Atoms and Elements

Introduction

Cutting graphite into smaller pieces eventually yields individual carbon atoms.
Atoms compose all ordinary matter; understanding matter requires understanding atoms.

Modern Atomic Theory and the Laws

Atomic theory is based on observations and laws.
Key laws leading to the atomic theory:
- Law of conservation of mass
- Law of definite proportions
- Law of multiple proportions

The Law of Conservation of Mass

Formulated by Antoine Lavoisier.
States that matter is neither created nor destroyed in a chemical reaction.
The total mass of substances in a chemical reaction remains constant.
Consistent with the idea that matter is composed of indestructible particles.

The Law of Definite Proportions

Observations made by Joseph Proust in 1797.
Also known as the law of constant composition.
All samples of a compound have the same element proportions, regardless of source or preparation.
Example:
- Decomposition of 18.0 g of water yields 16.0 g of oxygen and 2.0 g of hydrogen.
- Oxygen-to-hydrogen mass ratio: $\frac{16.0 \text{ g O}}{2.0 \text{ g H}} = 8.0$ or 8:1

The Law of Multiple Proportions

Published by John Dalton in 1804.
When two elements (A and B) form two different compounds, the masses of element B that combine with 1 gram of element A can be expressed as a ratio of small whole numbers.
An atom of A combines with one, two, three, or more atoms of B (AB, AB2, AB3, etc.).
Example: Carbon monoxide and carbon dioxide
- In carbon dioxide, the mass ratio of oxygen to carbon is 2.67:1 (2.67 g of oxygen per 1 g of carbon).
- In carbon monoxide, the mass ratio of oxygen to carbon is 1.33:1 (1.33 g of oxygen per 1 g of carbon).
- The ratio of these two masses: $\frac{2.67}{1.33} = 2$

Dalton’s Atomic Theory

Explained the laws as follows:
1. Each element is composed of tiny, indestructible particles called atoms.
2. Atoms of a given element have the same mass and properties.
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, atoms only change how they are bound together.

Discovery of the Electron

J. J. Thomson (1856–1940) conducted cathode ray experiments using a cathode ray tube.
Cathode rays are beams of particles traveling from the negatively charged electrode (cathode) to the positively charged electrode (anode).
Properties of cathode ray particles:
- Travel in straight lines
- Independent of the material's composition
- Carry a negative electrical charge
Thomson measured the charge-to-mass ratio of the particles:
- $1.76 \times 10^{8} \text{ coulombs per gram}$
Thomson discovered the electron: a negatively charged, low-mass particle present within all atoms.

Millikan’s Oil Drop Experiment

Robert Millikan (1868–1953) deduced the charge of a single electron.
By measuring the electric field strength required to halt the free fall of oil drops, Millikan calculated the charge of each drop.
The measured charge was always a whole-number multiple of the fundamental charge:
- $1.60 \times 10^{-19} \text{ C}$
Knowing Thomson’s mass-to-charge ratio, the mass of an electron was deduced.

Structure of the Atom

J. J. Thomson proposed the plum-pudding model: negatively charged electrons held within a positively charged sphere.

Rutherford’s Gold Foil Experiment

Ernest Rutherford directed positively charged alpha particles at an ultra-thin sheet of gold foil to confirm Thomson's model.
Results:
- Most particles passed through the foil.
- Some particles were deflected; approximately 1 in 20,000 bounced back.
Rutherford proposed the nuclear theory of the atom:
1. Most of the atom’s mass and positive charge are in a small core called the nucleus.
2. Most of the atom's volume is empty space with dispersed, tiny, negatively charged electrons.
3. The number of negatively charged electrons outside the nucleus equals the number of positively charged particles (protons) within the nucleus, making the atom electrically neutral.

The Neutrons

James Chadwick demonstrated that the previously unaccounted for mass was due to neutrons.
Neutrons are neutral particles within the nucleus.
The mass of a neutron is similar to that of a proton but with no electrical charge.
Example: Helium (2 protons, 2 neutrons) is four times as massive as hydrogen (1 proton, no neutrons).

Subatomic Particles

Atoms are composed of:
- Protons
- Neutrons
- Electrons
Protons and neutrons have nearly identical masses.
- Mass of proton: $1.67262 \times 10^{-27} \text{ kg}$
- Mass of neutron: $1.67493 \times 10^{-27} \text{ kg}$
- Mass of electron: $0.00091 \times 10^{-27} \text{ kg}$
Protons and electrons have equal but opposite charges; neutrons have no charge.

Elements: Defined by Their Numbers of Protons

The number of protons in the nucleus defines the element.
The atomic number (Z) represents the number of protons.

Isotopes: When the Number of Neutrons Vary

Atoms of a given element have the same number of protons but may have different numbers of neutrons.
Isotopes are atoms with the same number of protons but different numbers of neutrons.
The natural abundance is the relative amount of each isotope in a naturally occurring sample.

Isotopes

The mass number (A) is the sum of protons and neutrons in an atom:
- $A = \text{number of protons (p)} + \text{number of neutrons (n)}$
Isotope notation: ${}_{Z}^{A}X$
- X is the chemical symbol, A is the mass number, and Z is the atomic number.
Example: Neon isotopes - ${}<em>{10}^{20}Ne$ , ${}</em>{10}^{21}Ne$ , ${}_{10}^{22}Ne$
Another common notation: Chemical symbol (or name) - mass number (e.g., Ne-20, neon-20).

Ions: Losing and Gaining Electrons

In a neutral atom, the number of electrons equals the number of protons.
Ions are charged particles formed when atoms lose or gain electrons.
- Cations: positively charged ions (e.g., Na+)
- Anions: negatively charged ions (e.g., F-)

Finding Patterns: The Periodic Law and the Periodic Table

In 1869, Mendeleev observed that elements with similar properties recurred in a periodic pattern when listed in order of increasing mass.
Periodic means exhibiting a repeating pattern.

The Periodic Law

When elements are arranged in order of increasing mass, certain sets of properties recur periodically.

Periodic Table

Mendeleev organized known elements in a table with elements of similar properties in the same vertical columns.
He predicted the existence of undiscovered elements, such as eka-silicon (later discovered as germanium).
In the modern table, elements are listed by increasing atomic number.

Classification of Elements

Elements are classified as:
- Metals
- Nonmetals
- Metalloids

Metals

Located on the lower-left side and middle of the periodic table.
Properties:
- Good conductors of heat and electricity
- Malleable (can be pounded into flat sheets)
- Ductile (can be drawn into wires)
- Often shiny
- Tend to lose electrons
Examples: Chromium, copper, strontium, and lead.

Nonmetals

Located on the upper-right side of the periodic table.
Varied properties:
- Some are solids (C, P, S, Se, I).
- One is a liquid (Br).
- Eleven are gases (H, He, N, O, F, Ne, Cl, Ar, Kr, Xe, Rn).
Properties:
- Poor conductors of heat and electricity
- Not ductile or malleable
- Gain electrons
Examples: Oxygen, carbon, sulfur, bromine, and iodine.

Metalloids

Also called semimetals.
Lie along the zigzag diagonal line.
Exhibit mixed properties.
Several are semiconductors due to intermediate electrical conductivity.

Periodic Table Divisions

Main-group elements: Properties are largely predictable based on their position.
Transition elements (or transition metals): Properties are less predictable.

Periodic Table Structure

Vertical columns are groups (or families).
Horizontal rows are periods.
18 groups and 7 periods.
Groups are numbered 1–18 (or A and B grouping).

Group Designations

Main-group elements: Columns labeled with a number and the letter A (1A–8A or groups 1, 2, and 13–18).
Transition elements: Columns labeled with a number and the letter B (or groups 3–12).

Noble Gases

Group 8A elements.
Mostly unreactive.
Example: Helium (chemically stable and safe for balloons), neon (electronic signs), argon (atmosphere component).

Alkali Metals

Group 1A elements.
Reactive metals.
Example: Sodium (explodes in water), lithium, potassium, and rubidium.

Alkaline Earth Metals

Group 2A elements.
Fairly reactive but less so than alkali metals.
Example: Calcium (reacts with water), magnesium, strontium, and barium.

Halogens

Group 7A elements.
Very reactive nonmetals.
Examples: Fluorine (pale-yellow gas), chlorine (greenish-yellow gas), bromine (red-brown liquid), iodine (purple solid).

Ions and the Periodic Table

Main-group metals tend to lose electrons, forming cations with the same number of electrons as the nearest noble gas.
Main-group nonmetals tend to gain electrons, forming anions with the same number of electrons as the nearest noble gas.
Alkali metals (1A) tend to lose one electron and form 1+ ions.
Alkaline earth metals (2A) tend to lose two electrons and form 2+ ions.
Halogens (7A) tend to gain one electron and form 1- ions.
Oxygen family nonmetals (6A) tend to gain two electrons and form 2- ions.
For main-group elements forming cations with predictable charge, the charge equals the A-group number.
For main-group elements forming anions with predictable charge, the charge equals the A-group number minus eight.
Transition elements may form various ions with different charges (e.g., Fe2+, Fe3+).

Atomic Mass

Also called atomic weight or standard atomic weight.
Found directly beneath the element's symbol on the periodic table.
Represents the average mass of the isotopes, weighted according to their natural abundance.
$Atomic \ mass = \sum<em>{n} (fraction \ of \ isotope</em>n \times mass \ of \ isotope_n)$

Example: Atomic Mass Calculation

Naturally occurring chlorine consists of 75.77% chlorine-35 (mass 34.97 amu) and 24.23% chlorine-37 (mass 36.97 amu).
Cl-35: $0.7577 \times 34.97 \text{ amu} = 26.4968 \text{ amu}$
Cl-37: $0.2423 \times 36.97 \text{ amu} = 8.9578 \text{ amu}$
Atomic mass of Cl: $26.4968 + 8.9578 = 35.45 \text{ amu}$

Mass Spectrometry

A technique used to determine the masses of atoms and molecules.

Molar Mass: Counting Atoms by Weighing

Chemicals processes happen between particles.
Chemists count atoms by weighing them.

The Mole: A Chemist’s “Dozen”

Units for counting large numbers:
- 1 dozen = 12 objects
- 1 gross = 144 objects
The chemist’s “dozen” is the mole (mol).
1 mole = $6.02214 \times 10^{23} \text{ particles}$
This number is Avogadro’s number.

The Mole

1 mole of anything corresponds to $6.02214 \times 10^{23}$
Value of the mole is equal to the number of atoms in exactly 12 grams of pure C-12.
$12 \text{ g C} = 1 \text{ mol C atoms} = 6.022 \times 10^{23} \text{ C atoms}$

Converting Between Number of Moles and Number of Atoms

Use the conversion factor: 1 mol atoms = $6.022 \times 10^{23} \text{ atoms}$

Converting Between Mass and Amount (Number of Moles)

Molar mass: The mass of 1 mole of atoms of an element.
An element’s molar mass in grams per mole is numerically equal to the element’s atomic mass in atomic mass units (amu).
Examples:
- 26.98 g aluminum = 1 mol aluminum = $6.022 \times 10^{23} \text{ Al atoms}$
- 12.01 g carbon = 1 mol carbon = $6.022 \times 10^{23} \text{ C atoms}$
- 4.003 g helium = 1 mol helium = $6.022 \times 10^{23} \text{ He atoms}$
Molar mass is the conversion factor between mass (in grams) and amount (in moles).
For carbon: $\frac{12.01 \text{ g C}}{1 \text{ mol C}}$