General Chemistry: Atomic Structure, Properties, and Calculations – Study Guide

Atomic Structure and Quantum Numbers

Atomic Number, Mass Number, and Isotopes

Atoms are composed of protons, neutrons, and electrons. The atomic number (Z) is the number of protons in the nucleus, while the mass number (A) is the sum of protons and neutrons. Isotopes are atoms of the same element with different numbers of neutrons.

• Example: Oxygen-15 has 8 protons and 7 neutrons (A = 15, Z = 8).

• Calculating neutrons: Number of neutrons = Mass number – Atomic number.

Electron Configuration and Orbitals

Electrons are arranged in orbitals defined by quantum numbers:

• Principal quantum number (n): Indicates energy level (n = 1, 2, 3, ...).

• Angular momentum quantum number (l): Indicates orbital shape (s, p, d, f; l = 0, 1, 2, 3).

• Magnetic quantum number (ml): Indicates orientation (–l to +l).

• Spin quantum number (ms): Indicates electron spin (+1/2 or –1/2).

Electron configurations follow the Aufbau principle, Hund's rule, and the Pauli exclusion principle.

• Example: The ground state electron configuration for calcium (Ca, Z = 20) is 1s22s22p63s23p64s2.

• Valence electrons: Electrons in the outermost shell; for nitrogen (N), there are 5 valence electrons.

Orbital Diagrams and Unpaired Electrons

Orbital diagrams visually represent electron arrangements. Unpaired electrons are those not paired with another electron in an orbital.

• Example: Nitrogen's ground state has three unpaired electrons in the 2p orbitals.

Properties of Matter

Physical and Chemical Properties

Physical properties can be observed without changing the substance's identity (e.g., density, melting point, boiling point). Chemical properties describe a substance's ability to undergo chemical changes (e.g., rusting of iron).

• Example: The boiling point of carbon dioxide is a physical property; the rusting of iron is a chemical property.

States of Matter

• Solid: Fixed shape and volume.

• Liquid: Fixed volume, variable shape.

• Gas: Variable shape and volume.

Significant Figures and Calculations

Significant Figures

Significant figures reflect the precision of a measurement. When performing calculations, the result should be reported with the correct number of significant figures.

• Example: For the calculation (433.621 – 333.9) × 11.900, the answer should be rounded to three significant figures.

Unit Conversions

Unit conversions are essential in chemistry for expressing measurements in different units.

• Example: 3.20 × 101 mm = 32.0 mm.

• Density conversion: To convert g/cm3 to kg/m3, multiply by 1000.

Mixtures and Pure Substances

Elements, Compounds, and Mixtures

• Element: Pure substance of one type of atom (e.g., carbon).

• Compound: Substance composed of two or more elements chemically combined (e.g., water).

• Mixture: Physical combination of two or more substances.

• Homogeneous mixture: Uniform composition (e.g., air).

• Heterogeneous mixture: Non-uniform composition.

Light, Electromagnetic Radiation, and Atomic Spectra

Properties of Electromagnetic Radiation

• Wavelength (λ): Distance between two peaks of a wave.

• Frequency (ν): Number of wave cycles per second (Hz).

• Speed of light (c): $c = 3.00 \times 10^8$ m/s.

• Relationship: $c = \lambda \nu$

Energy of Photons

• Planck's equation: $E = h\nu$ where $h = 6.626 \times 10^{-34}$ J·s.

• Example: The energy of a photon with a wavelength of 95 nm can be calculated using $E = \frac{hc}{\lambda}$.

Photoelectric Effect

The photoelectric effect is the emission of electrons from a metal surface when light of sufficient frequency shines on it. The threshold frequency is the minimum frequency required to eject electrons.

Atomic Spectra and Electron Transitions

• When electrons transition between energy levels in an atom, they absorb or emit photons of specific energies.

• Hydrogen atom transitions: The energy change for a transition from $n_i$ to $n_f$ is given by: $\Delta E = -2.18 \times 10^{-18} \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$ J

• Shortest wavelength: Corresponds to the largest energy difference (e.g., $n = 4$ to $n = 1$).

Periodic Table and Electron Configurations

Electron Configurations

• Electron configurations show the distribution of electrons among orbitals.

• Example: Iodine (I, Z = 53): [Kr]5s24d105p5

• Transition metals: Often have partially filled d orbitals.

Valence Electrons

• Valence electrons are those in the outermost shell and determine chemical reactivity.

• Example: Aluminum (Al) has 3 valence electrons.

Calculations Involving Moles, Mass, and Avogadro's Number

Mole Concept

• 1 mole = $6.022 \times 10^{23}$ particles (Avogadro's number).

• Molar mass: Mass of 1 mole of a substance (g/mol).

• Example: To find the number of atoms in a given mass, use: $\text{Number of atoms} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \times 6.022 \times 10^{23}$

Isotopic Mass and Average Atomic Mass

• Average atomic mass is calculated using the masses and abundances of isotopes: $\text{Average atomic mass} = \sum (\text{isotopic mass} \times \text{fractional abundance})$

Sample Table: Comparison of Physical and Chemical Properties

Property	Physical Property	Chemical Property
Definition	Observed without changing identity	Observed during a chemical change
Examples	Density, melting point, color	Rusting, combustion, reactivity
Change	No new substance formed	New substance formed

Additional info:

• Some questions reference specific calculations (e.g., significant figures, energy of photons, isotopic mass) that are standard in general chemistry.

• Quantum numbers and electron configurations are foundational for understanding atomic structure and periodic trends.

• Physical vs. chemical properties and states of matter are core introductory topics.