Ch.13 - Solutions: Properties, Concentrations, and Colligative Effects

Solutions: Solubility and Intermolecular Forces

Definition and Types of Solutions

Solutions are homogeneous mixtures formed when a solute dissolves in a solvent. The solubility of a substance is a physical property describing its ability to become miscible in a solvent. If a solute cannot dissolve, a heterogeneous mixture results.

• Homogeneous mixture: Uniform composition throughout; solute is dissolved.

• Heterogeneous mixture: Non-uniform; solute is not dissolved.

• "Likes dissolve likes": Substances with similar polarity and intermolecular forces tend to form solutions together.

Types of Intermolecular Forces

Intermolecular forces determine solubility and miscibility. The main types are:

• Ion-Dipole: Major force in ionic compounds dissolved in polar solvents.

• Hydrogen Bonding: Occurs in compounds with hydrogen directly bonded to fluorine, oxygen, or nitrogen.

• Dipole-Dipole: Present in polar covalent compounds.

• London Dispersion (van der Waals): Found in all molecules, especially nonpolar covalent compounds.

Solubility of Gases in Water

The solubility of nonpolar gases in water varies and is influenced by intermolecular forces and polarity.

• Example: N2 and O2 have different solubilities; F2 is expected to have a solubility value between those of N2 and O2.

Types of Aqueous Solutions

Saturated, Unsaturated, and Supersaturated Solutions

When solutes dissolve in water, equilibrium is established between dissolution and recrystallization. The amount of dissolved solute at equilibrium defines the solution type:

• Saturated: Maximum solute dissolved; at equilibrium concentration.

• Unsaturated: Less solute than equilibrium; more can be dissolved.

• Supersaturated: More solute than equilibrium; unstable and may precipitate.

Concentration Units

Molality (m)

Molality is a concentration unit independent of temperature, defined as moles of solute per kilogram of solvent.

• Formula: $m = \frac{\text{moles of solute}}{\text{kg of solvent}}$

• Example: Calculating molality for a solution with known mass of solute and solvent.

Osmolality

Osmolality measures the total number of dissolved particles (ions) in a solution. For ionic compounds, count the number of ions produced and multiply by the molality.

• Formula: $\text{Osmolality} = (\text{number of ions}) \times m$

• Example: For NaCl, which dissociates into Na+ and Cl-, osmolality is 2 × molality.

Parts Per Million (ppm) and Parts Per Billion (ppb)

Extremely dilute concentrations are expressed in ppm or ppb, which can be mass or volume based.

• ppm (mass): $\text{ppm} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^6$

• ppb (mass): $\text{ppb} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^9$

• In aqueous solutions: 1 ppm = 1 mg/L; 1 ppb = 1 µg/L.

Mole Fraction (X)

Mole fraction represents the ratio of moles of solute to total moles in the solution.

• Formula: $X = \frac{\text{moles of solute}}{\text{total moles in solution}}$

Mass Percent

Mass percent is the mass of solute per mass of solution, multiplied by 100.

• Formula: $\text{Mass Percent} = \frac{\text{grams of solute}}{\text{grams of solution}} \times 100$

Colligative Properties

Overview of Colligative Properties

Colligative properties depend on the number of solute particles, not their identity. The four main colligative properties are:

• Boiling Point Elevation

• Freezing Point Depression

• Vapor Pressure Lowering

• Osmotic Pressure

Boiling Point Elevation

Adding a solute increases the boiling point of a solvent. The change is calculated using:

• Formula: $\Delta T_b = i \cdot k_b \cdot m$

• Variables: $i$ = van't Hoff factor (number of particles), $k_b$ = boiling point constant, $m$ = molality

Freezing Point Depression

Adding a solute decreases the freezing point of a solvent. The change is calculated using:

• Formula: $\Delta T_f = i \cdot k_f \cdot m$

• Variables: $i$ = van't Hoff factor, $k_f$ = freezing point constant, $m$ = molality

Vapor Pressure Lowering (Raoult's Law)

The vapor pressure of a solution is lower than that of the pure solvent. Raoult's Law describes this effect:

• Formula: $P_{\text{solution}} = X_{\text{solvent}} \cdot P_{\text{solvent}}$

• Variables: $X_{\text{solvent}}$ = mole fraction of solvent, $P_{\text{solvent}}$ = vapor pressure of pure solvent

Osmosis and Osmotic Pressure

Osmosis is the net movement of solvent across a semipermeable membrane from low to high solute concentration. Osmotic pressure is the force driving this movement.

• Formula: $\Pi = i \cdot M \cdot R \cdot T$

• Variables: $\Pi$ = osmotic pressure, $i$ = van't Hoff factor, $M$ = molarity, $R$ = gas constant, $T$ = temperature (K)

Tonicity and Effects on Cells

Hypotonic, Isotonic, and Hypertonic Solutions

Tonicity describes the relative solute concentration of solutions separated by a membrane. It affects cell volume and osmotic pressure:

• Hypotonic: Lower solute concentration outside the cell; water enters, causing cell swelling (hemolysis).

• Isotonic: Equal solute concentration; no net movement of water.

• Hypertonic: Higher solute concentration outside; water leaves, causing cell shrinkage (crenation).

Summary Table: Types of Aqueous Solutions

The following table summarizes the types of aqueous solutions:

Type of Solution	Amount of Dissolved Solute	Equilibrium Concentration	Example
Saturated	Maximum solute dissolved	At equilibrium	20 g/100 mL water
Unsaturated	Less solute can be dissolved	Below equilibrium	10 g/100 mL water
Supersaturated	More solute dissolved	Above equilibrium	40 g/100 mL water

Additional info: All equations are provided in LaTeX format for clarity and exam preparation.