SOLUTIONS

Covers various major areas in chemistry including:
- Thermochemistry
- Gases
- Liquids, Solids, & Intermolecular Forces
- Crystalline Solids & Modern Materials
- Solutions
- Free Energy & Thermodynamics
Text reference: Chemistry: Structure and Properties, 2nd edition (Nivaldo J. Tro, Pearson Education Inc., 2018)

Solution: A homogenous (uniform) mixture of two or more chemical components.
- Solute: The component present in the smaller amount.
- Solvent: The component present in the larger amount.
- Aqueous Solution: A solution where the solvent is water.
Definition of Solution: A liquid or solid phase containing more than one substance, with one substance (the solvent) treated differently from the others (the solutes) (Source: IUPAC Gold Book)

Solubility: The maximum amount of solute that can be dissolved in a given amount of solvent at equilibrium.
Soluble: A solute that dissolves in a solvent.
Insoluble: A solute that does not dissolve in a solvent.

In systems with non-interacting particles (like an ideal gas), mixing occurs due to an increase in Entropy, which is a statistical phenomenon resulting in the spreading out of energy.

The relative strength of intermolecular forces determines solution formation:
- “Like Dissolves Like” Rule:
- Non-polar molecules are soluble in non-polar solvents (e.g., Heptane (C₇H₁₆) and Pentane (C₅H₁₂) dissolve well).
- Polar molecules are soluble in polar solvents (e.g., Ethanol (C₂H₅OH) and Water (H₂O) are miscible in any proportions).
- Ionic compounds (e.g., NaCl) are more soluble in polar solvents (e.g., liquid H₂O or NH₃).

Hydrophilic compounds (e.g., Vitamin A and C) dissolve well in water (polar solvents).
Hydrophobic compounds (e.g., some vitamins) dissolve well in nonpolar solvents.

Enthalpy of Dissolution (ΔHₛₒₗₙ):
- Given by the equation:
  \Delta H{soln} = \Delta H{solute} + \Delta H{solvent} + \Delta H{mix}
- Strong solute-solvent interactions favor dissolution, which is energetically favored under specific conditions.
- Types of interactions:
- Solvent-Solvent interactions (Endothermic)
- Solute-Solute interactions (Endothermic)
- Solvent-Solute interactions (Exothermic)

ΔHₛₒₗₙ:
- Represents the enthalpy change when 1 mole of a substance is dissolved in excess solvent.
- Formula:
  \Delta H{soln} = \Delta H{solute} + \Delta H_{hydration}
- For ionic compounds dissolving in water, hydration is typically large and exothermic.
- The dissolution process is endothermic if the lattice energy (|ΔHₗₐₑₕₑ|) is greater than hydration energy (|ΔHₕʳₑ₍ₐ₌ₔ|).

Dissolution competes with re-crystallization, achieving dynamic equilibrium.
Saturated solution: Maximum solute dissolves at equilibrium under specific temperature.
Unsaturated solution: Contains less solute than its solubility capacity.
Supersaturated solution: Contains more solute than a saturated solution can hold at a given temperature.
Formation of sodium acetate crystals upon seeding leads to rapid crystallization and warming of the solution.

To create a supersaturated solution:
- Increase temperature to enhance solute solubility while adding more solute.
- Cooling leads to decreased solubility, retaining solid in solution due to nucleation energy barrier removal.

Generally, solubility of most solid substances increases as temperature rises.
Solubility of gases decreases with increased temperature, with lower temperatures causing precipitation.

Henry's Law: The concentration (C) of a gas in liquid is directly proportional to the partial pressure (P) of the gas: C [mol L^{-1}] = k_H [mol L^{-1} atm^{-1}] \times P [atm]
- Where $k_H$ is Henry's constant specific to the solvent-solute combination and temperature.

Volume changes upon dissolving solids in liquids are typically negligible.
The density of the liquid may change according to dissolving conditions and amounts.

Molarity (C) is measured in moles per liter of solution:
- C = \frac{\text{Moles of solute}}{\text{Volume of solution (L)}}
- Notable conversions:
- 1.0 M = 1.0 mol L⁻¹
- 1.0 mM = 0.0010 mol L⁻¹
Molarity often denoted by square brackets: [Cl⁻] means the concentration of Cl⁻ in moles per liter.
Solutions categorized by concentration—dilute (low concentration), concentrated (high concentration).

Molality (m): Alternate concentration measure defined by: m = \frac{\text{moles of solute (mol)}}{\text{mass of solvent (kg)}}
- Example calculation for NaCl:
- 19.8 g NaCl / 58.44 g/mol = 0.339 mol NaCl
- m = \frac{0.339 mol NaCl}{0.245 kg H_2O} = 1.38 m
Important distinction from molarity as it pertains to solvent mass.

Requires solution density. Example provided:
- 1.16 M sucrose (C₁₂H₂₂O₁₁, MW = 342.3 g/mol)
- Formula used for conversions with densities:
- Solve mass of solvent to derive molality, which yielded 1.48 m for the assumed example.

Molar Fraction (X): Dimensionless measure of concentration: X = \frac{\text{moles of a component}}{\text{total moles in solution}}
- For two components (solute + solvent):
  X{solute} = \frac{n{solute}}{n{solute} + n{solvent}}
  X{solvent} = \frac{n{solvent}}{n{solute} + n{solvent}}
The sum of molar fractions equals 1.

Weight Fraction (w): Common in analytical chemistry, dimensionless concept expressed in % or ppm: w = \frac{\text{mass of component}}{\text{mass of solution}}
- Example: 1% means 0.01 g solute in 1 g solution; 1 ppm means 10⁻⁶ g solute in 1 g solution.

Unit	Definition	Units
Molarity (M)	Amount of solute (in mol) / Volume of solution (in L)	mol/L
Molality (m)	Amount of solute (in mol) / Mass of solvent (in kg)	mol/kg
Mole Fraction (X)	Moles of solute / Total moles in solution	None
Weight Fraction (w)	Mass of component (g) / Mass of solution (g)	% or ppm
Parts by Mass	Mass solute / Mass solution	% or ppm

Understanding solution properties, interactions, and various concentration measures are essential for applications in chemistry, particularly in areas associated with solubility and reactions in solution.