Chapter 14: Solutions – General Chemistry Study Notes

Solutions

Definition and Components

Solutions are homogeneous mixtures composed of two or more substances. The majority component is called the solvent, while the minority component is the solute. Solutions form due to intermolecular forces between solute and solvent particles, resulting in uniform mixing.

• Solvent: The substance present in the largest amount.

• Solute: The substance present in a smaller amount.

• Homogeneous mixture: Appears as a single substance but contains multiple materials.

• Examples: Air, seawater.

Nature’s Tendency Toward Mixing

Mixing occurs spontaneously due to the drive toward increased entropy, which is the dispersal of energy in a system. Uniform mixing is energetically favorable, even if potential energy does not decrease.

• Entropy: Measure of energy dispersal; mixing increases entropy.

• Spontaneous mixing: Solutions with different solute concentrations mix to achieve uniform distribution.

Solubility

Solubility and Miscibility

Solubility is the maximum amount of solute that can dissolve in a given amount of solvent. Two liquids that are mutually soluble are miscible; if not, they are immiscible. Solubility depends on the tendency toward mixing and the types of intermolecular forces.

• Soluble: Substance dissolves in another (e.g., salt in water).

• Insoluble: Substance does not dissolve (e.g., oil in water).

• Miscible: Alcohol and water.

• Immiscible: Oil and water.

Intermolecular Forces and Solution Formation

For a solution to form, solute–solute and solvent–solvent attractions must be overcome, which are endothermic processes. New solute–solvent attractions are formed, which are exothermic. The overall energetics determine whether the process is endothermic or exothermic.

• Like dissolves like: Polar solutes dissolve in polar solvents; nonpolar solutes in nonpolar solvents.

• Relative interactions: If solute–solvent attractions are comparable to solute–solute and solvent–solvent, a homogeneous solution forms.

Energetics of Solution Formation

Enthalpy of Solution

The formation of a solution involves three steps:

1. Separating the solute into constituent particles (endothermic).

2. Separating solvent molecules (endothermic).

3. Mixing solute and solvent particles (exothermic).

The overall enthalpy change ($\Delta H_{\text{solution}}$) depends on the relative sizes of these energy changes.

• If energy released in mixing exceeds energy required to separate, process is exothermic.

• If energy required to separate exceeds energy released in mixing, process is endothermic.

Heats of Hydration

For ionic compounds in water, the heat of hydration combines the energy added to overcome water attractions and the energy released in forming ion–dipole attractions. Lattice energy (attraction between ions) and hydrogen bonding in water are key factors.

• Ion–dipole interactions: Ions surrounded by water molecules; highly exothermic.

• Heat of solution: Difference between heat of hydration and lattice energy.

Solution Equilibrium and Solubility Limits

Saturated, Unsaturated, and Supersaturated Solutions

The dissolution of a solute is an equilibrium process. When the rate of dissolution equals the rate of deposition, the solution is saturated. If less solute is present, the solution is unsaturated; if more, it is supersaturated.

• Saturated: No more solute dissolves.

• Unsaturated: More solute can dissolve.

• Supersaturated: More solute than equilibrium; unstable.

Temperature and Pressure Dependence

Solubility of solids generally increases with temperature, while solubility of gases decreases with temperature. The solubility of gases increases with pressure, described by Henry’s Law:

$C = k_P \cdot P$

where $C$ is solubility, $k_P$ is Henry’s law constant, and $P$ is partial pressure.

Concentration Units

Common Units

Concentration describes the amount of solute in a given amount of solution or solvent. Common units include:

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

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

• Percent by mass: Grams of solute per 100 grams of solution.

• Parts per million (ppm): Grams of solute per 1,000,000 grams of solution.

• Parts per billion (ppb): Grams of solute per 1,000,000,000 grams of solution.

• Mole fraction ($X_A$): Fraction of moles of one component in total moles.

Converting Units

To convert between concentration units, write the given concentration as a ratio, separate numerator and denominator, and convert each part to the required unit.

Colligative Properties

Definition

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

• Nonelectrolytes: Do not dissociate in solution.

• Electrolytes: Dissociate into ions; affect colligative properties differently.

Vapor Pressure Lowering and Raoult’s Law

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

$P_{\text{solution}} = X_{\text{solvent}} \cdot P^0_{\text{solvent}}$

where $P_{\text{solution}}$ is the vapor pressure of the solution, $X_{\text{solvent}}$ is the mole fraction of the solvent, and $P^0_{\text{solvent}}$ is the vapor pressure of the pure solvent.

Boiling Point Elevation and Freezing Point Depression

Adding solute raises the boiling point and lowers the freezing point of a solvent. The changes are proportional to the molal concentration of solute particles:

• Boiling point elevation: $\Delta T_b = K_b \cdot m$

• Freezing point depression: $\Delta T_f = K_f \cdot m$

• $K_b$ and $K_f$ are solvent-specific constants.

Osmosis and Osmotic Pressure

Osmosis is the flow of solvent from low to high concentration through a semipermeable membrane. Osmotic pressure ($\Pi$) is the pressure needed to stop this flow:

$\Pi = MRT$

where $M$ is molarity, $R$ is the gas constant, and $T$ is temperature.

Van’t Hoff Factor

The van’t Hoff factor ($i$) accounts for the number of particles produced by dissociation of ionic compounds. It affects colligative properties:

• Theoretical $i$: Ratio of moles of particles to moles of formula units.

• Measured $i$: Often less due to ion pairing.

Mixtures and Colloids

Types of Mixtures

Mixtures can be classified as:

• Solutions: Homogeneous, do not separate on standing.

• Suspensions: Heterogeneous, separate on standing.

• Colloids: Heterogeneous, do not separate on standing; particles can coagulate and show the Tyndall effect and Brownian motion.

Colloidal Suspensions

Colloids are stabilized by hydrophilic or hydrophobic interactions. Hydrophilic colloids are stabilized by attraction to water, while hydrophobic colloids are stabilized by charged surface repulsions.

Type	Example
Sol	Paints
Gel	Jelly
Emulsion	Milk
Foam	Whipped cream
Aerosol	Fog
Solid aerosol	Smoke
Solid sol	Opal
Additional info:	Table inferred from context and typical colloid types.

Soaps and Micelles

Soaps are fatty acid salts with a hydrophilic head and hydrophobic tail, allowing them to form micelles and emulsify oily substances in water.

The Tyndall Effect

Colloids scatter light, making the path of a beam visible. This is known as the Tyndall effect.

Brownian Motion

Colloidal particles exhibit random motion due to collisions with solvent molecules, known as Brownian motion.

Examples of Colloidal Dispersions

Colloidal dispersions are found in everyday life, such as smoke, whipped cream, and opal.

Summary Table: Types of Colloidal Dispersions

Type	Dispersed Phase	Dispersion Medium	Example
Sol	Solid	Liquid	Paints
Gel	Liquid	Solid	Jelly
Emulsion	Liquid	Liquid	Milk
Foam	Gas	Liquid	Whipped cream
Aerosol	Liquid	Gas	Fog
Solid aerosol	Solid	Gas	Smoke
Solid sol	Solid	Solid	Opal
Additional info:	Table entries inferred from context and standard chemistry references.