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

Solutions: Solubility and Intermolecular Forces

Definition and Types of Mixtures

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 dissolve and form a miscible mixture. If a solute cannot dissolve, a heterogeneous mixture results.

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

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

Theory of "Likes Dissolve Likes"

Solubility is governed by the principle that substances with similar intermolecular forces and polarity will dissolve in each other. 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.

Example: Predicting solubility by identifying intermolecular forces in solute and solvent.

Example: Solubility of nonpolar gases in water at 25°C.

Types of Intermolecular Forces

Classification and Properties

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

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

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

• Dipole-Dipole: Present in polar covalent compounds.

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

Concentration Units

Molality (m)

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

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

• Example: Calculating molality for sucrose in water.

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: $\text{Osmolality} = \text{number of ions} \times m$

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

Used for very dilute solutions, expressed as mass or volume of solute per million or billion parts of solution.

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

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

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: $\text{Mass Percent} = \frac{\text{g solute}}{\text{g solution}} \times 100$

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 determines the type of solution:

• Saturated: Maximum solute dissolved; at equilibrium concentration.

• Unsaturated: Less than equilibrium concentration; more solute can dissolve.

• Supersaturated: More than equilibrium concentration; unstable, excess solute may precipitate.

Henry’s Law

Gas Solubility and Pressure

The solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.

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

• Two-point form: $\frac{S_1}{S_2} = \frac{P_1}{P_2}$

Temperature affects solubility: increasing temperature decreases gas solubility, but increases solubility of most solids.

Colligative Properties

Overview

Colligative properties depend on the number of solute particles, not their identity. These include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

• Boiling Point Elevation: Adding solute raises the boiling point.

• Freezing Point Depression: Adding solute lowers the freezing point.

• Vapor Pressure Lowering: Adding solute lowers the vapor pressure.

• Osmotic Pressure: Pressure required to stop osmosis.

Van’t Hoff Factor (i)

The van’t Hoff factor represents the number of particles produced from a solute. For ionic compounds, it equals the total number of ions formed; for covalent compounds, it is 1.

• Example: NaCl dissociates into 2 ions, so i = 2.

Boiling Point Elevation

Boiling point increases when solute is added. The change is calculated as:

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

• BPsolution = BPsolvent + \Delta T_b$

Freezing Point Depression

Freezing point decreases when solute is added. The change is calculated as:

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

• FPsolution = FPsolvent - \Delta T_f$

Osmosis and Osmotic Pressure

Osmosis is the net movement of solvent across a semipermeable membrane from lower to higher solute concentration. Osmotic pressure is the force that drives this movement.

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

• R: Gas constant ($0.08206$ L·atm·mol-1·K-1)

• T: Temperature in Kelvin

Tonicity and Red Blood Cells

Hypotonic, Isotonic, and Hypertonic Solutions

Tonicity describes the relative solute concentration outside cells, affecting water movement and cell volume.

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

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

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

Vapor Pressure Lowering (Raoult’s Law)

Raoult’s Law and Calculations

Adding a nonvolatile solute lowers the vapor pressure of a solvent. Raoult’s Law relates the vapor pressure of the solution to the mole fraction of the solvent:

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

• Mole fraction: $X_{\text{solvent}} = \frac{\text{moles of solvent}}{\text{moles of solute} + \text{moles of solvent}}$

Summary Table: Colligative Properties

Property	Effect of Solute	Formula
Boiling Point Elevation	Increases	$\Delta T_b = i \cdot K_b \cdot m$
Freezing Point Depression	Decreases	$\Delta T_f = i \cdot K_f \cdot m$
Vapor Pressure Lowering	Decreases	$P_{\text{solution}} = X_{\text{solvent}} \cdot P_{\text{solvent}}$
Osmotic Pressure	Increases	$\Pi = i \cdot M \cdot R \cdot T$