General Chemistry I: Foundational Concepts, Atomic Structure, and Periodic Properties

Matter, Measurement & Problem Solving

Pure Substances and Mixtures

Understanding the classification of matter is fundamental in chemistry. Matter can be categorized as pure substances or mixtures based on composition and uniformity.

• Pure Substance: A material with a constant composition throughout, such as carbon dioxide or ethanol.

• Mixture: Contains two or more substances physically combined, such as air or salt water.

• Example: Carbon dioxide (CO2) is a pure substance, while air is a mixture.

Density and Unit Conversions

Density is a key physical property used to characterize substances and solve quantitative problems.

• Density: Defined as mass per unit volume.

• Formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Unit Conversion: Converting between units (e.g., mL to L) is essential for accurate calculations.

• Example: $827\ \text{mL} = 0.827\ \text{L}$

Physical and Chemical Changes

Chemical changes result in new substances, while physical changes do not alter chemical identity.

• Physical Change: Changes in state or appearance (e.g., melting, dissolving).

• Chemical Change: Formation of new substances (e.g., combustion, rusting).

• Example: Dissolving sugar in water is a physical change; burning magnesium is a chemical change.

Intensive and Extensive Properties

Properties of matter are classified as intensive or extensive based on dependence on sample size.

• Intensive Property: Independent of amount (e.g., density, melting point).

• Extensive Property: Dependent on amount (e.g., mass, volume).

Atoms & Elements

Atomic Structure and Isotopes

Atoms consist of protons, neutrons, and electrons. Isotopes are atoms of the same element with different numbers of neutrons.

• Proton: Positively charged particle in the nucleus.

• Neutron: Neutral particle in the nucleus.

• Electron: Negatively charged particle in orbitals around the nucleus.

• Isotope Notation: $^{A}_{Z}\text{X}$, where A = mass number, Z = atomic number.

• Example: For $^{40}_{20}\text{Ca}$: 20 protons, 20 electrons, 20 neutrons.

Electron Configuration and Orbital Diagrams

Electron configuration describes the arrangement of electrons in an atom. Orbital diagrams visually represent electron placement in orbitals.

• Electron Configuration: Notation showing distribution of electrons among orbitals (e.g., $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^6 7s^2$ for Rn).

• Orbital Diagram: Uses arrows to indicate electron spin in each orbital.

• Example: Aluminum (Al) orbital diagram shows electrons filling 1s, 2s, 2p, 3s, and 3p orbitals.

Quantum Numbers and Atomic Orbitals

Quantum numbers describe the properties of atomic orbitals and electrons.

• Principal Quantum Number (n): Indicates energy level.

• Angular Momentum Quantum Number (l): Indicates orbital shape (s, p, d, f).

• Magnetic Quantum Number (ml): Indicates orientation.

• Spin Quantum Number (ms): Indicates electron spin (+1/2 or -1/2).

• Example: For ground state electrons in carbon: n=2, l=1, ml=-1, ms=+1/2.

Atomic Theory and Experiments

Key experiments have shaped our understanding of atomic structure.

• Rutherford's Gold Foil Experiment: Demonstrated the existence of a small, dense nucleus.

• Plum Pudding Model: Earlier model proposing electrons embedded in a positive sphere.

Periodic Properties of the Elements

Periodic Trends

The periodic table organizes elements by increasing atomic number and reveals trends in properties.

• Atomic Radius: Increases down a group, decreases across a period.

• Ionization Energy: Energy required to remove an electron; increases across a period, decreases down a group.

• Electron Affinity: Energy change when an electron is added; generally increases across a period.

Electron Configuration and Periodic Table

Electron configurations explain the arrangement of elements in the periodic table.

• Valence Electrons: Electrons in the outermost shell, determine chemical reactivity.

• Example: Alkali metals have one valence electron; noble gases have full valence shells.

The Quantum-Mechanical Model of the Atom

Heisenberg Uncertainty Principle

The position and momentum of an electron cannot both be precisely known at the same time.

• Formula: $\Delta x \Delta p \geq \frac{h}{4\pi}$

• Application: Used to calculate uncertainty in position or momentum for electrons.

Atomic Orbitals and Nodes

Atomic orbitals have distinct shapes and contain nodes where the probability of finding an electron is zero.

• Node: A region where the wavefunction changes sign and probability density is zero.

• Types of Orbitals: s (spherical), p (dumbbell), d (cloverleaf), f (complex).

• Example: The 2p orbital has one node; the 3d orbital has two nodes.

Calculating Wavelength and Energy

Electrons exhibit wave-like properties, and their energy and wavelength can be calculated using physical constants.

• Formula for Wavelength: $\lambda = \frac{h}{mv}$

• Example: For an electron moving at $4.11 \times 10^7$ m/s, $\lambda = 1.77 \times 10^{-10}$ m.

Lab Techniques and Mathematical Operations

Stoichiometry and Mole Calculations

Stoichiometry involves quantitative relationships in chemical reactions and conversions between mass, moles, and number of particles.

• Avogadro's Number: $6.022 \times 10^{23}$ particles/mol.

• Example: Calculating atoms in 10.0 mL of Hg using density and molar mass.

Atomic Mass Calculations

Atomic mass is determined by the weighted average of isotopic masses and their natural abundances.

• Formula: $\text{Atomic Mass} = \sum (\text{Isotopic Mass} \times \text{Fractional Abundance})$

• Example: For Carbon: $12.000000 \times 0.9893 + 13.003355 \times 0.0107 = 12.01$ amu

Reference Tables

Physical Constants and Periodic Table

Reference tables provide essential constants and the periodic table for solving problems.

• Physical Constants: Includes Planck's constant, Avogadro's number, speed of light, etc.

• Periodic Table: Used to determine atomic numbers, masses, and element properties.

Constant	Symbol	Value
Avogadro's number	NA	6.022 x 1023 mol-1
Planck's constant	h	6.626 x 10-34 J·s
Speed of light	c	2.998 x 108 m/s
Ideal gas constant	R	0.08206 L·atm·K-1·mol-1
Electron mass	me	9.109 x 10-31 kg

Unit	Value of R
J·K-1·mol-1	8.314
L·atm·K-1·mol-1	0.08206
L·bar·K-1·mol-1	0.08314
L·Torr·K-1·mol-1	62.36

Additional info: These notes cover foundational topics from Ch.1 (Matter, Measurement & Problem Solving), Ch.2 (Atoms & Elements), Ch.8 (Quantum-Mechanical Model of the Atom), and Ch.9 (Periodic Properties of the Elements), as well as essential lab and mathematical techniques relevant for General Chemistry I exam preparation.