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A solution is prepared by dissolving 40.0 g of sucrose, in 250 g of water at 25°C. What is the vapor pressure of the solution if the vapor pressure of water at 25°C is 23.76 mm Hg?

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Edufirst

Answer:

  • The vapor pressure of the solution at 25°C is 23.6 mmHg

Explanation:

1) Data:

  • 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

2) Principles and formulae:

  • 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

       

3) Solution:

a) Mole fraction of the solvent (water)

  • 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) Vapor pressure of the solution:

  • p = p⁰ X = 23.76 mmHg × 0.99 = 23.56 mm Hg

Rounding to three significant figures: 23.6 mm Hg.

ardni313

The vapor pressure of the solution : P = 23.57 mmHg

Further explanation

Solution properties are the properties of a solution that don't depend on the type of solute but only on the concentration of the solute.

Solution properties of electrolyte solutions differ from non-electrolyte solutions because electrolyte solutions contain a greater number of particles because electrolytes break down into ions. So the Solution properties of electrolytes is greater than non-electrolytes.

The term is used in the Solution properties

  • 1. molal

that is, the number of moles of solute in 1 kg of solvent

[tex] \large {\boxed {\bold {m = mole. \frac {1000} {mass \: of \: solvent (in \: grams)}}} [/tex]

  • 2. mole fraction

the ratio of the number of moles of solute to the mole of solution

[tex] \large {\boxed {\bold {Xa = \frac {na} {na + nb}}} [/tex]

  • 3. Vapor pressure

Vapor pressure depends on the mole fraction of the components in the solution

P = Xs. P °

P = vapor pressure solution

P ° = pure vapor pressure

Xs = mole fraction solvent

ΔP = P ° - P where

ΔP = change in vapor pressure

Molar mass of sucrose-C₁₂H₂₂O₁₁: 342  g/mole

mole sucrose = 40.0 g : 342 = 0.116

Molar mass of water = 18

mole water = 250 g : 18 = 13.88

Xs = mole fraction solvent = mole of water : total mole

Xs = 13.88 : (13.88 + 0.116)

Xs = 0.992

P° = 23.76 mm Hg

so that

P = 0.992. 23.76

P = 23.57 mmHg

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Keywords: vapor pressure, sucrose, water

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