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

CONCEPT: SOLUTIONS – SOLUBILITY AND INTERMOLECULAR FORCES

Definitions and Types of Mixtures

Solubility is a physical property describing the ability of a solute to dissolve (become miscible) in a solvent, forming a solution. A solution is a homogeneous mixture created when a solvent dissolves a solute. If the solvent cannot dissolve the solute, a heterogeneous mixture results.

• Homogeneous mixture: Uniform composition throughout (e.g., salt water).

• Heterogeneous mixture: Non-uniform composition (e.g., sand in water).

Theory of "Likes Dissolve Likes"

Compounds with similar intermolecular forces and/or polarity will dissolve into each other to form a solution. Polar solvents dissolve polar solutes, and nonpolar solvents dissolve nonpolar solutes.

• Polar-polar: Will dissolve (e.g., salt in water).

• Nonpolar-nonpolar: Will dissolve (e.g., oil in hexane).

• Polar-nonpolar: Will not mix (e.g., oil in water).

Example: Predicting solution formation between AsCl5 (nonpolar) and H2O (polar): They do not mix, so no solution forms.

Types of Intermolecular Forces

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

• Hydrogen Bonding: Occurs in compounds containing hydrogen directly bonded to F, O, or N.

• Dipole-Dipole: Present in polar covalent compounds.

• London Dispersion: Present in all molecules, but dominant in nonpolar covalent compounds.

Solubility of Gases in Water

Solubility of nonpolar gases in water varies. For example, O2 is more soluble than N2. F2 is expected to have a solubility value between N2 and O2.

CONCEPT: TYPES OF AQUEOUS SOLUTIONS

Saturated, Unsaturated, and Supersaturated Solutions

When solutes dissolve in water, an equilibrium process occurs. The rate of dissolution equals the rate of recrystallization at equilibrium. Three types of solutions are possible:

• 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.

CONCEPT: SOLUTION CONCENTRATION UNITS

Molality (m)

Molality is a temperature-independent concentration unit, representing the number of moles of solute per kilogram of solvent.

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

• Used for colligative property calculations.

Mole Fraction (X)

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

• Formula: $X = \frac{\text{moles of solute}}{\text{moles of solute} + \text{moles of solvent}}$

Mass Percent

Mass percent expresses grams of solute per grams of solution, multiplied by 100.

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

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

Used for very dilute solutions. In aqueous solutions, 1 ppm = 1 mg/L and 1 ppb = 1 µg/L.

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

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

CONCEPT: COLLIGATIVE PROPERTIES

Overview of Colligative Properties

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

• Boiling Point Elevation: Adding solute increases boiling point.

• Freezing Point Depression: Adding solute decreases freezing point.

• Vapor Pressure Lowering: Adding solute lowers vapor pressure.

• Osmotic Pressure: Pressure required to stop osmosis.

Boiling Point Elevation

When a solute is added to a pure solvent, the boiling point increases. The change is calculated using:

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

• $i$ = van't Hoff factor (number of particles formed)

• $k_b$ = boiling point constant (°C/m)

• $m$ = molality (mol/kg)

Freezing Point Depression

Adding solute lowers the freezing point of the solvent.

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

• $k_f$ = freezing point constant (°C/m)

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

• $X_{\text{solvent}}$ = mole fraction of solvent

• $P_{\text{solvent}}$ = vapor pressure of pure solvent

Osmosis and Osmotic Pressure

Osmosis is the net movement of solvent (usually water) across a semipermeable membrane from a region of lower solute concentration to higher solute concentration. Osmotic pressure is the force required to stop this flow.

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

• $\Pi$ = osmotic pressure (atm)

• $i$ = van't Hoff factor

• $M$ = molarity (mol/L)

• $R$ = gas constant ($0.08206$ L·atm·mol-1·K-1)

• $T$ = temperature (K)

CONCEPT: TONICITY AND RED BLOOD CELLS

Tonicity of Solutions

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

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

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

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

CONCEPT: HENRY'S LAW

Solubility of Gases and Henry's Law

The solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. Henry's Law is used to calculate this relationship:

• Formula: $S_{\text{gas}} = k_H \cdot P_{\text{gas}}$

• $S_{\text{gas}}$ = solubility of gas (M)

• $k_H$ = Henry's Law constant (M/atm)

• $P_{\text{gas}}$ = partial pressure of gas (atm)

As pressure increases, gas solubility increases. As temperature increases, gas solubility decreases, but solid solubility generally increases.

CONCEPT: SUMMARY TABLES

Summary of Key Solution Properties

• Intermolecular Forces: Ion-dipole, hydrogen bonding, dipole-dipole, London dispersion.

• Types of Solutions: Saturated, unsaturated, supersaturated.

• Colligative Properties: Boiling point elevation, freezing point depression, vapor pressure lowering, osmotic pressure.

• Concentration Units: Molality, mole fraction, mass percent, ppm, ppb.

• Osmosis and Tonicity: Effects on cells and solution behavior.

Example: A red blood cell placed in pure water will swell due to higher osmotic pressure inside the cell compared to outside.