General Chemistry Fundamentals: Atomic Structure, Mole Calculations, and Quantum Theory

Mole Concept and Chemical Calculations

Grams, Moles, and Particles

The mole is a fundamental unit in chemistry used to express amounts of a chemical substance. It links mass, number of particles, and chemical reactions.

• Definition of Mole: 1 mole contains $6.022 \times 10^{23}$ particles (Avogadro's number).

• Conversions:

  • Grams to moles: $\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

  • Moles to particles: $\text{particles} = \text{moles} \times 6.022 \times 10^{23}$

• Example: How many atoms are in 44.7 g Zn (molar mass = 65.38 g/mol)? $\frac{44.7}{65.38} \times 6.022 \times 10^{23} = 4.117 \times 10^{23}$ atoms

• Example: How many atoms are in 111.1 g of Li (molar mass = 6.941 g/mol)? $\frac{111.1}{6.941} \times 6.022 \times 10^{23} = 9.64 \times 10^{24}$ atoms

Mixtures and Pure Substances

Chemical substances can be classified as pure substances or mixtures based on their composition.

• Pure Substance: Contains only one type of element or compound.

• Mixture: Contains two or more substances physically combined.

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

  • Heterogeneous mixture: Non-uniform composition (e.g., oil and water).

• Compounds: Substances formed by chemical bonds between elements; can only be separated by chemical reactions.

• Mixtures: Can be separated by physical means (e.g., filtration, distillation).

Atomic Structure and Isotopes

Elements, Isotopes, and Abundance

Atoms of the same element can have different numbers of neutrons, resulting in isotopes. The abundance of isotopes affects the average atomic mass.

Element	Isotope	% Abundance	Isotope	% Abundance
Li	6Li	7.5	7Li	92.5
B	10B	19.8	11B	80.2
C	12C	98.9	13C	1.1

• Isotope: Atoms of the same element with different numbers of neutrons.

• Average Atomic Mass: Weighted average based on isotopic abundance.

Law of Conservation of Mass

During chemical reactions, the total mass of reactants equals the total mass of products.

• Example Reaction: $\mathrm{CH}_4(g) + 2\mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g) + 2\mathrm{H}_2O(g)$

• The number of atoms and total mass are conserved, even though the arrangement changes.

Chemical and Physical Changes

Types of Changes

Chemical changes involve breaking and forming bonds, while physical changes involve rearrangement without altering chemical identity.

• Chemical Change: Bonds are broken and new bonds are formed (e.g., combustion, rusting).

• Physical Change: No new substances are formed; includes dissolving, evaporation, melting, and boiling.

Electromagnetic Spectrum and Light

Wavelength, Frequency, and Energy

Light is a form of electromagnetic radiation characterized by its wavelength ($\lambda$), frequency ($\nu$), and energy ($E$).

• Relationship: $c = \lambda \nu$ Where $c$ is the speed of light ($3.00 \times 10^8$ m/s).

• Energy of a photon: $E = h \nu$ Where $h$ is Planck's constant ($6.626 \times 10^{-34}$ Joule·seconds).

• Visible Spectrum: Ranges from approximately 400 nm (violet) to 700 nm (red).

• Red light: Least energy; Purple light: Most energy.

• Infrared: Associated with heat.

Electromagnetic Spectrum Table

Type	Wavelength	Energy
Radio waves	Longest	Lowest
Microwaves	Long	Low
Infrared	Medium	Medium-low
Visible light	400-700 nm	Medium
Ultraviolet	Short	High
X-rays	Shorter	Higher
Gamma rays	Shortest	Highest

Quantum Mechanical Model of the Atom

Amplitude vs Frequency

Amplitude refers to the height of a wave, while frequency is the number of cycles per second. Both affect the properties of light.

• Amplitude: Related to the intensity or brightness of light.

• Frequency: Related to the energy of light.

• Waves with the same frequency but different amplitude appear brighter or dimmer.

Photon and Energy Calculations

A photon is the smallest quantum of light. The energy of a photon is directly proportional to its frequency.

• Energy of a photon: $E = h \nu$

• Frequency and Wavelength: $\nu = \frac{c}{\lambda}$

• Example Calculation: For $\lambda = 579 \times 10^{-9}$ m: $E = (6.626 \times 10^{-34} \text{ J·s}) \times (3.00 \times 10^8 \text{ m/s}) / (579 \times 10^{-9} \text{ m})$

Hydrogen Atom and Electron Transitions

Electrons in atoms occupy discrete energy levels. When an electron transitions between levels, energy is absorbed or released as photons.

• Energy Change Equation: $\Delta E = -2.178 \times 10^{-18} \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$ Where $n_i$ is the initial energy level and $n_f$ is the final energy level.

• Negative $\Delta E$: Energy is released (emission).

• Positive $\Delta E$: Energy is absorbed (excitation).

• Example: Electron transition from $n=3$ to $n=2$: $\Delta E = -2.178 \times 10^{-18} \left( \frac{1}{2^2} - \frac{1}{3^2} \right)$

Periodic Table and Atomic Structure

Protons, Neutrons, and Electrons

The periodic table organizes elements by atomic number, which equals the number of protons. Neutrons and electrons are determined as follows:

• Protons: Atomic number.

• Neutrons: Mass number minus atomic number.

• Electrons:

  • Neutral atom: electrons = protons.

  • Negative ion: electrons = protons + charge.

  • Positive ion: electrons = protons - charge.

Additional info:

• Examples and calculations are based on standard general chemistry curriculum.

• Some diagrams and images referenced in the notes are described in text for clarity.