Solutions: Properties, Formation, and Concentration in General Chemistry

Solutions

Introduction to Solutions

Solutions are homogeneous mixtures in which atoms, ions, or molecules of two or more substances are uniformly mixed. The majority component is called the solvent, and the minority component is the solute. For example, in seawater, water is the solvent and sodium chloride is the primary solute.

• Homogeneous mixture: Uniform composition throughout.

• Solvent: The component present in the largest amount.

• Solute: The component present in a lesser amount.

• Example: Ocean water, gasoline, and air are all solutions.

Why Solutions Form

Solutions form due to the natural tendency toward mixing and increased entropy (energy dispersal). Unless energetically unfavorable, substances tend to mix spontaneously, leading to uniform mixtures.

• Spontaneous mixing: Driven by entropy, not always by a decrease in potential energy.

• Example: When pure water and a sodium chloride solution are separated by a barrier, removing the barrier leads to spontaneous mixing and a uniform solution.

Osmosis and Biological Relevance

Seawater is a more concentrated solution than the fluids in body cells. When seawater passes through the digestive tract, it draws water out of body tissues due to osmosis, leading to dehydration.

• Osmosis: Movement of water from a region of lower solute concentration to higher solute concentration through a semipermeable membrane.

• Biological impact: Drinking seawater causes dehydration because it draws water out of cells.

Types of Solutions and Solubility

Types of Solutions

Solutions can be composed of various combinations of solids, liquids, and gases. In aqueous solutions, water is the solvent, and the solute can be a solid, liquid, or gas.

• Examples: Salt water (solid in liquid), club soda (gas in liquid), vodka (liquid in liquid), brass (solid in solid).

Solution Phase	Solute Phase	Solvent Phase	Example
Gaseous	Gas	Gas	Air (O2 and N2)
Liquid	Gas	Liquid	Club soda (CO2 in water)
Liquid	Liquid	Liquid	Vodka (ethanol and water)
Liquid	Solid	Liquid	Seawater (salt in water)
Solid	Solid	Solid	Brass (copper and zinc)

Solubility and Intermolecular Forces

The solubility of a substance is the amount that will dissolve in a given amount of solvent. Solubility depends on the tendency toward mixing (entropy) and the types of intermolecular forces present.

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

• Intermolecular forces: Dispersion, dipole-dipole, hydrogen bonding, ion-dipole.

Energetics of Solution Formation

Enthalpy Changes in Solution Formation

Solution formation involves three steps, each with an associated enthalpy change:

1. Separating solute particles: $\Delta H_{solute} > 0$ (endothermic)

2. Separating solvent particles: $\Delta H_{solvent} > 0$ (endothermic)

3. Mixing solute and solvent: $\Delta H_{mix} < 0$ (exothermic)

The overall enthalpy change is:

$\Delta H_{soln} = \Delta H_{solute} + \Delta H_{solvent} + \Delta H_{mix}$

Heats of Hydration

For ionic compounds in water, the heat of hydration ($\Delta H_{hydration}$) is the enthalpy change when 1 mol of gaseous ions dissolves in water. It is always exothermic due to strong ion-dipole interactions.

$\Delta H_{soln} = \Delta H_{solute} + \Delta H_{hydration}$

Solution Equilibrium and Factors Affecting Solubility

Dynamic Equilibrium in Solutions

When a solute dissolves in a solvent, an equilibrium is established between dissolution and recrystallization. A saturated solution contains the maximum amount of dissolved solute at equilibrium. An unsaturated solution contains less than the equilibrium amount, and a supersaturated solution contains more (unstable).

Temperature and Solubility

The solubility of most solids in water increases with temperature, while the solubility of gases decreases with temperature. Pressure increases the solubility of gases in liquids (Henry's Law).

• Henry's Law: $S_{gas} = k_H P_{gas}$

Expressing Solution Concentration

Common Concentration Units

• Molarity (M): $\text{M} = \frac{\text{mol solute}}{\text{L solution}}$

• Molality (m): $\text{m} = \frac{\text{mol solute}}{\text{kg solvent}}$

• Percent by mass: $\frac{\text{mass solute}}{\text{mass solution}} \times 100\%$

• Parts per million (ppm): $\frac{\text{mass solute}}{\text{mass solution}} \times 10^6$

• Mole fraction (x): $x_{solute} = \frac{n_{solute}}{n_{solute} + n_{solvent}}$

Colligative Properties

Vapor Pressure Lowering

The addition of a nonvolatile solute to a solvent lowers the vapor pressure of the solution compared to the pure solvent. This is described by Raoult's Law:

$P_{solution} = x_{solvent} P^\circ_{solvent}$

The decrease in vapor pressure is proportional to the mole fraction of the solute:

$\Delta P = x_{solute} P^\circ_{solvent}$

Freezing Point Depression and Boiling Point Elevation

The presence of a solute lowers the freezing point and raises the boiling point of a solvent. These are colligative properties, depending only on the number of solute particles.

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

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

Osmotic Pressure

Osmotic pressure is the pressure required to stop the flow of solvent through a semipermeable membrane from a dilute to a concentrated solution:

$\Pi = MRT$

Colligative Properties of Electrolyte Solutions

For electrolytes, the van't Hoff factor (i) accounts for the number of particles produced per formula unit dissolved:

$i = \frac{\text{moles of particles in solution}}{\text{moles of formula units dissolved}}$

Colligative property equations for electrolytes:

• $\Delta T_f = i m K_f$

• $\Delta T_b = i m K_b$

• $\Pi = i M R T$

Colloids

Colloidal Dispersions

A colloid is a mixture where the dispersed particles are intermediate in size between those in solutions and suspensions (1 nm to 1000 nm). Colloids scatter light (Tyndall effect) and remain dispersed due to Brownian motion and electrostatic repulsions.

• Examples: Fog, milk, whipped cream, soapy water.

Summary Table: Types of Solutions

Type	Solute	Solvent	Example
Gas in gas	O2	N2	Air
Gas in liquid	CO2	H2O	Club soda
Liquid in liquid	Ethanol	Water	Vodka
Solid in liquid	NaCl	Water	Seawater
Solid in solid	Zn	Cu	Brass

Key Equations

• Henry's Law: $S_{gas} = k_H P_{gas}$

• Molarity: $M = \frac{\text{mol solute}}{\text{L solution}}$

• Molality: $m = \frac{\text{mol solute}}{\text{kg solvent}}$

• Percent by mass: $\frac{\text{mass solute}}{\text{mass solution}} \times 100\%$

• Raoult's Law: $P_{solution} = x_{solvent} P^\circ_{solvent}$

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

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

• Osmotic pressure: $\Pi = i M R T$