⚛️ Unit 1: Atomic Structure and Properties

1.1 — Moles and Molar Mass

Chemistry deals with incredibly large numbers of atoms and molecules. A single drop of water contains roughly 10²¹ molecules. To make these numbers manageable, chemists use the mole (abbreviated mol), one of the seven SI base units. The mole bridges the gap between the atomic world (individual atoms and molecules) and the macroscopic world (grams, liters) that we can measure in the lab.

The molar mass of an element is the mass of one mole of that element, expressed in grams per mole (g/mol). It is numerically equal to the element’s average atomic mass found on the periodic table (in amu). For compounds, the molar mass is the sum of the molar masses of all atoms in the chemical formula.

The Mole Roadmap — Dimensional Analysis

Dimensional analysis (factor-label method) is the core problem-solving strategy for mole conversions. Always start with what you know, then multiply by conversion factors until you reach the desired unit. Units must cancel properly.

Common Mistakes on the AP Exam

• Confusing atoms with molecules: 1 mol of H₂O = 6.022 × 10²³ molecules, but 3 × 6.022 × 10²³ atoms (2H + 1O per molecule).
• Forgetting subscripts when calculating molar mass: Ca(OH)₂ = 40.08 + 2(16.00 + 1.008) = 74.10 g/mol, not 57.09.
• Not properly canceling units in dimensional analysis — always write out units to check.

1.2 — Mass Spectrometry of Elements

A mass spectrometer is an instrument that separates atoms or molecules based on their mass-to-charge ratio (m/z). In AP Chemistry, you will encounter mass spectra of elements to determine isotopic composition and calculate average atomic mass. Understanding mass spectrometry is essential because it provides direct experimental evidence for the existence of isotopes.

Block diagram of a mass spectrometer — sample is ionized, accelerated, deflected by a magnetic field, and detected. (Wikimedia Commons)

How a Mass Spectrometer Works

1. Vaporization: The sample is converted into a gas.
2. Ionization: Atoms are bombarded with high-energy electrons to form positive ions (lose one electron). This gives a charge of +1 for most atoms, so m/z ≈ mass number.
3. Acceleration: Ions are accelerated through an electric field. All ions with the same charge gain the same kinetic energy.
4. Deflection: A magnetic field deflects the ions. Lighter ions are deflected more, heavier ions are deflected less. This separates isotopes.
5. Detection: The detector records the relative abundance of each ion as a current. More ions → stronger signal → taller peak.

Reading a Mass Spectrum

The x-axis shows m/z (mass-to-charge ratio, which for singly-charged ions equals the mass number). The y-axis shows relative abundance (%). Each peak represents a different isotope of the element.

AP Exam Tips

• If the average atomic mass is given and one isotope mass and abundance is known, you can work backward to find the other isotope’s mass or abundance.
• For elements with 2 isotopes, if you know the average atomic mass, you can determine which isotope is more abundant — the average will be closer to the more abundant isotope.
• On the AP exam, mass spectra are always for singly charged ions (z = 1), so m/z = mass number directly.

1.3 — Elemental Composition of Pure Substances

Every pure substance has a fixed, definite composition by mass. This is described by the Law of Definite Proportions (also known as the Law of Constant Composition): a given compound always contains the same elements in the same proportions by mass, regardless of the sample size or source.

Percent Composition by Mass

Percent composition tells you the percentage of the total mass contributed by each element in a compound. This is useful for identifying unknown compounds and verifying purity.

Empirical vs. Molecular Formulas

• Empirical formula: The simplest whole-number ratio of atoms in a compound (e.g., CH₂O for glucose).
• Molecular formula: The actual number of atoms in one molecule (e.g., C₆H₁₂O₆ for glucose). It is always a whole-number multiple of the empirical formula.

Step-by-Step: Finding the Empirical Formula

1. Start with percent composition (or mass data). Assume 100 g of the compound so percentages become grams directly.
2. Convert grams to moles for each element (divide by atomic mass).
3. Divide each by the smallest number of moles to get the mole ratio.
4. If the ratios are not whole numbers, multiply all by the smallest integer that converts them to whole numbers (e.g., if you get 1.5, multiply all by 2).

Finding the Molecular Formula

Combustion Analysis

Combustion analysis is used to determine the empirical formula of organic compounds (containing C, H, and sometimes O). The compound is burned in excess O₂, and the masses of CO₂ and H₂O produced are measured.

1.4 — Composition of Mixtures

Unlike pure substances, mixtures can vary in composition. They are classified as either homogeneous (uniform throughout, e.g., saltwater, air, brass) or heterogeneous (non-uniform, e.g., sand and water, granite). The key distinction from pure substances is that mixtures do not have a fixed composition.

Analyzing Mixtures

When a mixture contains substances with known formulas, you can use elemental analysis, mass data, or reaction data to determine the amount of each component present. These are often algebraic problems.

Separation Techniques

Mixtures can be separated based on differences in physical properties:

Pure Substance vs. Mixture — How to Tell

• A pure substance has a sharp, fixed melting point and boiling point.
• A mixture melts/boils over a range of temperatures.
• If chromatography produces only one spot/band, it is likely a pure substance.

1.5 — Atomic Structure and Electron Configuration

Atoms consist of a dense, positively charged nucleus (containing protons and neutrons) surrounded by electrons occupying energy levels (shells) and subshells. Understanding electron configurations is foundational — it explains periodic trends, bonding, and reactivity.

Bohr model of the atom showing discrete energy levels (shells). (Wikimedia Commons)

Shapes of s, p, d, and f orbitals. Each orbital holds a maximum of 2 electrons. (Wikimedia Commons)

Subatomic Particles

Atomic number (Z) = number of protons = defines the element. Mass number (A) = protons + neutrons. Isotopes have the same Z but different A (different numbers of neutrons).

Three Key Principles for Electron Configuration

• Aufbau Principle: Electrons fill orbitals in order of increasing energy: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → ... Use the diagonal rule or the periodic table as a guide (each row corresponds to filling a specific set of subshells).
• Pauli Exclusion Principle: No two electrons in the same atom can have identical sets of four quantum numbers. This means each orbital holds at most 2 electrons with opposite spins (↑↓).
• Hund’s Rule: Within a subshell, electrons fill each orbital singly (with parallel spins) before any orbital gets a second electron. This minimizes electron-electron repulsion.

Subshell Capacities

Writing Electron Configurations

List each occupied subshell with a superscript for the number of electrons. Noble-gas shorthand uses brackets around the previous noble gas core.

Electron Configurations of Ions

This is a critical concept that appears frequently on the AP exam:

• Cations (positive ions): Remove electrons from the highest principal energy level first (outermost shell). For transition metals, this means removing s electrons before d electrons.
• Anions (negative ions): Add electrons to the lowest available subshell.

Quantum Numbers (Supplemental)

Each electron is described by four quantum numbers:

• n (principal): Energy level (1, 2, 3...). Larger n = farther from nucleus, higher energy.
• l (angular momentum): Subshell shape (0 = s, 1 = p, 2 = d, 3 = f). Range: 0 to n−1.
• m_l (magnetic): Specific orbital orientation. Range: −l to +l.
• m_s (spin): +½ or −½ (spin-up or spin-down).

1.6 — Photoelectron Spectroscopy (PES)

Photoelectron spectroscopy provides direct experimental evidence for the shell structure of atoms and validates electron configurations. It works by hitting atoms with high-energy photons (usually X-rays or UV light) and measuring the kinetic energy of the ejected electrons. The difference between the photon energy and the kinetic energy gives the binding energy of each electron.

The electromagnetic spectrum — PES uses high-energy UV or X-ray photons to eject core and valence electrons. (Wikimedia Commons)

Reading a PES Diagram — Step by Step

• The x-axis shows binding energy (decreasing from left to right). Electrons closer to the nucleus have higher binding energies.
• The y-axis shows relative number of electrons (signal intensity).
• Each peak corresponds to a subshell. The height (or area) of the peak is proportional to the number of electrons in that subshell.
• The leftmost peak (highest binding energy) always corresponds to the 1s electrons.
• Moving right, peaks correspond to 2s, 2p, 3s, 3p, etc., in order of decreasing binding energy.

What PES Reveals

• Subshell structure is real: Electrons in different subshells have different binding energies, confirming the quantum mechanical model.
• Core vs. valence electrons: Core electrons (1s, 2s, 2p for period 3 elements) have much higher binding energies than valence electrons.
• Nuclear charge effect: As atomic number increases, the binding energy of every subshell increases because the nucleus has more protons pulling on all electrons.
• Shielding effect: Outer electrons are shielded from the full nuclear charge by inner electrons, so they have lower binding energies.

Common AP Exam Mistakes

• Confusing the x-axis direction: binding energy decreases from left to right.
• Forgetting that peak height represents electron count, not energy.
• Not recognizing that two elements with the same number of electrons (isoelectronic species) would have different PES spectra because their nuclear charges differ (binding energies shift).

1.7 — Periodic Trends

The periodic table organizes elements so that properties change predictably. Understanding these trends is fundamental to predicting chemical behavior. The underlying explanation for all periodic trends is effective nuclear charge (Z_eff) and electron shielding.

Major periodic trends: atomic radius, ionization energy, electron affinity, and electronegativity. (Wikimedia Commons)

Atomic Radius

• Across a period (left → right): Decreases. Higher Z_eff pulls electrons closer to the nucleus, shrinking the atom.
• Down a group (top → bottom): Increases. Each period adds a new principal energy level, increasing the distance of valence electrons from the nucleus.

Ionization Energy (IE)

• Definition: The energy required to remove the most loosely bound electron from a gaseous atom or ion.
• Across a period: Generally increases (higher Z_eff → harder to remove electrons).
• Down a group: Decreases (valence electrons are farther from nucleus and easier to remove).

First ionization energies of elements, showing the periodic pattern and notable exceptions. (Wikimedia Commons)

Successive Ionization Energies

Each successive ionization energy is larger than the previous one (removing an electron from a more positive ion is harder). A large jump in successive IEs indicates that a core electron is being removed (breaking into the next shell).

Electronegativity

• Definition: A measure of an atom’s ability to attract shared electrons in a chemical bond.
• Across a period: Increases (higher Z_eff attracts bonding electrons more strongly).
• Down a group: Decreases (valence electrons farther from nucleus, weaker attraction).
• Fluorine is the most electronegative element (3.98 on the Pauling scale). Noble gases are generally not assigned electronegativity values.

Electron Affinity

• Definition: The energy change when an atom in the gas phase gains an electron. A more negative value means the atom more readily accepts an electron.
• Generally becomes more negative (more favorable) across a period.
• Halogens (Group 17) have the most negative electron affinities — they need only one electron to complete their octet.
• Exceptions: Group 2 and Group 15 elements have surprisingly low electron affinities because adding an electron means entering a new, higher-energy subshell (Group 2) or pairing in a half-filled subshell (Group 15).

1.8 — Valence Electrons and Ionic Compounds

Valence electrons are the electrons in an atom’s outermost energy level (highest principal quantum number). They determine an element’s chemical properties, bonding behavior, and reactivity. Elements in the same group have the same number of valence electrons, which is why they exhibit similar chemistry.

Finding Valence Electrons

Ionic Compounds

Ionic compounds form when metals transfer electrons to nonmetals. The result is oppositely charged ions held together by electrostatic attraction (the ionic bond). Both ions typically achieve a noble-gas electron configuration.

Coulomb’s Law and Ionic Bond Strength

Lattice Energy

Lattice energy is the energy released when gaseous ions come together to form a solid ionic compound (or equivalently, the energy required to completely separate an ionic solid into gaseous ions). It directly correlates with the strength of ionic bonds in the crystal:

• Higher charges → higher lattice energy → higher melting point
• Smaller ions → higher lattice energy → higher melting point
• Lattice energy affects solubility, melting point, and hardness of ionic compounds

Properties of Ionic Compounds

• High melting and boiling points (strong electrostatic forces between ions)
• Hard but brittle (shifting layers of ions causes like charges to align, which repel and crack the crystal)
• Conduct electricity when dissolved in water or melted (free-moving ions carry charge), but not as a solid (ions locked in place)
• Often soluble in polar solvents like water (ion-dipole interactions with water molecules)