Atoms, Elements, and the Foundations of Atomic Theory

Significant Figures in Measurements

Understanding Significant Figures

Significant figures are the digits in a measurement that are known with certainty plus one digit that is estimated. They reflect the precision of a measuring instrument and are crucial for reporting scientific data accurately.

• Markings and Estimation: The last digit in any measured value is estimated. For example, if a balance has markings every 1 g, a mass might be recorded as 12.5 g, where the '5' is estimated.

• Reading the Meniscus: When measuring liquid volume in a graduated cylinder, always read from the bottom of the meniscus at eye level. For example, a reading might be 4.56 mL.

Example: If a balance reads 1.27 g with markings every 0.1 g, the '7' is the estimated digit, indicating the measurement's precision.

Atoms and Elements

Learning Objectives

• Identify the mass laws that are the basis of modern atomic theory.

• Describe the experiments that led to the discovery of the electron and its charge.

• Explain the structure of an atom.

• Describe the properties of subatomic particles and interpret isotope symbols.

• Relate the periodic law to the organization of the periodic table.

• Predict the charge of ions.

• Determine the atomic mass of elements.

• Apply the mole concept.

Evolution of Atomic Theory

Early Ideas: Democritus and the Concept of the Atom

The concept of the atom dates back to ancient Greece. Democritus (c. 460–370 BCE) proposed that all matter is composed of tiny, indivisible particles called atomos, meaning "uncuttable." This idea laid the groundwork for modern atomic theory, although it was not widely accepted until much later.

• Atoms and Empty Space: Democritus believed that everything is made of atoms and empty space.

• Contrast with Aristotle: Aristotle and others believed matter was continuous and composed of four elements (fire, air, earth, water).

Dalton's Atomic Theory (John Dalton, 1766–1844)

Dalton's atomic theory, formulated in the early 19th century, provided a scientific basis for the concept of the atom and explained several fundamental laws of chemistry.

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

• All atoms of a given element are identical in mass and properties.

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

• Atoms of one element cannot change into atoms of another element in a chemical reaction; they only rearrange.

Mass Laws and Their Explanation by Dalton's Theory

Law	How Dalton's Theory Explains It
Law of Conservation of Mass	In a chemical reaction, matter is neither created nor destroyed.
Law of Definite Proportions	All samples of a given compound have the same proportions of their constituent elements.
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.

Examples of Mass Laws

• Law of Conservation of Mass: The total mass of reactants equals the total mass of products in a chemical reaction. For example, burning sugar ($C_6H_{12}O_6$) produces $CO_2$ and $H_2O$, and the total mass remains constant.

• Law of Definite Proportions: Water ($H_2O$) always contains hydrogen and oxygen in a mass ratio of 1:8. For 36 g of water, decomposition yields 32 g of oxygen and 4 g of hydrogen ($\frac{32}{4} = 8:1$).

• Law of Multiple Proportions: When elements combine in different ratios, they form different compounds. For example, carbon and oxygen form both $CO$ and $CO_2$.

Example Calculation: If you have 35.2 g of $CO_2$, how much oxygen is present?

• Mass ratio in $CO_2$: $\frac{32\ g\ O}{12\ g\ C} = 8:3$

• Total parts = 8 + 3 = 11

• Oxygen in 35.2 g $CO_2$: $35.2\ g \times \frac{8}{11} = 25.6\ g$

Structure of the Atom

Subatomic Particles

Atoms are composed of three main subatomic particles:

Particle	Symbol	Charge	Relative Mass
Proton	p+	+1	1
Neutron	n0	0	1
Electron	e-	-1	~0 (1/1836 of a proton)

• Protons define the element (atomic number, Z).

• Neutrons contribute to the mass but not the charge.

• Electrons determine chemical behavior and charge.

Isotopes

Isotopes are atoms of the same element (same number of protons) but different numbers of neutrons. They are represented as:

• Symbol: $^{A}_{Z}X$ where A = mass number (protons + neutrons), Z = atomic number (protons), X = element symbol.

• Example: Chlorine-35 ($^{35}_{17}Cl$) and Chlorine-37 ($^{37}_{17}Cl$) are isotopes of chlorine.

The Periodic Table

Organization and Periodic Law

The periodic table arranges elements by increasing atomic number and groups elements with similar properties into columns (groups or families). The periodic law states that properties of elements recur periodically when arranged by atomic number.

• Periods: Horizontal rows.

• Groups: Vertical columns with similar chemical properties.

Classification of Elements

• Metals: Located on the left and center. Shiny, malleable, ductile, good conductors of heat and electricity. Solid at room temperature (except Hg).

• Nonmetals: Upper right corner (plus hydrogen). Poor conductors, can be gases, liquids (Br), or solids (C, S, P).

• Metalloids: Border between metals and nonmetals. Exhibit properties intermediate between metals and nonmetals (e.g., Si, As).

Major Groups of the Periodic Table

Group	Common Name	Properties
1	Alkali Metals	Very reactive, soft, react with water
2	Alkaline Earth Metals	Reactive, but less so than group 1
17	Halogens	Reactive nonmetals, form salts with metals
18	Noble Gases	Unreactive, gases at room temperature

Atomic Mass and the Mole Concept

Atomic Mass

The atomic mass of an element is the weighted average mass of all its naturally occurring isotopes, measured in atomic mass units (amu).

• Calculation: $\text{Atomic mass} = \sum (\text{Fraction of isotope}) \times (\text{Mass of isotope})$

• Example: If an element has two isotopes: 70% at 10 amu and 30% at 11 amu, atomic mass = $0.70 \times 10 + 0.30 \times 11 = 10.3$ amu.

The Mole

The mole is a counting unit in chemistry, defined as the amount of substance containing as many entities (atoms, molecules) as there are atoms in exactly 12 g of carbon-12. This number is Avogadro's number ($6.022 \times 10^{23}$).

• 1 mole = $6.022 \times 10^{23}$ particles

• Molar mass: The mass of 1 mole of a substance, numerically equal to its atomic or molecular mass in grams.

Example: 1 mole of $H_2O$ has a mass of 18.02 g and contains $6.022 \times 10^{23}$ molecules.