Phase Diagrams, Solutions, and Solubility: Study Notes for General Chemistry

Recap of Intermolecular Forces and Solids

Types of Solids and Their Bonding

Solids are classified based on the nature of the forces holding their particles together. These forces determine the physical properties of solids, such as melting point, hardness, and electrical conductivity.

• Metallic solids: Exhibit hexagonal closest or cubic closest packing, maximizing interparticle attractions. Metallic bonds involve delocalized electrons described as bands of molecular orbitals (MOs).

• Ionic solids: Pack similarly to metals, but consist of cations and anions with charges and different sizes.

• Molecular solids: Held together by van der Waals forces (dispersion, dipole-dipole, hydrogen bonding).

• Covalent network solids: Held together by covalent bonds throughout the structure.

Phase Changes and Vapor Pressure

Phase changes are physical changes that leave the chemical identity of a substance intact. Vapor pressure is the pressure exerted by a vapor over its liquid.

• The relationship between vapor pressure and temperature is given by the Clausius-Clapeyron equation:

$ext{ln}P_{ ext{vap}} = - rac{ riangle H_{ ext{vap}}}{R} rac{1}{T} + C$

Phase Diagrams

Water (H2O) Phase Diagram

A phase diagram shows the pressure-temperature dependency of a substance, indicating regions of stability for solid, liquid, and gas phases.

• Boundary lines: Represent pressure-temperature combinations where two phases are in equilibrium (phase transitions occur).

• Triple point: The unique pressure-temperature combination where all three phases coexist in equilibrium.

• Normal melting point: Temperature at which melting occurs at 1 atm pressure.

• Normal boiling point: Temperature at which boiling occurs at 1 atm pressure.

• Critical point: The end of the liquid-gas boundary; beyond this, the substance becomes a supercritical fluid.

• Negative slope of solid-liquid boundary: Indicates that the melting point of water decreases with increasing pressure, and liquid water is denser than ice.

Carbon Dioxide (CO2) Phase Diagram

• Displays a positive slope for the solid-liquid boundary, typical for most substances.

• Melting point increases with increasing pressure; solid CO2 is denser than liquid CO2.

• Contains triple and critical points at different temperature-pressure combinations.

• CO2 sublimes at 1 atm and -78.5°C (no normal melting/boiling points).

Mixtures and Solutions

Heterogeneous vs Homogeneous Mixtures

A mixture is a combination of two or more substances in which each retains its identity.

• Heterogeneous mixture: Visually nonuniform mixing (e.g., salt and pepper).

• Homogeneous mixture: Visually uniform mixing (e.g., ethanol-water solution).

Solutions vs Colloids

• Solutions: Homogeneous mixtures with particle diameters 0.1–2 nm (ions or small molecules); transparent.

• Colloids: Homogeneous mixtures with particle diameters 2–500 nm; often murky or opaque (e.g., milk).

Types of Solutions

Solutions are classified by the physical state of solute and solvent. See the table below for examples.

Kind of Solution	Example
Gas in gas	Air (O2, N2, Ar, other gases)
Gas in liquid	Carbonated water (CO2 in water)
Gas in solid	H2 in palladium metal
Liquid in liquid	Gasoline (mixture of hydrocarbons)
Liquid in solid	Dental amalgam (mercury in silver)
Solid in liquid	Seawater (NaCl and other salts in water)
Solid in solid	Metal alloys (e.g., sterling silver: 92.5% Ag, 7.5% Cu)

• Solute: Component present in lesser amount.

• Solvent: Component present in greater amount.

Forces in Solutions

Interparticle Forces

The properties of solutions depend on the nature of interparticle forces between solute and solvent molecules.

• Condensed phases (liquids and solids) are held together by interparticle forces.

• Similar forces in solute and solvent favor mixing.

Like Dissolves Like

The phrase "like dissolves like" summarizes the observation that substances with similar types and magnitudes of intermolecular forces tend to form homogeneous solutions.

• Polar solutes dissolve in polar solvents.

• Nonpolar solutes dissolve in nonpolar solvents.

Example: Sodium Chloride in Water

• NaCl (polar solute) dissolves in water (polar solvent).

• Ion-dipole attractions between Na+, Cl- ions and water molecules are similar in strength to ionic bonds and hydrogen bonds.

Energetics of Dissolution

Thermodynamics of Solution Formation

The dissolution of a solute in a solvent involves changes in enthalpy and entropy, described by the free energy change:

$riangle G_{ ext{soln}} = riangle H_{ ext{soln}} - T riangle S_{ ext{soln}}$

• Entropy ($riangle S_{ ext{soln}}$) is typically positive, favoring dissolution due to increased molecular randomness.

Heat of Solution

The enthalpy change for solution formation is the sum of three terms:

$riangle H_{ ext{soln}} = riangle H_{ ext{solute}} + riangle H_{ ext{solvent}} + riangle H_{ ext{mix}}$

• $riangle H_{ ext{solute}}$: Energy required to separate solute particles (always positive; for ionic solids, this is lattice energy).

• $riangle H_{ ext{solvent}}$: Energy required to separate solvent particles (always positive).

• $riangle H_{ ext{mix}}$: Energy released when solute and solvent particles interact (always negative).

Spontaneity and "Like Dissolves Like"

• If the three types of interparticle forces are similar, $| riangle H_{ ext{solute}} + riangle H_{ ext{solvent}}| hickapprox | riangle H_{ ext{mix}}|$ and $riangle H_{ ext{soln}} hickapprox 0$.

• With positive entropy, dissolution is spontaneous ($riangle G_{ ext{soln}} < 0$).

Units of Concentration

Common Concentration Units

• Molarity (M): Moles of solute per liter of solution. $M = rac{ ext{moles of solute}}{ ext{liters of solution}}$

• Mole fraction (X): Moles of component divided by total moles in solution. $X = rac{ ext{moles of component}}{ ext{total moles in solution}}$

• Mass percent (mass %): Mass of component divided by total mass of solution, times 100%. $ext{Mass percent} = rac{ ext{mass of component}}{ ext{total mass of solution}} imes 100 ext{ ext{%}}$

• Molality (m): Moles of solute per kilogram of solvent. $m = rac{ ext{moles of solute}}{ ext{kilograms of solvent}}$

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

• $ext{ppm} = rac{ ext{mass of component}}{ ext{total mass of solution}} imes 10^6$

• $ext{ppb} = rac{ ext{mass of component}}{ ext{total mass of solution}} imes 10^9$

Comparison of Concentration Units

Name	Unit	Advantages	Disadvantages
Molarity (M)	mol solute / L solution	Useful in stoichiometry; measure by volume	Temperature-dependent; must know density to find solvent mass
Mole fraction (X)	mol component / total mol	Temperature-independent; useful in special applications	Measure by mass; must know density to convert to molarity
Mass %	g component / g solution	Temperature-independent; useful for small amounts	Measure by mass; must know density to convert to molarity
Molality (m)	mol solute / kg solvent	Temperature-independent; useful in special applications	Measure by mass; must know density to convert to molarity

Types of Solutions: Saturation

Unsaturated, Saturated, and Supersaturated Solutions

• Unsaturated solution: Contains less than the maximum amount of solute; more solute can dissolve.

• Saturated solution: Contains the maximum amount of solute; additional solute will not dissolve and will remain undissolved.

• Supersaturated solution: Contains more than the equilibrium amount of solute; excess solute will crystallize if disturbed.

Solubility and Temperature

Temperature Dependence

• Solubility: Amount of substance per unit volume needed to form a saturated solution.

• Solubility is a physical property characteristic of each substance.

• Solubilities of most molecular and ionic solids increase with increasing temperature.

Gas Solubility and Temperature

• Most gases become less soluble in water as temperature increases.

Solubility and Pressure

Pressure Effects

• Pressure has no significant effect on the solubility of liquids and solids.

• Pressure has a strong effect on the solubility of gases.

• Henry's Law describes the relationship between gas pressure and gas solubility:

$ext{Solubility} = kP$

• Where k is the Henry's law constant and P is the partial pressure of the gas.

• Example calculation: For Ar in water at 20°C, $k = 1.5 imes 10^{-3}$ mol/L·atm, $P = 7.1$ torr:

$ext{Solubility} = (1.5 imes 10^{-3} ext{ mol/L·atm}) imes (7.1 ext{ torr}) imes rac{1 ext{ atm}}{760 ext{ torr}} = 1.4 imes 10^{-5} ext{ mol/L}$

Summary

• Solutions are homogeneous mixtures in which the sum of the properties depends on the nature of the components and their interactions.

• "Like dissolves like" is a useful principle for predicting solubility.

• Concentration can be expressed in several units: molarity, mole fraction, mass percent, ppm, ppb, and molality.

• Solutions can be unsaturated, saturated, or supersaturated.

• Solubility of most solids increases with temperature; solubility of gases decreases with temperature.

• Pressure strongly affects gas solubility, described by Henry's Law.

Additional info: Some diagrams and tables were described in text for clarity. All equations are provided in LaTeX format as required.