Chapter 11: Properties of Solutions

Chapter Overview

  • 11.1 Solution Composition

  • 11.2 The Energies of Solution Formation

  • 11.3 Factors Affecting Solubility

  • 11.4 The Vapor Pressures of Solutions

  • 11.5 Boiling-Point Elevation and Freezing-Point Depression

  • 11.6 Osmotic Pressure

  • 11.7 Colligative Properties of Electrolyte Solutions

  • 11.8 Colloids

11.1 Solution Composition

  • Definition of Solutions: A solution is a homogeneous mixture that can consist of gases, liquids, or solids. Most focus will be on liquid solutions, especially aqueous solutions, since many essential reactions occur in water.

  • Describing Solution Composition:

    • Molarity (M): Moles of solute per liter of solution.

    • M = rac{ ext{moles of solute}}{ ext{liters of solution}}

    • Mass Percent (Weight Percent): Ratio of mass of solute to mass of solution, expressed as a percentage.

    • ext{Mass percent} = rac{ ext{mass of solute}}{ ext{mass of solution}} imes 100 ext{%}

    • Mole Fraction (x): Ratio of moles of a component to total moles in the solution.

    • For a two-component solution:

    • xA = rac{nA}{nA + nB}

    • Molality (m): Moles of solute per kilogram of solvent.

    • m = rac{ ext{moles of solute}}{ ext{kilograms of solvent}}

Additional note: The distinctions between the parameters help in stoichiometric calculations, as evidenced in previous chapters.

Example Calculation: For mixing 1 g of ethanol (C2H5OH) with 100 g of water:

  • Molar mass of C2H5OH = 46.07 g/mol → Calculate moles of solute:

    • 1.00 ext{ g} imes rac{1 ext{ mol}}{46.07 ext{ g}}
      ightarrow 2.17 imes 10^{-2} ext{ mol}

  • Calculate other metrics (Molarity, Mass percent, Mole fraction, and Molality).

11.2 The Energies of Solution Formation

  • Dissolving Processes: Various processes like cooking, cleaning, and carbonation are examples of dissolving solutes in liquids. Solubility is affected by structural properties and external factors.

  • Enthalpy (Heat) of Solution ($ΔH_{soln}$): The total energy changes in three steps:

  1. Step 1 (ΔH1): Expanding solute (requires energy).

  2. Step 2 (ΔH2): Expanding solvent (requires energy).

  3. Step 3 (ΔH3): Solute-solvent interaction (generally releases energy).

ΔH_{soln} = ΔH1 + ΔH2 + ΔH3

Important Notes:

  • Polar and nonpolar behaviors (e.g., oil is not soluble in water due to significant ΔH values).

  • Example: Dissolving NaCl in water has distinct energy calculations indicating it is exothermic overall despite needing energy to separate the ions.

11.3 Factors Affecting Solubility

  • General Rule: “Like dissolves like.” Polar solvents dissolve polar solutes, nonpolar dissolves nonpolar solutes.

  • Impact of Structure: The inherent structure of a molecule dictates its polarity and thus its dissolving behavior. Vitamins can be categorized into fat-soluble or water-soluble.

  • Effects of Pressure and Temperature:

    • Pressure has little effect on solids or liquids, but greatly increases gas solubility.

    • Temperature generally increases solid solubility but can decrease gas solubility.

    • Henry's Law: Connects gas solubility (C) with partial pressure (P) of the gas.

C = kP
where C = concentration of the dissolved gas, k = constant, P = partial pressure.

11.4 The Vapor Pressures of Solutions

  • Vapor Pressure Lowering: Solutions with nonvolatile solutes have lower vapor pressures than pure solvents.

  • Raoult’s Law:

P{soln} = x{solvent} P^{0}_{solvent}
This implies that the vapor pressure of a solvent in a solution is proportional to the mole fraction of the solvent in the solution.

Example of Calculation: Mixing 158 g of sucrose in 643.5 cm³ of water; calculating vapor pressure using Raoult’s Law and accounting for mole fractions can yield observable vapor pressure changes.

11.5 Boiling-Point Elevation and Freezing-Point Depression

  • Colligative Properties: These depend on the number of solute particles rather than the type of solute. They include boiling-point elevation and freezing-point depression:

    • Boiling-Point Elevation Formula:

ΔTb = Kb imes m{solute} where ΔTb is the change in boiling point, Kb = molal boiling-point elevation constant, m{solute} is molality.

  • Freezing-Point Depression Formula:

ΔTf = Kf imes m{solute} where ΔTf is the change in freezing point, K_f = molal freezing-point depression constant.

Example Calculation: For a mass of glucose dissolved to determine molar mass from observed changes in boiling and freezing points.

11.6 Osmotic Pressure

  • Definition: Osmotic pressure is the pressure needed to stop osmosis when a solution and pure solvent are separated by a semipermeable membrane.

  • Formula:
    P = MRT where M = molarity, R = universal gas constant, and T = temperature in Kelvin.

Example Calculation: For a protein dissolved in solution, determining molarity and osmotic pressure can establish insights into its behavior in a biological context.

11.7 Colligative Properties of Electrolyte Solutions

  • Electrolyte Behavior: Colligative properties scale with the total concentration of solute particles.

  • Van’t Hoff Factor ($i$): Relates to the number of particles produced by a solute:

i = rac{ ext{moles of particles in solution}}{ ext{moles of solute dissolved}} .

Example: Calculating freezing point or boiling point adjustments in electrolyte solutions and correlating with concentrations and ion pair formation.

11.8 Colloids

  • Definition: A colloids are mixtures containing particles suspended in a medium. They are significant in various natural and technological applications.

  • Stability of Colloids: Electrostatic repulsion keeps colloidal particles separated and in suspension, while conditions like temperature and the addition of electrolytes can induce coagulation.

  • Examples and Applications: The Tyndall effect is utilized to explore colloidal suspensions, and these effects can have significant practical applications in areas like water purification.

Conclusion: Collectively, understanding the properties and behaviors of solutions, especially under varying conditions, is crucial for a variety of scientific and industrial applications, from crafting better medicines to managing ecological components.