Atoms, Isotopes, and Atomic Mass: General Chemistry Study Notes (Worksheet Review)

Atoms and Atomic Structure

Modern View of Atomic Structure

The modern atomic theory describes atoms as the fundamental units of matter, composed of a nucleus containing protons and neutrons, surrounded by electrons in defined energy levels.

• Atoms consist of a dense nucleus (protons and neutrons) and electrons in orbitals.

• Protons are positively charged, neutrons are neutral, and electrons are negatively charged.

• The nucleus is extremely small compared to the overall size of the atom.

• Most of the atom's mass is concentrated in the nucleus.

• Electrons occupy most of the atom's volume.

Example: The atomic number (Z) of an element is equal to the number of protons in its nucleus.

Isotopes

Definition and Representation

Isotopes are atoms of the same element (same number of protons) that have different numbers of neutrons, resulting in different mass numbers.

• Isotopes are represented as AZ X, where X is the chemical symbol, Z is the atomic number, and A is the mass number.

• Isotopes of an element have identical chemical properties but different physical properties (e.g., mass).

Example: 126C and 136C are isotopes of carbon.

Atomic Mass and Moles

Atomic Mass Unit (amu) and Molar Mass

The atomic mass unit (amu) is a standard unit for expressing atomic and molecular masses. The molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol).

• 1 amu = $1.66054 \times 10^{-24}$ g

• 1 mole contains Avogadro's number ($6.022 \times 10^{23}$) of particles.

• The molar mass of an element (in g/mol) is numerically equal to its average atomic mass (in amu).

Example: The molar mass of carbon-12 is 12.00 g/mol.

Calculations Involving Atoms, Moles, and Mass

Conversions Between Mass, Moles, and Number of Atoms

To convert between mass, moles, and number of atoms, use the following relationships:

• Number of moles: $\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

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

• Mass from atoms: $\text{mass (g)} = \frac{\text{number of atoms}}{6.022 \times 10^{23}} \times \text{molar mass (g/mol)}$

Example: Calculate the mass of $1.00 \times 10^{23}$ atoms of lithium ($\text{molar mass} = 6.94$ g/mol): $\text{mass} = \frac{1.00 \times 10^{23}}{6.022 \times 10^{23}} \times 6.94$ g

Classification of Elements

Metals, Nonmetals, and Metalloids

Elements are classified based on their physical and chemical properties:

• Metals: Shiny, good conductors, malleable, ductile (e.g., sodium, magnesium).

• Nonmetals: Dull, poor conductors, brittle (e.g., sulfur, chlorine).

• Metalloids: Properties intermediate between metals and nonmetals (e.g., silicon).

Example: Silicon is a metalloid, magnesium is a metal, and sulfur is a nonmetal.

Tabular Data: Atomic Mass and Isotopes

Comparison Table of Elements and Isotopes

The following table summarizes the atomic mass and isotopic composition of selected elements:

Element	Average Atomic Mass (in amu)	Average Atomic Mass (in g)	Molar Mass (g/mol)
Hydrogen	1.008	1.6735 × 10-24	1.008
Carbon	12.01	1.994 × 10-23	12.01
Lithium	6.94	1.151 × 10-23	6.94
Additional info: Table entries inferred for illustration; actual worksheet may require completion by students.

Sample Calculations and Applications

Determining Number of Atoms and Mass

Sample problems often require determining the number of atoms in a given mass, or the mass of a given number of atoms.

• To find the number of atoms in 1 g of an element, divide 1 g by the molar mass to get moles, then multiply by Avogadro's number.

• To find the mass of a sample containing a known number of atoms, use the relationships above.

Example: How many atoms are in 2.40 g of sodium ($\text{molar mass} = 22.99$ g/mol)? $\text{moles} = \frac{2.40}{22.99} = 0.104$ mol $\text{atoms} = 0.104 \times 6.022 \times 10^{23} = 6.26 \times 10^{22}$ atoms

Additional info: Contextual Expansion

• Questions on the worksheet cover fundamental concepts in atomic theory, isotopes, atomic mass, and mole calculations, which are essential for understanding chemical reactions and stoichiometry.

• Students should be familiar with using the periodic table to find atomic numbers, mass numbers, and to classify elements.

• Practice with these calculations is critical for success in General Chemistry.