Properties of Solutions: Structure, Formation, and Colligative Effects

Properties of Solutions

Introduction to Solutions

Solutions are homogeneous mixtures composed of a solute and a solvent. The solvent is the major component, while the solute is the minor component, uniformly dispersed throughout the solvent. Solutions can exist in various states: gas, liquid, or solid.

• Solute: The substance being dissolved.

• Solvent: The substance doing the dissolving.

• Homogeneous: Uniform composition throughout.

State of Solution	State of Solvent	State of Solute	Example
Gas	Gas	Gas	Air
Liquid	Liquid	Gas	Oxygen in water
Liquid	Liquid	Liquid	Alcohol in water
Liquid	Liquid	Solid	Salt in water
Solid	Solid	Gas	Hydrogen in palladium
Solid	Solid	Liquid	Mercury in silver
Solid	Solid	Solid	Silver in gold

Energy Changes in Solution Formation

The formation of a solution involves three main energy changes:

• \( \Delta H_1 \): Separation of solute particles (endothermic, \( \Delta H_1 > 0 \)).

• \( \Delta H_2 \): Separation of solvent particles (endothermic, \( \Delta H_2 > 0 \)).

• \( \Delta H_3 \): Formation of solute-solvent interactions (exothermic, \( \Delta H_3 < 0 \)).

The overall enthalpy change for solution formation is:

$\Delta H_{soln} = \Delta H_1 + \Delta H_2 + \Delta H_3$

If \( \Delta H_3 > (\Delta H_1 + \Delta H_2) \), the process is exothermic. If \( \Delta H_3 < (\Delta H_1 + \Delta H_2) \), the process is endothermic.

• Example (Exothermic): MgSO4 in water, \( \Delta H_{soln} = -91.21 \) kJ/mol.

• Example (Endothermic): NH4NO3 in water, \( \Delta H_{soln} = +26.4 \) kJ/mol.

Entropy and Solution Formation

In addition to enthalpy, entropy (S)—a measure of randomness—also favors solution formation. Higher entropy means greater disorder:

• $S(g) > S(l) > S(s)$

The Solution Process

Solvation and Dissolution

As a solution forms, the solvent pulls solute particles apart and surrounds them, a process called solvation (or hydration in water).

For ionic salts, ion-dipole interactions between ions and water molecules overcome the lattice energy of the salt crystal, allowing dissolution.

Distinguishing Dissolution from Disappearance

Not all substances that disappear in a solvent are dissolved; some may react or form a suspension.

Saturated Solution and Solubility

Types of Solutions

Solutions can be classified based on the amount of solute relative to solvent:

• Unsaturated: Contains less solute than the solvent can hold.

• Saturated: Solute and solvent are in equilibrium; maximum solute dissolved.

• Supersaturated: Contains more solute than the solvent can normally hold.

Factors Affecting Solubility

Solute-Solvent Interactions

The solubility of a solute depends on the strength of attractive forces between solute and solvent molecules. Substances with similar intermolecular forces tend to dissolve in one another:

• Polar substances dissolve in polar solvents.

• Non-polar substances dissolve in non-polar solvents.

• "Like dissolves like" is a useful rule of thumb.

For example, water (polar) and hexane (non-polar) will not mix; they are immiscible.

Glucose, which forms hydrogen bonds, is highly soluble in water, while cyclohexane, which only has dispersion forces, is not.

Pressure Effect

The solubility of gases in liquids increases with increasing pressure, described by Henry's Law:

$S_g = k P_g$

• $S_g$ = solubility of the gas

• $k$ = Henry's Law constant

• $P_g$ = partial pressure of the gas above the liquid

Example: The solubility of O2 in water at 25°C and 0.21 atm is $S_g = 1.3 \times 10^{-3} \text{ M/atm} \times 0.21 \text{ atm} = 2.73 \times 10^{-4} \text{ M}$.

Temperature Effect

Generally, the solubility of solid solutes in liquid solvents increases with temperature, while the solubility of gases decreases with temperature.

Warm lakes have less dissolved O2 than cool lakes, and carbonated drinks lose their fizz when warm.

Expressing Concentrations of Solutions

Mass Percent

Mass percent is the mass of solute divided by the total mass of solution, multiplied by 100:

$\text{Mass % of A} = \frac{\text{mass of A in solution}}{\text{total mass of solution}} \times 100$

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

These units are used for very dilute solutions:

• $\text{ppm} = \frac{\text{mass of A in solution}}{\text{total mass of solution}} \times 10^6$

• $\text{ppb} = \frac{\text{mass of A in solution}}{\text{total mass of solution}} \times 10^9$

Mole Fraction (X)

The mole fraction is the ratio of moles of a component to the total moles in the solution:

$X_A = \frac{\text{moles of A}}{\text{total moles in solution}}$

Molarity (M)

Molarity is the number of moles of solute per liter of solution:

$M = \frac{\text{moles of solute}}{\text{liter of solution}}$

Note: Molarity is temperature-dependent because volume changes with temperature.

Molality (m)

Molality is the number of moles of solute per kilogram of solvent:

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

Molality is not temperature-dependent.

Colligative Properties

Definition and Types

Colligative properties depend only on the number of solute particles, not their identity. These include:

• Vapor pressure lowering

• Boiling point elevation

• Freezing point depression

• Osmotic pressure

Vapor Pressure Lowering

Dissolving a non-volatile solute lowers the vapor pressure of the solvent, described by Raoult's Law:

$P_A = X_A P_A^\circ$

• $X_A$ = mole fraction of solvent

• $P_A^\circ$ = vapor pressure of pure solvent

• $P_A$ = vapor pressure of solution

Boiling Point Elevation

Adding a nonvolatile solute increases the boiling point of the solvent:

$\Delta T_b = K_b \cdot m$

• $K_b$ = molal boiling point elevation constant

• $m$ = molality

Boiling point of solution: $T_b(\text{solution}) = T_b(\text{solvent}) + \Delta T_b$

Solvent	Normal Boiling Point (°C)	Kb (°C/m)
Water, H2O	100.0	0.51
Benzene, C6H6	80.1	2.53
Ethanol, C2H5OH	78.4	1.22
Carbon tetrachloride, CCl4	76.8	5.02
Chloroform, CHCl3	61.2	3.63

Freezing Point Depression

Adding a nonvolatile solute lowers the freezing point of the solvent:

$\Delta T_f = K_f \cdot m$

• $K_f$ = molal freezing point depression constant

• $m$ = molality

Freezing point of solution: $T_f(\text{solution}) = T_f(\text{solvent}) - \Delta T_f$

Osmosis and Osmotic Pressure

Osmosis is the movement of solvent molecules from an area of higher solvent concentration to lower solvent concentration through a semi-permeable membrane. Osmotic pressure (\( \pi \)) is the pressure required to stop osmosis:

$\pi = MRT$

• $M$ = molarity

• $R$ = ideal gas constant

• $T$ = temperature (K)

Osmosis in Blood Cells

Hypertonic, Hypotonic, and Isotonic Solutions

Blood cells respond to the osmotic pressure of their environment:

• Hypertonic: Solute concentration outside the cell is greater; water flows out, causing crenation.

• Hypotonic: Solute concentration outside the cell is less; water flows in, causing hemolysis.

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

Additional info: All equations are provided in LaTeX format for clarity. Tables are recreated for comparison and classification. Images are included only when directly relevant to the explanation of the paragraph.