AP Chem Unit 1.1-1.5: Moles, Isotopes, Formulas, and Electron Structure

Avogadro's number

6.022×10^23 particles per mole.

molar mass

Molar mass is the mass of one mole of a substance, usually in g/mol; for elements, it's numerically equal to atomic weight on the periodic table.

How many moles are in 12.044 × 10²³ atoms?

2.0 moles (since 12.044×10^23÷6.022×10^23=2).

molar mass of water (H₂O)

≈ 18.02 g/mol (2 × 1.01 + 16.00).

How many molecules are in 0.5 moles of CO₂?

0.5×6.022×10^23=3.011×10^23 molecules.

Convert 5.00 g of NaCl (MM ≈ 58.44 g/mol) to moles.

5.00÷58.44≈0.0856 mol.

How many grams are in 0.250 moles of CaCO₃ (MM ≈ 100.09 g/mol)?

0.250×100.09≈25.02 g.

What volume (at STP, 22.4 L/mol) does 1.00 mole of an ideal gas occupy?

22.4 L.

Why is the mole unit useful in chemistry?

It links the microscopic number of particles with macroscopic mass measurements using a scalable counting unit (moles), as reflected in AP content.

How many moles do you have if you have 4.00 × 10²³ atoms of helium?

4.00×10^23÷6.022×10^23≈0.664 mol.

What is an atomic mass unit (amu)?

Approximately 1/12 the mass of a carbon-12 atom; roughly the mass of one proton or neutron.

isotope

Atoms of the same element (same protons) with different numbers of neutrons (different mass numbers).

In mass spectrometry, what does the peak's height represent?

The relative abundance of an isotope.

How is the atomic mass of an element determined?

It's a weighted average of all isotopes' masses based on their abundances.

If an element has two isotopes: A (10 amu, 75%) and B (11 amu, 25%), what is its atomic mass?

(0.75×10)+(0.25×11)=10.25 amu.

What is mass spectrometry used for in Unit 1?

To determine isotope masses and their relative abundances from spectra.

Why does carbon's atomic weight appear as 12.01 on the periodic table?

Because it's a weighted average of its natural isotopic distribution.

How would you identify isotopic peaks on a mass spectrum?

By different m/z values corresponding to different isotopes.

If one isotope peak is twice as tall (abundant) as another, what does that imply?

Its relative abundance is double that of the other isotope.

Can mass spectrometry differentiate isotopes of different elements?

Yes—each element's isotopes have unique mass-to-charge (m/z) ratios.

What is an empirical formula?

The simplest whole-number ratio of atoms in a compound (e.g., CH₂O).

What is a molecular formula?

The actual number of atoms in a molecule (e.g., C₆H₁₂O₆).

How do you determine empirical formula from mass percentages?

Convert mass percentages to moles, divide by smallest mole value to get ratios, then convert to whole numbers.

A compound is 40% C, 6.7% H, and 53.3% O by mass. What is its empirical formula?

C₁H₂O₁ (approximately), because moles: C (3.33), H (6.67), O (3.33) → ratio ~1:2:1.

Molecular formula

C₆H₁₂O₆ (empirical mass 30 → 180/30 = 6; multiply subscripts by 6).

Empirical formula

Gives lowest ratio; molecular gives actual number of atoms per molecule.

True or False: Two substances with the same empirical formula must be the same compound.

False—they could differ in molecular formula or structure (e.g., glucose vs. fructose).

Initial data needed to find an empirical formula

Mass percentages or grams of each element in a sample.

Empirical formula for Na and Cl

NaCl (0.688:1 → approximately 1:1 when normalized).

Empirical formula calculations in Unit 1

Yes—they're integral to elemental composition learning in topics 1.3 and 1.4.

Mixture vs. pure substance

Pure substances have uniform composition with unique properties; mixtures combine two or more substances physically, maintaining identities.

Difference between homogeneous and heterogeneous mixtures

Homogeneous mixtures (solutions) are uniform throughout; heterogeneous mixtures are not.

Example of a homogeneous mixture

Salt water (uniform solution).

Example of a heterogeneous mixture

Sand in water (non-uniform, visibly separate phases).

Can mixtures be separated by physical means?

Yes—such as filtration, distillation, chromatography.

Why are mixtures included in AP Chem Unit 1?

To reinforce difference between pure substances and mixtures, and to practice compositional analysis.

Grams of A in a 100 g mixture containing 30% A and 70% B

30 g of A.

Percent by volume of gas X in a 1:1 mixture of gas X and gas Y at STP

50% by volume (mole fraction equals volume fraction for gases at same conditions).

Why might mixtures confuse empirical formula calculations?

Because composition varies and isn't fixed like in pure substances.

Strategy to analyze a mixture's composition

Use separation techniques to isolate components, then determine their amounts individually.

Principle used to determine electron configuration

The Aufbau principle (fill lowest energy orbitals first).

Pauli exclusion principle

No two electrons in the same atom may have the same set of four quantum numbers (max two electrons per orbital, with opposite spins).

Hund's rule

Electrons occupy degenerate orbitals singly first, with parallel spins, before pairing up.

Electron configuration for carbon (Z = 6)

1s² 2s² 2p².

Electron configuration for S²⁻ (sulfide ion, Z = 16)

1s² 2s² 2p⁶ 3s² 3p⁶ (same as Ar).

Ground-state electron configuration

The arrangement of electrons in the lowest possible energy levels for an atom or ion.

Electron configuration for Fe³⁺ (Z = 26)

Remove three electrons from neutral Fe: [Ar] 3d⁵ (configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵).

Lower energy: 4s or 3d orbital?

4s fills before 3d, but once filled, 3d is lower in energy when losing electrons.

True or False: Electron configurations must obey Aufbau, Pauli, and Hund's rules.

True.

Importance of understanding electron configuration in AP Chemistry

It's foundational for predicting chemical behavior, bonding, periodic trends, and aligns with College Board's essential knowledge.

Coulomb’s Law

The force between two charged particles increases with charge magnitude and decreases with distance. Explains attraction between nucleus and electrons.

Photoelectron Spectroscopy (PES) Principle

The energy needed to remove electrons can be measured; peaks show electron binding energies and relative abundance.

Hund’s Rule

Electrons fill orbitals singly with parallel spins before pairing up (to minimize repulsion).

Aufbau Principle

Electrons occupy lowest energy orbitals available first (fill order: 1s → 2s → 2p …).