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Colligative Properties and Vapor Pressure

Colligative Properties I: Vapor Pressure

Introduction to Colligative Properties

  • Definition: Colligative properties are physical characteristics of a solution that are dependent primarily on the number of solute particles in a solution rather than the type of particles.

  • Measurement of Particles: The number of solute particles is typically measured in moles.

  • Concentration Measurements: Concentrations can be expressed in three ways:

    • Mole fraction:

    • Molality:

    • Molarity:

  • Types of Colligative Properties to Discuss: There are four key colligative properties:

    • Vapor Pressure Lowering

    • Freezing Point Depression

    • Boiling Point Elevation

    • Osmotic Pressure

Vapor Pressure Lowering

  • Definition of Vapor Pressure: The vapor pressure of a liquid is defined as the pressure exerted by the vapor in equilibrium with the liquid at a given temperature. All liquids possess some degree of volatility, hence they have a measurable vapor pressure.

  • Impact of Non-Volatile Solute: Adding a non-volatile solute (e.g., a solute that does not readily escape into the vapor phase, like a solid) to a solvent affects its vapor pressure significantly.

    • Mechanism of Vapor Pressure Lowering:

    • The inclusion of a non-volatile solute lowers the effective concentration of the solvent in the solution.

    • As a result, fewer solvent molecules are able to escape into the vapor phase.

    • The addition of the solute increases the overall entropy of the solution, which consequently decreases the entropy change associated with vaporization, thereby reducing the vaporization rate.

    • The net result is a lower vapor pressure in comparison to that of the pure solvent.

Demonstration of Vapor Pressure Lowering

  • Experimental Setup:

    • Place two beakers containing equal volumes of liquid: one with pure solvent and the other with a concentrated solution of the same solvent into a sealed container.

    • Since both liquids are volatile, they will evaporate into the enclosed space.

  • Outcome Post-Equilibrium:

    • Once equilibrium is re-established, the level of the liquid in the beaker containing pure solvent will be lower than that in the beaker containing the solution.

    • The transfer of solvent from the pure solvent beaker to the solution indicates that the vapor pressure of the solution is lower than that of the pure solvent.

    • Over time, the liquid level in the concentrated solution will remain higher because it retains solvent vapor more effectively, leading to an ongoing decrease in concentration.

Raoult's Law

  • Statement of Raoult's Law: Raoult's Law dictates that the vapor pressure of a solution is directly proportional to the mole fraction of the solvent present within that solution.

  • Components of Raoult's Law: For solutions containing non-volatile, non-electrolyte solutes:

    • P_{solution}: Vapor pressure of the solvent within the solution.

    • P°_{solvent}: Vapor pressure of the pure solvent.

    • χ_{solvent}: Mole fraction of the solvent in the solution.

Example Problem on Vapor Pressure Calculation

  • Given Problem: Calculate the vapor pressure of a 30.3% m/m ethylene glycol solution (molar mass = 62.07 g/mol) at 90 °C, knowing that the vapor pressure of pure water at this temperature is 525.8 torr.

  • Required Calculation Details:

    1. Find the mole fraction of the solvent.

    2. Use Raoult's Law to calculate the solution's vapor pressure.

Additional TopHat Question on Vapor Pressure

  • Question: Calculate the vapor pressure (in torr) at 25 °C of a solution containing 99.5 g sucrose (C12H22O11, MW = 342.34 g/mol) and 200.0 mL water, given the vapor pressure of pure water at 25 °C is 23.7 torr, and the density of water is 1.00 g/mL.

Volatile Non-Electrolyte Solutes

  • Definition: In cases where both solute and solvent are volatile, both will contribute to the overall vapor pressure of the solution.

  • Raoult's Law and Dalton's Law of Partial Pressures:

    • The total vapor pressure of the solution can be determined by combining Raoult's Law and Dalton's Law of Partial Pressures.

    • Dalton's Law of Partial Pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas.

    • Ideal Solutions: This method is applicable only to ideal solutions where the intermolecular interactions between solute and solvent are comparable to those between solute-solute and solvent-solvent pairs.

Deviations from Raoult's Law

  • Not Ideal Solutions: It is essential to note that not all solutions behave ideally. If either solute-solvent interactions are significantly stronger or weaker than the broken interactions during dissolution, deviations from Raoult's Law will occur, impacting the vapor pressure measurements.

Example Problem on Total Vapor Pressure Calculation

  • Example: A solution contains 3.95 g carbon disulfide (CS2, 76.13 g/mol) and 2.43 g acetone (CH3COCH3, 70.10 g/mol). Calculate the total vapor pressure at 35 °C, knowing that the pure vapor pressures are 515 torr for CS2 and 332 torr for acetone under similar conditions, assuming ideal behavior.

Raoult's Law for Non-Volatile Electrolyte Solutions

  • Components: For solutions containing ionic compounds (electrolytes):

    • P_{solution}: Vapor pressure of the solvent present in the solution.

    • P_{solvent}: Vapor pressure of the pure solvent.

    • X_c: Colligative mole fraction.

    • i: Van't Hoff factor, which accounts for the number of particles into which a compound dissociates in solution.

Van't Hoff Factor (i)

  • Definition: The theoretical van't Hoff factor is defined as the ratio of the number of moles of solute particles produced to the number of moles of ionic formula units present in a solution.

  • Factors Affecting Measurement: The measured van't Hoff factors are often less than expected theoretical values due to occurrences of ion pairing within the solution. If not provided, it is standard to use the theoretical value in calculations.

Check Your Understanding of the Van't Hoff Factor

  • Questions to Evaluate Understanding:

    • Determine the van't Hoff factor for the following aqueous solutions:
      I. KI
      II. MgSO4
      III. C12H22O11
      IV. CaCl2
      V. AlCl3

TopHat Question on Vapor Pressure Comparison

  • Question: Which among the following aqueous solutions possesses the lowest vapor pressure? Note that each solute is non-volatile. Computing the mole fraction is unnecessary as it is directly proportional to molality (χ ∝ m):
    A. 0.120 m C2H6O2
    B. 0.040 m (NH4)2SO4
    C. 0.060 m Li2CO3
    D. 0.030 m RbCH3COO
    E. Cannot be determined
    F. All have the same vapor pressure