Ch.13 - Solutions: Solubility, Concentration, and Colligative Properties

Solutions: Solubility and Intermolecular Forces

Definition and Types of Mixtures

Solubility is a physical property describing the ability of a solute to dissolve in a solvent, forming a homogeneous mixture called a solution. If the solute does not dissolve, a heterogeneous mixture results.

• Solution: Homogeneous mixture where solute is dissolved in solvent.

• Heterogeneous mixture: Solute is not dissolved; phases are visible.

Theory of "Likes Dissolve Likes"

Solubility depends on the similarity of intermolecular forces and polarity between solute and solvent. Polar solutes dissolve in polar solvents, nonpolar in nonpolar.

• Polarity: Polar and ionic compounds dissolve in polar solvents (e.g., water).

• Intermolecular Forces: Types include ion-dipole, hydrogen bonding, dipole-dipole, and London dispersion.

Solubility of Gases in Water

Solubility of nonpolar gases in water is low and varies by gas. For example, O2 is more soluble than N2.

• Example: Predicting solubility of F2 based on N2 and O2 values.

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.

Concentration Units

Molality (m)

Molality expresses concentration as moles of solute per kilogram of solvent. It is temperature independent.

• 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.

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

• Example: Pb(NO3)4 produces 5 ions per formula unit.

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

Used for very dilute solutions, expressing concentration as mass or volume per million or billion parts.

• 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 100 grams of solution.

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

Solubility and Henry's Law

Henry's Law

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: $\frac{S_1}{S_2} = \frac{P_1}{P_2}$

Colligative Properties

Overview of Colligative Properties

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

• Boiling Point Elevation: Adding solute raises boiling point.

• Freezing Point Depression: Adding solute lowers freezing point.

• Vapor Pressure Lowering: Solute reduces vapor pressure of solvent.

• Osmotic Pressure: Pressure required to stop osmosis.

Van't Hoff Factor (i)

The Van't Hoff factor is the number of particles produced from dissolving a solute. For ionic compounds, it equals the total number of ions.

• Example: NaCl produces 2 ions, so i = 2.

Boiling Point Elevation

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

• 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 using:

• 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

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

• Hypotonic: Lower solute concentration outside cell; cell swells (hemolysis).

• Isotonic: Equal solute concentration; no net movement.

• Hypertonic: Higher solute concentration outside cell; cell shrivels (crenation).

Vapor Pressure Lowering (Raoult's Law)

Raoult's Law

Raoult's Law describes how the vapor pressure of a solvent decreases when a nonvolatile solute is added.

• 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	$\Pi = i \cdot M \cdot R \cdot T$