General Chemistry Study Notes: Essentials, Atoms, and Quantum-Mechanical Model

Chapter 0: Essentials: Units, Measurements, and Problem Solving

SI Units and the Metric System

The International System of Units (SI) provides a standardized set of units for scientific measurements. The metric system is widely used in chemistry for expressing quantities such as length, mass, and volume.

• Key SI Units: meter (m) for length, kilogram (kg) for mass, second (s) for time, mole (mol) for amount of substance, kelvin (K) for temperature.

• Metric Prefixes: kilo-, centi-, milli-, micro-, nano-, etc., are used to express multiples or fractions of base units.

Temperature Scales

Temperature can be measured in Celsius (°C), Kelvin (K), and Fahrenheit (°F). Conversions between these scales are essential in chemistry.

• Conversion formulas:

• $K = ^ ext{°}C + 273.15$

• $^ ext{°}F = (^\text{°}C \times \frac{9}{5}) + 32$

Density and Calculations

Density is a physical property defined as mass per unit volume.

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

• Used to identify substances and solve problems involving mass and volume.

Significant Figures and Rounding

Significant figures reflect the precision of a measurement. Proper rounding is important in reporting results.

• Nonzero digits are always significant.

• Zeros between nonzero digits are significant.

• Trailing zeros in a decimal number are significant.

Counting and Recognizing Exact Numbers

Exact numbers have an infinite number of significant figures and arise from counting objects or defined quantities.

• Examples: 12 eggs, 1000 g in 1 kg.

Chapter 1: Atoms

Atomic Structure and Experiments

The structure of the atom has been elucidated through key experiments.

• Cathode Ray Experiment (J.J. Thomson): Discovered the electron and its negative charge.

• Oil Drop Experiment (Millikan): Measured the charge of the electron.

• Gold Foil Experiment (Rutherford): Revealed the existence of the atomic nucleus.

Periodic Table and Atomic Mass

The periodic table organizes elements by increasing atomic number and groups elements with similar properties.

• Atomic Mass: The weighted average mass of an element's isotopes.

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

Symbols and Isotope Notation

Chemical symbols represent elements, and isotope notation specifies the atomic number and mass number.

• Isotope Notation: $^{A}_{Z}\text{X}$, where X is the element symbol, A is the mass number, and Z is the atomic number.

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

Atomic Number and Mass Number

• Atomic Number (Z): Number of protons in the nucleus.

• Mass Number (A): Total number of protons and neutrons.

Key Concept: Avogadro's Number

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

Chapter 2: The Quantum-Mechanical Model of the Atom

Nature of Light and Electromagnetic Radiation

Light exhibits both wave-like and particle-like properties. The quantum-mechanical model describes the behavior of electrons in atoms.

• Speed of Light: $c = 3.00 \times 10^8 \text{ m/s}$

• Frequency ($\nu$) and Wavelength ($\lambda$): $c = \lambda \nu$

• Photoelectric Effect: Demonstrates that light can eject electrons from a metal surface, supporting the particle nature of light.

Atomic Spectra and Energy Levels

Atoms emit light at specific wavelengths, producing line spectra that reveal quantized energy levels.

• Energy of a Photon: $E = h\nu$ where $h$ is Planck's constant ($6.626 \times 10^{-34} \text{ J} \cdot \text{s}$).

• Bohr Model: Electrons occupy discrete energy levels; transitions between levels emit or absorb photons.

Quantum Numbers and Orbitals

Quantum numbers describe the properties of atomic orbitals and the electrons within them.

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

• Angular Momentum Quantum Number ($l$): Indicates the shape of the orbital.

• Magnetic Quantum Number ($m_l$): Indicates the orientation of the orbital.

• Spin Quantum Number ($m_s$): Indicates the spin direction of the electron.

Uncertainty Principle

The Heisenberg Uncertainty Principle states that it is impossible to simultaneously know both the exact position and momentum of an electron.

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

Writing Electron Configurations

Electron configurations describe the arrangement of electrons in an atom's orbitals.

• Follow the Aufbau principle, Pauli exclusion principle, and Hund's rule.

• Example: Carbon: $1s^2 2s^2 2p^2$

Periodic Table and Quantum Model

The periodic table reflects the arrangement of electrons and the quantum-mechanical principles governing atomic structure.

• Periodic trends such as atomic radius, ionization energy, and electron affinity are explained by electron configurations.

*Additional info: Fundamental equations and conversion factors from the textbook should be reviewed alongside the periodic table for mastery of these topics.*