Fundamental Gas Laws, Stoichiometry and Atomic Theory

Gas Laws

Boyle's law: For a gas at constant temperature, the product of pressure and volume is constant. P1 · V1 = P2 · V2 = P3 · V3.

Gay-Lussac / Charles's law

At constant pressure, the volume of a gas is proportional to its absolute temperature (in Kelvin). The relationship is expressed as:

V1 / T1 = V2 / T2

Note: Celsius temperatures are converted to Kelvin by adding 273.15 (historically approximated as 273). For small temperature changes near 0 °C, the historical approximation 1/273 was often used to relate incremental volume change per degree Celsius to the initial volume.

Solutions and Concentration Formulas

Common concentration expressions and relations:

• Mass percent (w/w): mass% solute = m_s / m_total × 100
• Percent by volume (v/v): % solute (v/v) = V_s / V_total × 100
• Grams per liter: g L^-1 = mass of solute (g) / volume of solution (L)
• Molarity (M): M = n_solute / V (in liters)
• Molality (m): m = n_solute / mass of solvent (kg)
• Mole fraction (χ): χ_i = n_i / Σ n_all

Conservation and Definite Proportions

Lavoisier — Law of Conservation of Mass

Lavoisier: Matter is neither created nor destroyed in a chemical reaction; the total mass of the products equals the total mass of the reactants.

Proust — Law of Definite Proportions

Proust: When elements combine to form a compound, they do so in a constant (definite) proportion by mass. If a fixed amount of one element reacts with two different amounts of another to form two different compounds, the quantities of the second element are in ratios of small whole numbers.

Quantum and Atomic Theory

Planck's Hypothesis

Planck: Energy is emitted or absorbed in discrete packets called quanta. The energy of a quantum is E = h ν (E = hν), where h is Planck's constant and ν is the frequency.

Bohr Atomic Model

Bohr: An atomic model building on Rutherford's nucleus that summarized earlier findings:

1. Electrons orbit the nucleus only in certain stationary orbits and do not radiate energy while in those orbits.
2. These allowed orbits correspond to discrete energy levels.
3. The farther the orbit from the nucleus, the greater the electron's energy.
4. When an electron jumps from a larger orbit to a smaller one, the excess energy is emitted as radiation.

Quantum Numbers

Four quantum numbers describe electron states:

• n (principal): indicates the main energy level/orbital; n = 1, 2, 3, 4, ...
• l (azimuthal or angular momentum): indicates the sublevel (subshell), l = 0, 1, 2, ..., n-1
• m_l (magnetic): indicates the orientation of the orbital, m_l = -l, ... , 0, ... , +l
• s (spin): indicates the spin quantum number, s = -1/2 or +1/2

Pauli Exclusion Principle

Pauli: No two electrons in the same atom can have the same set of all four quantum numbers. Each orbital (defined by n, l, m_l) can hold a maximum of two electrons with opposite spins.

Hund's Rule (Maximum Multiplicity)

Hund's rule: For degenerate orbitals (orbitals with the same energy, e.g., the three p orbitals or five d orbitals), electrons occupy empty orbitals singly first, with parallel spins, before pairing occurs.

Covalent Bonding Properties

Covalent substances can show different macroscopic behaviors depending on their structure:

1. Most simple covalent molecules (small numbers of atoms) are gases or liquids and typically have low melting and boiling points.
2. Covalent network (giant) solids are extended structures of atoms linked by covalent bonds. These materials are usually very hard, have high melting and boiling points, are insoluble in most solvents, and are generally non-conductive.