General Chemistry I: Foundational Concepts, Atomic Structure, and Molecular Geometry

Conversions and Dimensional Analysis

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert units from one system to another using conversion factors.

• Conversion Factors: Ratios derived from the equality between two different units that can be used to convert from one unit to another.

• Example: $1\ \text{dozen} = 12\ \text{eggs}$, $1\ \text{mile} = 5280\ \text{ft}$

• Application: Used to solve problems involving measurements and unit conversions.

Example Calculation:

• How many eggs are in 50 dozen?

• $50\ \text{dozen} \times \frac{12\ \text{eggs}}{1\ \text{dozen}} = 600\ \text{eggs}$

Law of Multiple Proportions

Definition and Application

The law of multiple proportions states that if two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other are in ratios of small whole numbers.

• Example: Nitrogen oxides (NO and NO2)

• For a fixed mass of nitrogen, the ratio of the masses of oxygen that combine with it is a small whole number.

Sample Calculation:

• Compound 1: 1.14 g O per 1.00 g N

• Compound 2: 2.29 g O per 1.00 g N

• Ratio: $\frac{2.29}{1.14} = 2:1$

Atomic Theory and Structure

Dalton's Atomic Theory

• All matter is composed of atoms.

• Atoms of a given element are identical in mass and properties.

• Atoms cannot be created or destroyed in chemical reactions.

• Compounds are formed by the combination of atoms in simple whole-number ratios.

Discovery of Subatomic Particles

• Electron: Discovered by J.J. Thomson (1897) using cathode ray tubes.

• Proton: Identified as a positively charged particle in the nucleus.

• Neutron: Discovered by James Chadwick (1932); neutral particle in the nucleus.

Key Experiments

• Millikan Oil Drop Experiment: Measured the charge of the electron ($-1.60 \times 10^{-19}$ C).

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

Atomic Models

• Plum Pudding Model: Electrons embedded in a positively charged sphere (Thomson).

• Nuclear Model: Dense nucleus with electrons orbiting around it (Rutherford).

Nuclear Symbols and Isotopes

Nuclear Notation

• Element symbol with mass number (A) and atomic number (Z): $^{A}_{Z}\text{X}$

• Example: $^{12}_{6}\text{C}$ for carbon-12

Isotopes

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

• Example: $^{12}\text{C}$, $^{13}\text{C}$, $^{14}\text{C}$

Weighted Average Atomic Mass

• Calculated using the relative abundances and masses of isotopes:

$\text{Average atomic mass} = \sum (\text{fractional abundance} \times \text{isotope mass})$

Atomic Mass Unit (amu) and Avogadro's Number

• 1 amu = $1.67 \times 10^{-24}$ g

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

• Used to relate atomic scale to macroscopic quantities (grams, moles).

Atomic Structure and Quantum Theory

Light and Atomic Structure

• Light exhibits wave-particle duality.

• Wavelength ($\lambda$), frequency ($\nu$), and speed of light ($c$) are related:

$c = \lambda \nu$

• Energy of a photon: $E = h\nu$ (Planck's constant $h = 6.63 \times 10^{-34}$ J·s)

Photoelectric Effect

• Light can eject electrons from a metal surface if above a threshold frequency.

• Demonstrates particle nature of light (photons).

$E_{\text{photon}} = h\nu$

Bohr Model of the Atom

• Electrons occupy quantized energy levels.

• Energy transitions correspond to absorption or emission of photons.

$E_n = -\frac{2.18 \times 10^{-18}\ \text{J}}{n^2}$

Quantum Numbers and Orbitals

• Principal quantum number ($n$): energy level

• Angular momentum quantum number ($l$): shape of orbital

• Magnetic quantum number ($m_l$): orientation

• Spin quantum number ($m_s$): electron spin

Electron Configuration and Periodic Trends

Electron Configuration

• Describes the arrangement of electrons in an atom.

• Filling order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, etc.

• Hund's rule, Pauli exclusion principle, and Aufbau principle guide electron filling.

Periodic Trends

• Atomic Size: 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 released when an atom gains an electron.

Molecules and Compounds

Chemical Bonds

• Ionic Bonds: Transfer of electrons from metal to nonmetal.

• Covalent Bonds: Sharing of electrons between nonmetals.

• Polar Covalent Bonds: Unequal sharing of electrons due to differences in electronegativity.

Naming Compounds

• Ionic compounds: Name cation first, then anion (e.g., NaCl = sodium chloride).

• Covalent compounds: Use prefixes to indicate number of atoms (e.g., CO2 = carbon dioxide).

• Polyatomic ions: Recognize common ions (e.g., SO42-, NO3-).

Covalent Compounds and Lewis Structures

Lewis Structures

• Show arrangement of valence electrons in molecules.

• Single, double, and triple bonds represent shared electron pairs.

• Formal charge helps determine the most stable structure.

Resonance

• Some molecules have multiple valid Lewis structures (resonance forms).

• The actual structure is a hybrid of all resonance forms.

VSEPR Theory and Molecular Shapes

Valence Shell Electron Pair Repulsion (VSEPR) Theory

• Predicts the 3D shape of molecules based on repulsion between electron groups.

• Electron group geometry (EGG) and molecular shape depend on the number of bonding and lone pairs.

Electron Groups	Geometry	Bond Angle
2	Linear	180°
3	Trigonal planar	120°
4	Tetrahedral	109.5°
5	Trigonal bipyramidal	90°, 120°
6	Octahedral	90°

Polarity of Molecules

• Determined by the shape and the distribution of polar bonds.

• Nonpolar molecules have symmetrical charge distribution; polar molecules do not.

Summary Table: Subatomic Particles

Particle	Relative Mass	Charge	Location
Proton	1	+1	Nucleus
Neutron	1	0	Nucleus
Electron	~0	-1	Outside nucleus

Additional info: These notes cover foundational topics in General Chemistry, including measurement, atomic theory, quantum mechanics, periodic trends, chemical bonding, molecular geometry, and resonance. They are suitable for exam preparation and provide a comprehensive overview of the first several chapters of a college-level General Chemistry course.