Atoms and the Foundations of Modern Chemistry

Chapter 1: Atoms (and Ions and Molecules)

Introduction

This chapter introduces the fundamental concepts of atoms, ions, and molecules, which are the building blocks of matter. It also explores the historical development of atomic theory and the scientific revolution that shaped our modern understanding of chemistry.

Understanding of Matter

Scientific Revolution

The scientific revolution in the late 16th century marked a shift toward systematic observation and experimentation in understanding nature. Over the next 150+ years, new discoveries challenged the ancient idea that matter was infinitely divisible.

• Scientific Method: Emphasized observation, hypothesis, experimentation, and theory development.

• Challenge to Indivisibility: Observations could not be explained by the idea that matter could be divided endlessly without changing its nature.

Laws Governing Matter

Law of Conservation of Mass

Formulated by Antoine Lavoisier (1743–1794), this law states that in a chemical reaction, matter is neither created nor destroyed. The total mass of reactants equals the total mass of products.

• Example: $\mathrm{KI} + \mathrm{Hg(NO_3)_2} \rightarrow \mathrm{KNO_3} + \mathrm{HgI_2}$

• Mass before reaction = Mass after reaction

Law of Definite Proportions

Proposed by Joseph Proust (1754–1826), this law states that different samples of a pure chemical compound always contain the same proportion of elements by mass.

• Example: Sodium chloride (NaCl) always contains 39.3% sodium and 60.7% chlorine by mass, regardless of the sample size.

Law of Multiple Proportions

John Dalton (1766–1844) observed that elements can combine in different ratios to form different compounds, and these ratios are small whole numbers.

• Example: Carbon and oxygen form both CO and CO2, with mass ratios of oxygen to carbon being simple multiples.

Dalton’s Atomic Theory

Postulates of Atomic Theory

• Elements are made of tiny, indestructible particles called atoms.

• Atoms of the same element have the same mass; atoms of different elements have different masses.

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

• Chemical reactions rearrange atoms but do not change the atoms themselves.

Subatomic Particles

Discovery of the Electron

J.J. Thomson (1856–1940) used cathode-ray tubes to show that atoms contain tiny, negatively charged particles called electrons.

• The beam in the tube was deflected toward the positive plate, indicating negative charge.

• Charge-to-mass ratio of the electron: $-1.76 \times 10^{8} \ \mathrm{C/g}$

Millikan’s Oil Drop Experiment

Robert A. Millikan (1868–1953) measured the charge of the electron using oil drops and X-rays.

• Electron charge: $-1.60218 \times 10^{-19} \ \mathrm{C}$

• Electron mass: $9.10938 \times 10^{-28} \ \mathrm{g}$

Plum Pudding Model

Thomson proposed that electrons were embedded in a sphere of positive charge, like plums in a pudding.

• This model was later disproved by further experiments.

Radioactivity and the Nucleus

Henri Becquerel (1852–1908) discovered that uranium emits radiation. Ernest Rutherford (1871–1937) identified different types of radiation and conducted the gold-foil experiment.

• Alpha particles: Positively charged helium nuclei

• Beta particles: High-energy electrons

Rutherford’s Gold-Foil Experiment

Rutherford’s experiment showed that most alpha particles passed through gold foil, but some were deflected at large angles, indicating a dense, positively charged nucleus.

• The atom is mostly empty space.

• The nucleus contains most of the atom’s mass and is positively charged.

• Electrons are dispersed in the empty space around the nucleus.

Subatomic Particle Properties

Particle	Mass (kg)	Mass (amu)
Neutron	1.67493 × 10-27	1.00866
Proton	1.67262 × 10-27	1.00728
Electron	9.10938 × 10-31	0.00054858

• 1 atomic mass unit (amu) = 1/12 the mass of a carbon-12 atom; also called a Dalton (Da).

Elements and Isotopes

Atomic Number and Mass Number

• Atomic number (Z): Number of protons in the nucleus; also equals the number of electrons in a neutral atom.

• Mass number (A): Total number of protons and neutrons in the nucleus.

Isotopes

Atoms of the same element with different numbers of neutrons are called isotopes.

• Example: Carbon-12 (6 protons, 6 neutrons), Carbon-13 (6 protons, 7 neutrons)

Ions

Atoms become charged (ions) when they gain or lose electrons.

• Cations: Positively charged ions (loss of electrons)

• Anions: Negatively charged ions (gain of electrons)

• Example Table:

Symbol	Protons	Neutrons	Electrons
Na	11	12	10
Cl	17	18	18

Atomic Mass

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

• Example (Neon):

Isotope	Protons	Neutrons	Mass (amu)	Natural Abundance (%)
Ne-20	10	10	19.9924	90.48
Ne-21	10	11	20.9940	0.27
Ne-22	10	12	21.9914	9.25

Average atomic mass calculation:

• $\text{Average mass} = (0.9048 \times 19.9924) + (0.0027 \times 20.9940) + (0.0925 \times 21.9914) = 20.180$

The Mole and Avogadro’s Number

Definition of the Mole

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

• Used to relate microscopic particles to macroscopic quantities

Conversions Involving the Mole

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

• Moles to mass: $\text{Mass (g)} = \text{Number of moles} \times \text{Molar mass (g/mol)}$

• Example: $0.0265\,\mathrm{g}\,\text{C} \times \frac{1\,\text{mol}}{12.01\,\mathrm{g}} = 2.21 \times 10^{-3}\,\text{mol C}$

• Example: $3.10\,\mathrm{g}\,\text{Cu} \times \frac{1\,\text{mol}}{63.55\,\mathrm{g}} \times 6.022 \times 10^{23}\,\text{atoms} = 2.94 \times 10^{22}\,\text{Cu atoms}$

Comparing Samples by Number of Atoms

• For equal masses, the element with the smallest molar mass contains the most atoms.

• Example: 1 g of carbon contains more atoms than 1 g of copper or uranium.