Solutions and Their Properties: Solubility, Thermodynamics, and Raoult's Law

Types of Solutions

Classification of Solutions

Solutions are homogeneous mixtures composed of two or more substances. The classification depends on the physical state of the solute and solvent.

• Solid in Liquid: e.g., sugar in water

• Gas in Liquid: e.g., carbon dioxide in water (soda)

• Gas in Solid: e.g., hydrogen in palladium

• Liquid in Liquid: e.g., ethanol in water

Principle of Solubility: "Like Dissolves Like"

Intermolecular Forces and Solubility

The solubility of a substance is largely determined by the similarity of intermolecular forces between solute and solvent.

• Polar substances dissolve polar or ionic substances.

• Non-polar substances dissolve non-polar substances.

• When a solute dissolves, solute-solute and solvent-solvent interactions are replaced by solute-solvent interactions.

• The relative strengths of these interactions determine whether a solution forms.

Solids in Liquids

Solvation Process

Solvation is the process by which solvent molecules surround and interact with solute particles to form a solution. In water, this process is called hydration.

• Attractive forces exist among all particles.

• If solute-solvent attractions are stronger than solute-solute attractions, the solute dissolves.

• Solvation involves energy changes: breaking solute and solvent interactions (endothermic), and forming solute-solvent interactions (exothermic).

Energy Changes in Solvation

• Separation of solute particles requires energy (endothermic).

• Separation of solvent particles also requires energy (endothermic).

• Mixing solute and solvent releases energy (exothermic).

• The overall energy change is called the heat of solution ($\Delta H_{soln}$).

Example: Solvation of NaCl in Water

• Na+ and Cl- ions are surrounded by water molecules (hydration).

• Hydrogen bonding and ion-dipole interactions stabilize the ions in solution.

Example: Solubility of Sucrose in Water

• Sucrose has multiple O-H bonds, allowing extensive hydrogen bonding with water.

• This strong interaction explains why sugar dissolves readily in water.

Mechanism of Dissolution

1. Breakage of bonds in the solid (endothermic, lattice energy, $\Delta H_{lattice} > 0$)

2. Formation of solute-solvent attractions (exothermic, solvation energy, $\Delta H_{solvation} < 0$)

• If lattice energy > solvation energy, dissolution is endothermic.

• If lattice energy < solvation energy, dissolution is exothermic.

Heats of Solution and Solution Cycles

1. Solute particles separate: $\text{solute (aggregated)} + \text{heat} \rightarrow \text{solute (separated)}$    $\Delta H_{solute} > 0$

2. Solvent particles separate: $\text{solvent (aggregated)} + \text{heat} \rightarrow \text{solvent (separated)}$    $\Delta H_{solvent} > 0$

3. Mixing: $\text{solute (separated)} + \text{solvent (separated)} \rightarrow \text{solution} + \text{heat}$    $\Delta H_{mix} < 0$

Total heat of solution:

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

Solubility and Temperature

• Most solids are more soluble at higher temperatures.

• If dissolution is endothermic ($\Delta H$ is positive), solubility increases with temperature.

• If dissolution is exothermic ($\Delta H$ is negative), solubility decreases with temperature.

Gases in Liquids

Solubility of Gases in Liquids

The solubility of a gas is the volume of gas (in mL) that saturates 1 mL of liquid at a given temperature and pressure.

Effect of Temperature on Gas Solubility

• Solubility of gases generally decreases with increasing temperature.

• Dissolution of gases is exothermic (releases heat):

$\text{Gas} + \text{solvent} \rightarrow \text{solution} + \text{heat}$

• Increased temperature increases kinetic energy, causing gas to escape from solution.

For all gases: $\Delta H_{solute} = 0$, $\Delta H_{hydr} < 0$, so $\Delta H_{soln} < 0$

$\text{solute}_{(g)} + \text{water}_{(l)} \rightarrow \text{saturated solution}_{(aq)} + \text{heat}$

Implication: Gas solubility in water decreases with increasing temperature.

Effect of Pressure on Gas Solubility

• Increasing pressure increases the solubility of gases in liquids (Henry's Law).

• Gas volume is reduced, concentration increases, and more collisions occur with the liquid surface.

Gases in Solids

Solubility of Gases in Solids

• Solid molecules at the surface have unbalanced forces, attracting gas molecules.

• High surface area (corners, curves) enhances gas adsorption.

• Adsorption: Gas molecules adhere to the surface.

• Absorption: Gas molecules penetrate into the solid.

• Solids are the solvent; gas is the solute. Concentration is measured by mass.

Factors Affecting Gas Solubility in Solids

1. Nature of gas (intermolecular forces between solid and gas)

2. Temperature: Solubility decreases with heating.

3. Pressure: At constant temperature, solubility is proportional to pressure.

Activation of solids before use is done by lowering pressure and increasing temperature.

Relationship: $\frac{X}{m} = K P^{1/n}$ Where X = mass of gas adsorbed, m = mass of solid, K and n are constants.

Liquids in Liquids

Types of Liquid Pairs

• Completely miscible: Mix in any proportion to form a homogeneous solution (e.g., alcohol and water, benzene and toluene).

• Partially miscible: Separate into two layers after saturation (e.g., water and phenol).

• Completely immiscible: Do not dissolve in one another (e.g., water and oil).

Completely Miscible Liquids and Ideal Solutions

• Attractive forces between A and B are the same as between AA and BB.

• No heat is evolved or absorbed during mixing; final volume is the sum of the two volumes.

• Properties (vapor pressure, refractive index, viscosity, surface tension) are averages of the pure liquids.

Raoult's Law

In an ideal solution, the partial vapor pressure of each component is proportional to its mole fraction and the vapor pressure of the pure component.

$P_A = X_A P_A^0$ $P_B = X_B P_B^0$ $P_{total} = P_A + P_B$

• $P_A^0$ and $P_B^0$ are vapor pressures of pure A and B, $X_A$ and $X_B$ are mole fractions.

• The partial pressure of each component is reduced by dilution.

Ideal Behaviour of Liquid Mixtures

Total pressure in a mixture (e.g., toluene and benzene) is the sum of the vapor pressures of the components:

$P_{total} = P_{ben}^0 X_{ben} + P_{tol}^0 X_{tol}$

Example Calculations

• Given mole fractions and vapor pressures, calculate total vapor pressure:

$P_{total} = P_{ben}^0 X_{ben} + P_{ethylene\,chloride}^0 X_{ethylene\,chloride}$ $P = 268 \times 0.6 + 236 \times 0.4 = 255.2$ mm Hg

• Composition of vapor over an ideal solution:

$P(A) = 0.25 \times 60 = 15$ mmHg $P(B) = 0.75 \times 100 = 75$ mmHg $P_{total} = 15 + 75 = 90$ mmHg

In vapor state: $X(A) = \frac{P(A)}{P_{total}} = \frac{15}{90} = 0.166$ $X(B) = \frac{P(B)}{P_{total}} = \frac{75}{90} = 0.834$

Vapor Pressure Composition Curve for Ideal Solution

• For mixtures obeying Raoult's law (e.g., water-acetone), there is no heat change ($\Delta H_{mix} = 0$).

Completely Immiscible Liquids

• Liquids do not dissolve in each other; form two layers based on density.

• Examples: water-bromobenzene, water-benzene.

• Vapor pressure of the mixture is higher than that of each pure component; boiling point is lower than either pure liquid.

Partially Miscible Liquids

• Miscible under certain conditions; at saturation, two layers form.

• Example: hexane-nitrobenzene.

• On increasing one component, the number of layers changes accordingly.

Effect of Temperature on Miscibility

• Miscibility curves show the relationship between composition and temperature (e.g., water and phenol).

• Critical solution temperature (Tc): The temperature above which two liquids are completely miscible in any proportion.

• Lower Tc: Below this temperature, phase separation occurs.

Example: Water-nicotine system shows both upper and lower critical solution temperatures.

Summary Table: Types of Solutions and Key Properties

Type of Solution	Example	Key Factors Affecting Solubility
Solid in Liquid	Sugar in water	Intermolecular forces, temperature, lattice and solvation energy
Gas in Liquid	CO2 in water	Temperature (inverse), pressure (direct), exothermic dissolution
Gas in Solid	H2 in palladium	Surface area, temperature, pressure, adsorption/absorption
Liquid in Liquid	Ethanol in water	Miscibility, intermolecular forces, temperature

Additional info: This summary integrates physical chemistry concepts relevant to organic chemistry, such as intermolecular forces, solution thermodynamics, and Raoult's law, which are foundational for understanding solubility and reactivity in organic systems.