5% urea solution.

Molar mass of urea = 60 g/mol

Densities of both solutions = 1.0 g/cm³

Isotonic solutions have equal osmotic pressure

π = CRT

⇒ C₁ = C₂

Molarity (M) = `"mass of solute"/("molar mass" xx "volume")`

For 1 L of solution 

Urea `1.5/60` = 0.025 mol/L

Unknown substance:

`5.25/M` = 0.025 mol/L

M = `5.25/0.025`

M = 210 g/mol