Chapter 2 Atoms and Elements: Structure, Isotopes, Periodic Table, and the Mole

Atoms and Elements

Introduction to Atoms

An atom is the fundamental unit of matter, representing the smallest portion of an element that retains its chemical properties. Modern imaging techniques, such as scanning tunneling microscopy (STM), allow us to visualize individual atoms and their arrangements.

• Atomic structure can be depicted using classical and quantum mechanical models.

• Atoms are composed of a nucleus (protons and neutrons) surrounded by electrons.

Atomic Theory and Historical Development

Early Theories and Discoveries

• Leucippus and Democritus first proposed that matter is made of small, indivisible particles called atomos (Greek for "indivisible").

• John Dalton formulated the atomic theory, supported by the law of multiple proportions.

• J.J. Thomson discovered the electron using cathode ray experiments.

• Robert Millikan measured the electron's charge.

• Ernest Rutherford's gold foil experiment led to the nuclear model of the atom.

• Rutherford and Chadwick discovered the neutron.

Laws Leading to Atomic Theory

• Law of Conservation of Mass (Antoine Lavoisier): Mass is neither created nor destroyed in chemical reactions.

• Law of Definite Proportions (Joseph Proust): A compound always contains the same elements in the same proportion by mass.

• Law of Multiple Proportions (John Dalton): When two elements form more than one compound, the ratios of the masses of the second element combine with a fixed mass of the first element in small whole numbers.

Additional info: These laws support the concept that atoms are the basic building blocks of matter and that chemical reactions involve rearrangements of linkages (bonds) between atoms.

Subatomic Particles

Protons, Neutrons, and Electrons

Particle	Mass (kg)	Mass (amu)	Charge (relative)	Charge (C)
Proton	1.67262 × 10^−27	1.00727	+1	+1.60218 × 10^−19
Neutron	1.67493 × 10^−27	1.00866	0	0
Electron	0.00091 × 10^−27	0.00055	−1	−1.60218 × 10^−19

• The proton and electron have equal but opposite charges; the neutron is neutral.

• 1 atomic mass unit (amu) = $1.66054 \times 10^{-24}$ g

• Charge of 1 electron = $1.60 \times 10^{-19}$ C

Elements and Atomic Number

Defining Elements

• The number of protons in the nucleus defines the element and is called the atomic number (Z).

• Each element has a unique atomic number.

Example: Chlorine (Cl) has atomic number 17; every Cl atom has 17 protons.

Isotopes

Varied Number of Neutrons

• Atoms of the same element can have different numbers of neutrons, called isotopes.

• Isotopes have the same atomic number (Z) but different mass numbers (A).

Mass number (A): $A = \text{number of protons (p)} + \text{number of neutrons (n)}$

• Isotopic notation: $^{A}_{Z}X$ (e.g., $^{20}_{10}\text{Ne}$, $^{21}_{10}\text{Ne}$, $^{22}_{10}\text{Ne}$)

• Alternative notation: Symbol or name followed by mass number (e.g., Ne-20, neon-20)

Natural Abundance of Isotopes

The relative amount of each isotope in a naturally occurring sample is called its natural abundance.

Symbol	Number of Protons	Number of Neutrons	Mass Number (A)	Natural Abundance (%)
Ne-20	10	10	20	90.48
Ne-21	10	11	21	0.27
Ne-22	10	12	22	9.25

Atomic Mass

The Average Mass of an Element’s Atoms

• Atomic mass (atomic weight) is the weighted average of the masses of an element’s isotopes, according to their natural abundance.

• It is listed beneath the element’s symbol in the periodic table.

Calculation:

$\text{Atomic mass}=\sum_{n}(\text{fraction of isotope }n)\times(\text{mass of isotope }n)$

Example: Chlorine has two isotopes: Cl-35 (34.97 amu, 75.77%) and Cl-37 (36.97 amu, 24.23%).

• Atomic mass of Cl = $(0.7577 \times 34.97) + (0.2423 \times 36.97) = 26.4968 + 8.9578 = 35.45$ amu

Ions: Losing and Gaining Electrons

Formation of Ions

• In a neutral atom, the number of electrons equals the number of protons.

• Atoms can lose or gain electrons to form ions:

  • Cations: Positively charged ions (e.g., Na+), formed by losing electrons.

  • Anions: Negatively charged ions (e.g., Cl−), formed by gaining electrons.

• The charge number equals the number of electrons lost or gained.

Example: Aluminum (atomic number 13) forms Al3+ by losing 3 electrons (13 protons, 10 electrons).

The Periodic Table and Periodic Law

Development and Structure

• Mendeleev arranged elements by increasing mass and recurring properties (periodic law).

• Modern periodic table arranges elements by increasing atomic number.

• Elements with similar properties are in the same vertical columns (groups).

Classification of Elements

• Metals: Lower left, middle, and bottom of the table; good conductors, malleable, ductile, shiny, tend to lose electrons.

• Nonmetals: Upper right; poor conductors, not ductile or malleable, tend to gain electrons.

• Metalloids: Along the zigzag line; mixed properties, often semiconductors.

Groups and Periods

• Groups (columns): Elements with similar chemical properties.

• Periods (rows): Horizontal arrangement by increasing atomic number.

Group	Example Elements
8A (Noble Gases)	He, Ne, Ar, Kr, etc.
1A (Alkali Metals)(except H)	Li, Na, K, etc.
2A (Alkaline Earth Metals)	Be, Mg, Ca, etc.
6A (Chalcogens)	O, S, Se, etc.
7A (Halogens)	F, Cl, Br, I, etc.

Ions and the Periodic Table

Predicting Ion Charges

• Main-group metals form cations with charge equal to the group number.

• Main-group nonmetals form anions with charge equal to the group number minus eight.

• Transition metals can form multiple ions with different charges.

Example: AgCl is composed of Ag+ and Cl−; since the compound is neutral, Ag must be +1.

The Mole and Molar Mass

Counting Atoms by Weighing

• Atoms are counted by weighing because samples contain enormous numbers of particles.

• Atomic mass unit (amu) relates to grams via Avogadro’s number ($N_A = 6.02214 \times 10^{23}$).

The Mole Concept

• 1 mole (mol) = $6.02214 \times 10^{23}$ particles (Avogadro’s number).

• 1 mole of a substance with mass X amu has a mass of X grams (molar mass).

Example: The atomic mass of Na is 23 amu, so 1 mol Na = 23 g.

Converting Between Mass and Moles

• Molar mass (g/mol) is numerically equal to atomic mass (amu).

• Conversion formulas:

• To calculate mass from moles: $\text{mass (g)} = \text{moles} \times \text{molar mass (g/mol)}$

• To calculate moles from mass: $\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

• To calculate number of particles: $\text{number of particles} = \text{moles} \times N_A$

Example Calculations:

• How many moles of Na in 46 g? $46 \text{ g} \times (1 \text{ mol}/23 \text{ g}) = 2 \text{ mol}$

• How many Na atoms in 46 g? $2 \text{ mol} \times 6.022 \times 10^{23} = 1.204 \times 10^{24}$ atoms

Molar Mass of Molecules

• The molar mass of a molecule is the sum of the molar masses of all its atoms.

Example: Water (H2O): (2 × 1) + 16 = 18 g/mol

Practice Problems

• Calculate the molar mass of Ca(OH)2.

• Which sample has the greatest number of moles: 44.01 g CO2, 1.0 mol C2H6, 6.022 × 1023 molecules C2H6, 18.02 g H2O?

Additional info: All samples with 1 mole have the same number of particles (Avogadro’s number).