Answer:
- <em>The vapor pressure of the solution at 25°C is </em><u><em>23.6 mmHg</em></u>
Explanation:
<u>1) Data:</u>
- Mass of solute, sucroese, m₁ = 40.0 g
- Mass of solvent, water, m₂ = 250. g
- Vapor pressure of solution, p = ?
- Vapor pressure of pure water, p⁰ = 23.76 mm Hg
<u>2) Principles and formulae:</u>
- Raoult's law states that the vapor pressure of a solution is equal to the mole fraction of the solvent times the vapor pressure of the pure liquid.
p = X p⁰
<u>3) Solution:</u>
a) <u>Mole fraction of the solvent (water)</u>
- X = number of moles of solvent / number of moles of solution
- number of moles of solvent, n₁ = mass in grams / molar mass
n₁ = 250. g / 18.015 g/mol = 13.88 moles
- number of moles of solute, n₂ = mass in grams / molar mass
n₂ = 40.0 g / 342,3 g/mol = 0.12 moles
- total number of moles, n₁ + n₂ = 13.88 moles + 0.12 moles = 14.0 moles
- moles fraction of water, X = 13.88 moles / 14.0 moles = 0.99
b) <u>Vapor pressure of the solution</u>:
- p = p⁰ X = 23.76 mmHg × 0.99 = 23.56 mm Hg
Rounding to three significant figures: 23.6 mm Hg.
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