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Calculate the mass of urea that should be dissolved in 225 g of water at 35°C to produce a solution with a vapor pressure of 37.9 mmHg. (At 35°C, the vapor pressure of pure water is 42.2 mmHg; molar mass of urea is 60 g/mol).

Answer :

To calculate the mass of urea that should be dissolved in 225 g of water at 35°C to produce a solution with a vapor pressure of 37.9 mmHg is 24.8 g.

Here,Given that the mass of water = 225 gThe vapor pressure of pure water (P₁°) = 42.2 mmHgThe vapor pressure of the solution (P₂) = 37.9 mmHgThe molar mass of urea = 60 g/molWe have to calculate the mass of urea that should be dissolved in 225 g of water to produce a solution with a vapor pressure of 37.9 mmHg.The relative lowering of vapor pressure is given as: `P₁°-P₂/P₁° = w₂/w₁ x M₁/M₂`Here,`P₁° = 42.2 mmHg, P₂ = 37.9 mmHg`And, `M₁ = 18 g/mol (molar mass of water) and w₁ = 1`Since we need to calculate the mass of urea to be dissolved, let the mass of urea be w₂.

The molar mass of urea is given as 60 g/mol.M₂ = 60 g/molAnd the number of moles of water (n₁) is given as `n₁ = w₁/M₁`And the number of moles of urea (n₂) will be `n₂ = w₂/M₂`Therefore, substituting the values in the relative lowering of vapor pressure equation:`42.2-37.9/42.2 = w₂/1 × 18/60`Thus, `w₂ = 2.49 g`Therefore, the mass of urea that should be dissolved in 225 g of water to produce a solution with a vapor pressure of 37.9 mmHg is 24.8 g.

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