Atoms, Moles, and Chemical Composition: Study Notes for Introductory Chemistry

Atoms and Atomic Mass

Definition and Properties of Atoms

An atom is the smallest unit of an element that retains the chemical properties of that element. Atoms of different elements have distinct masses and sizes, making direct counting impractical due to their extremely small mass.

• Atomic mass is typically measured in grams, but is extremely small for individual atoms.

• Example: Mass of a hydrogen atom = $1.67 \times 10^{-24}$ g; Mass of a carbon atom = $1.99 \times 10^{-23}$ g.

• Because atoms are so small, chemists use mass rather than counting individual atoms, similar to how a grocer sells rice by weight rather than by counting grains.

The Mole Concept

Definition of the Mole

The mole is a fundamental unit in chemistry used to express amounts of a chemical substance. It allows chemists to count atoms by weighing them.

• One mole of any substance contains $6.022 \times 10^{23}$ entities (Avogadro's number).

• Example: 12.01 g of carbon contains $6.022 \times 10^{23}$ atoms; 1.00 g of hydrogen contains $6.022 \times 10^{23}$ atoms.

• Therefore, one mole of anything = $6.022 \times 10^{23}$ of anything.

Mass of One Mole of Different Elements

Although one mole of any element contains the same number of atoms, the mass of one mole varies depending on the element.

• Example: 1 mole of sulfur (S) = 32.07 g; 1 mole of carbon (C) = 12.01 g.

• This difference is due to the varying atomic masses of elements.

Table: Average Mass of Each Element

Element	Number of atoms/mole	Average mass each atom (grams)/mole
Helium	6.022 × 1023 atoms	4.003 g
Carbon	6.022 × 1023 atoms	12.01 g
Potassium	6.022 × 1023 atoms	39.10 g
Neon	6.022 × 1023 atoms	20.18 g

Avogadro's Number

Definition and Application

Avogadro's number ($6.022 \times 10^{23}$) is the number of atoms, molecules, or particles in one mole of a substance. It is a fundamental constant in chemistry used for conversions between moles and number of particles.

• Example question: What is the correct value for Avogadro's number? Answer: $6.022 \times 10^{23}$.

Conversions Involving Moles, Mass, and Number of Particles

Converting Moles to Number of Atoms

To convert moles of an element to the number of atoms, multiply the number of moles by Avogadro's number.

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

• Example: $3.5 \text{ mol He} \times \frac{6.022 \times 10^{23} \text{ He atoms}}{1 \text{ mol He}} = 2.1 \times 10^{24} \text{ He atoms}$

Converting Number of Atoms to Moles

To convert the number of atoms to moles, divide the number of atoms by Avogadro's number.

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

• Example: $1.1 \times 10^{22} \text{ Ag atoms} \times \frac{1 \text{ mol Ag}}{6.022 \times 10^{23} \text{ Ag atoms}} = 1.8 \times 10^{-2} \text{ mol Ag}$

Molar Mass

The molar mass of an element is the mass of one mole of its atoms, expressed in grams per mole (g/mol). It is numerically equal to the atomic mass in atomic mass units (amu).

• Example: 32.07 g sulfur = 1 mol sulfur = $6.022 \times 10^{23}$ S atoms

• 12.01 g carbon = 1 mol carbon = $6.022 \times 10^{23}$ C atoms

• 6.94 g lithium = 1 mol lithium = $6.022 \times 10^{23}$ Li atoms

• The lighter the atom, the less mass in one mole of that atom.

Converting Between Grams and Moles

To convert mass (grams) to moles, divide the mass by the molar mass of the element.

• Formula: $\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g/mol)}}$

• Example: $57.8 \text{ g S} \times \frac{1 \text{ mol S}}{32.07 \text{ g S}} = 1.80 \text{ mol S}$

Additional info:

• These notes cover foundational concepts from Chapters 4, 5, and 6 of a typical introductory chemistry textbook, including atoms, moles, Avogadro's number, molar mass, and basic stoichiometric conversions.