General Chemistry Fundamentals: Atomic Structure, Measurement, and Chemical Laws

Atomic Structure and Chemical Laws

Law of Conservation of Mass

The Law of Conservation of Mass states that matter is neither created nor destroyed in a chemical reaction. The total mass of reactants equals the total mass of products.

• Example: If 4.04 g of H2 gas reacts with 32.0 g of O2 gas to produce H2O, the total mass of H2O produced should be 36.04 g.

Law of Definite Proportions

The Law of Definite Proportions (or Law of Constant Composition) states that all samples of a given compound have the same proportions of their constituent elements, regardless of the source or method of preparation.

• Example: Water (H2O) always contains hydrogen and oxygen in a 2:1 ratio by atoms.

Law of Multiple Proportions

The Law of Multiple Proportions states that when two elements 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: CO and CO2 both contain carbon and oxygen, but the ratio of oxygen to carbon is different and can be expressed as a simple whole number ratio.

Dalton's Atomic Theory

Dalton's Atomic Theory provides a foundation for understanding chemical reactions and the nature of matter.

• Elements are composed of tiny, indivisible particles called atoms.

• Atoms of the same element are identical in mass and properties.

• Atoms of different elements differ in mass and properties.

• Atoms combine in simple whole-number ratios to form compounds.

• Chemical reactions involve rearrangement of atoms; atoms are not created or destroyed.

Subatomic Particles and Atomic Experiments

Discovery of the Electron

Experiments with cathode rays led to the discovery of the electron, a subatomic particle with a negative charge.

• J.J. Thomson: Demonstrated the existence of electrons and measured their charge-to-mass ratio.

• Robert Millikan: Determined the fundamental charge of the electron using the oil drop experiment.

• Ernest Rutherford: Disproved the Plum Pudding model, showing that atoms have a dense nucleus containing most of the mass and a positive charge.

Structure of the Atom

• Protons: Positively charged particles in the nucleus.

• Neutrons: Neutral particles in the nucleus.

• Electrons: Negatively charged particles orbiting the nucleus.

Atomic Mass and Isotopes

Atomic Mass Calculation

The atomic mass of an element is the weighted average of the masses of its naturally occurring isotopes.

• Formula:

$atomic\ mass = a_1m_1 + a_2m_2 + \ldots$

where $a_1, a_2$ are the fractional abundances and $m_1, m_2$ are the masses of the isotopes.

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

Electromagnetic Radiation and Quantum Theory

Electromagnetic Spectrum

The electromagnetic spectrum includes all types of electromagnetic radiation, classified by wavelength and frequency.

• Visible Light: Wavelengths from about 400 nm (violet) to 750 nm (red).

• Ultraviolet, X-ray, Gamma ray: Higher energy, shorter wavelength.

• Radio, Microwave, Infrared: Lower energy, longer wavelength.

Key Equations

• Energy of a photon: $E_p = \frac{hc}{\lambda}$

• Planck's equation: $E_p = h\nu$

• Kinetic energy of ejected electron: $KE = E_p - \phi$

• Threshold energy: $\phi = h\nu_{threshold}$

• de Broglie wavelength: $\lambda_{dB} = \frac{h}{mv}$

• Speed of light: $c = 3.0 \times 10^8$ m/s

• Planck's constant: $h = 6.626 \times 10^{-34}$ J·s

Measurement and Significant Figures

Metric Prefixes

• 1 μm = $1 \times 10^{-6}$ m

• 1 Gm = $1 \times 10^9$ m

• 1 s = $1 \times 10^0$ s

• 1 Hz = $1 \times 10^0$ Hz

• 1 MHz = $1 \times 10^6$ Hz

• 1 Mbyte = $1 \times 10^6$ bytes

• 1 μm = $1 \times 10^{-6}$ m

• 1 pmol = $1 \times 10^{-12}$ mol

• 1 ms = $1 \times 10^{-3}$ s

Significant Figures

Significant figures reflect the precision of a measured value.

• Nonzero digits are always significant.

• Zeros between nonzero digits are significant.

• Leading zeros are not significant.

• Trailing zeros in a decimal number are significant.

• Example: 0.0055 has 2 significant figures; 5500 may have 2, 3, or 4 depending on context.

Physical and Chemical Properties

Intensive vs. Extensive Properties

• Intensive properties: Do not depend on the amount of substance (e.g., density, boiling point).

• Extensive properties: Depend on the amount of substance (e.g., mass, volume).

Physical and Chemical Changes

• Physical change: Change in state or appearance without changing composition (e.g., melting, boiling).

• Chemical change: Change in composition; new substances are formed (e.g., combustion).

Periodic Table and Electron Configuration

Periodic Table Organization

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

• Groups: Vertical columns; elements in the same group have similar valence electron configurations.

• Periods: Horizontal rows; elements in the same period have the same number of electron shells.

Electron Configuration Principles

• Aufbau Principle: Electrons fill the lowest energy orbitals first.

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of quantum numbers.

• Hund's Rule: Electrons fill degenerate orbitals singly first, with parallel spins, before pairing.

Quantum Numbers

• Principal quantum number (n): Indicates the shell (energy level).

• Angular momentum quantum number (l): Indicates the subshell (shape of orbital).

• Magnetic quantum number (ml): Indicates the orientation of the orbital.

• Spin quantum number (ms): Indicates the spin direction (+1/2 or -1/2).

Electromagnetic Spectrum Table

The following table summarizes the main regions of the electromagnetic spectrum:

Region	Wavelength (nm)	Frequency (Hz)	Energy
Radio	> 106	< 109	Low
Microwave	105 - 103	109 - 1012	Low
Infrared	103 - 700	1012 - 1014	Low
Visible	700 - 400	1014 - 1015	Medium
Ultraviolet	400 - 10	1015 - 1017	High
X-ray	10 - 0.01	1017 - 1020	High
Gamma ray	< 0.01	> 1020	Very High

Additional info:

• Some content inferred from context and standard General Chemistry curriculum, such as definitions and examples for laws and quantum numbers.

• Periodic table image referenced for electron configuration and element identification.