Ch. E: Essentials – Roots of Atomic Theory

Law of Conservation of Mass

The Law of Conservation of Mass states that in a chemical reaction, matter is neither created nor destroyed. This principle is foundational to all chemical equations and reactions.

• Implication: The total mass of reactants equals the total mass of products.

• Example: Burning of methane: ; mass before and after reaction remains constant.

Law of Definite Proportions

All samples of a given compound, regardless of their source or preparation, have the same proportions of their constituent elements.

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

Law of Multiple Proportions

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: Carbon and oxygen form both CO and CO2; the ratio of oxygen masses that combine with 1 g of carbon is 1.33:2.66, or 1:2.

Dalton’s Atomic Theory

John Dalton proposed a theory to explain the laws above:

1. Each element is composed of tiny, indestructible particles called atoms.

2. All atoms of a given element have the same mass and properties that distinguish them from atoms of other elements.

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

4. Atoms of one element cannot change into atoms of another element in chemical reactions; they only change the way they are bound together.

• Note: The existence of isotopes (atoms of the same element with different masses) contradicts Dalton’s second postulate.

First Law of Thermodynamics

Energy is conserved in all processes; it can be converted from one form to another but cannot be created or destroyed.

• Example: Chemical energy in gasoline is converted to kinetic energy in a moving car.

System vs. Surroundings

In thermodynamics, the system is the part of the universe under study (e.g., a chemical reaction), and the surroundings are everything else.

• Endothermic process: System gains energy from surroundings (e.g., melting ice).

• Exothermic process: System loses energy to surroundings (e.g., combustion).

Phase Changes

Precision and Accuracy

• Precision: How close repeated measurements are to each other (assessed by standard deviation).

• Accuracy: How close a measurement is to the true value (assessed by average).

• Random error: Error with equal probability of being too high or too low; can be reduced by averaging.

• Systematic error: Error that is consistently in one direction; affects accuracy but not precision.

Units and Prefixes

• Temperature: Kelvin (K) is the SI base unit; absolute scale.

• Conversions:

• Temperature measures average kinetic energy and determines direction of heat flow (from high to low temperature).

• Unit conversions: Use dimensional analysis:

Dimensional Analysis and Density

• Density:

• Density is an intensive property (independent of amount).

• Mass is an extensive property (depends on amount).

• 1 cm3 = 1 mL

Significant Figures

• The number of significant figures in a measurement reflects the precision of the measurement.

• In calculations, the result should have the same number of significant figures as the measurement with the fewest significant figures.

Ch. 1: Matter and Its Classification

Definition and Classification of Matter

Matter is anything that occupies space and has mass. It can be classified by its physical state and composition.

• Pure substance: Composed of only one type of particle (atom or molecule); e.g., water, hydrogen, sodium chloride.

• Mixture: Composed of two or more types of particles; can vary in composition (e.g., iced tea, mud, smoke).

• Mixtures:

  • Heterogeneous: Composition varies throughout (e.g., salad, sand in water).

  • Homogeneous: Uniform composition (e.g., saltwater, air).

• Types of Pure Substances:

  • Element: Cannot be broken down chemically (e.g., O2, Fe).

  • Compound: Composed of two or more elements in fixed, definite proportions (e.g., H2O, NaCl).

Subatomic Particles and Atomic Theory

• Atom: Smallest unit of an element retaining its properties.

• Dalton’s Atomic Theory: Explained conservation of mass, definite proportions, and multiple proportions, but did not predict isotopes.

• J.J. Thomson: Discovered the electron and its charge-to-mass ratio using the cathode ray tube.

• Robert Millikan: Measured the charge of the electron via the oil drop experiment.

• Plum-Pudding Model: Thomson’s model with electrons embedded in a positive sphere (later disproven).

• Rutherford’s Gold Foil Experiment: Showed that atoms have a small, dense, positively charged nucleus; most of the atom is empty space.

• James Chadwick: Discovered the neutron, a neutral particle in the nucleus.

Nuclear Theory of the Atom

1. Most of the atom’s mass and all its positive charge are in the nucleus.

2. Most of the atom’s volume is empty space, with electrons dispersed throughout.

3. Number of electrons equals number of protons in a neutral atom.

Subatomic Particles Table

Elements, Atomic Number, and Mass

• Atomic number (Z): Number of protons in the nucleus; defines the element.

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

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

• Formula mass: Sum of atomic masses in a molecule or formula unit.

• Molar mass (M): Mass in grams of 1 mole of a substance; numerically equal to atomic mass in amu, but units are g/mol.

The Mole and Avogadro’s Number

• Mole (mol): particles (Avogadro’s number, ).

• Defined as the number of atoms in 12 g of carbon-12.

• Conversions:

  • Number of moles =

  • Number of particles = moles Avogadro’s number

Ions

• Cations: Positively charged ions (lost electrons); typically formed by metals.

• Anions: Negatively charged ions (gained electrons); typically formed by nonmetals.

• Ion symbol: Element symbol with charge (e.g., Na+, Cl-).

• Example: Atomic number 35, protons 35, electrons 36, ion charge 1- (Br-).

Ch. 2: Electronic Structure and Quantum Mechanics

Wave-Particle Duality of Electrons and Light

Electrons and light exhibit both wave-like and particle-like properties, a concept central to quantum mechanics.

• Wavelength (λ): Distance between wave peaks (units: m, nm).

• Amplitude: Height from center to peak; relates to intensity.

• Frequency (ν): Number of cycles per second (Hz or s-1).

• Speed of light (c): m/s.

• Relationship:

Electromagnetic Spectrum

• Shorter wavelength (higher frequency) light has higher energy (e.g., gamma rays).

• Longer wavelength (lower frequency) light has lower energy (e.g., radio waves).

Interference and Diffraction

• Constructive interference: Waves add to make a larger wave (in phase).

• Destructive interference: Waves cancel each other (out of phase).

• Diffraction: Bending of waves around obstacles; leads to interference patterns (e.g., double-slit experiment).

The Photoelectric Effect

• Light can eject electrons from a metal surface if its frequency exceeds a threshold value.

• Energy of a photon: or

• Planck’s constant (): J·s

• One photon can eject one electron if (work function).

Bohr Model and Atomic Spectra

• Electrons travel in fixed orbits with quantized energies.

• Energy is emitted or absorbed when electrons move between orbits.

• Emission spectroscopy: Electron drops from higher to lower energy state, emitting a photon.

• Absorption spectroscopy: Electron absorbs energy and moves to a higher energy state.

Wave Behavior of Electrons

• Electrons exhibit diffraction and interference, confirming their wave-like nature.

• De Broglie wavelength:

• Where is mass, is velocity, is Planck’s constant.

Heisenberg Uncertainty Principle

• It is impossible to simultaneously know both the exact position and momentum of an electron.

• Leads to the concept of probability distributions (orbitals) rather than fixed paths.

Quantum Numbers and Atomic Orbitals

• Principal quantum number (n): Energy level; n = 1, 2, 3, ...

• Angular momentum quantum number (l): Shape of orbital; l = 0 to n-1

  • l = 0: s (spherical)

  • l = 1: p (dumbbell)

  • l = 2: d (cloverleaf)

  • l = 3: f (complex)

• Magnetic quantum number (ml): Orientation; values from -l to +l

• Spin quantum number (ms): Electron spin; +1/2 or -1/2

Pauli Exclusion Principle

• No two electrons in an atom can have the same set of four quantum numbers (n, l, ml, ms).

• Each orbital can hold a maximum of two electrons with opposite spins.

Summary Table: Quantum Numbers

Electron Spin and Stern-Gerlach Experiment

• Electrons have intrinsic spin, with two possible orientations (up or down).

• Stern-Gerlach experiment demonstrated quantized spin states.

• Electrons in the same orbital must have opposite spins (paired).

Additional info:

• For more details on units, conversions, and quantum numbers, refer to the indicated textbook pages.

• Understanding these foundational concepts is essential for later topics such as chemical bonding, periodic trends, and reaction stoichiometry.