The Mole Concept, Molar Mass, and Molecular/Formula Mass in General Chemistry

The Mole Concept

Definition and Significance

The mole is the SI unit for the amount of a substance, used to count entities such as atoms, molecules, or ions. It provides a bridge between the atomic scale (amu) and the macroscopic scale (grams), allowing chemists to relate the number of particles to measurable quantities.

• Avogadro's number (NA): $6.022 \times 10^{23}$ particles per mole.

• Defined as the number of atoms in 12 grams of carbon-12.

• One mole of any substance contains Avogadro's number of entities.

• Avogadro's number is extremely large, reflecting the small size of atoms and molecules.

Key Equation:

$\text{Number of units} = \text{Number of moles} \times \frac{6.022 \times 10^{23} \text{ units}}{1 \text{ mol}}$

Example: Converting Molecules to Moles

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

• Example: How many moles of H2O are in a drop of water containing $1.67 \times 10^{21}$ molecules?

$1.67 \times 10^{21} \text{ H}_2\text{O molecules} \times \frac{1 \text{ mol H}_2\text{O}}{6.022 \times 10^{23} \text{ H}_2\text{O molecules}} = 2.77 \times 10^{-3} \text{ mol H}_2\text{O}$

Molar Mass

Definition and Calculation

Molar mass is the mass in grams of one mole of a substance. It serves as a conversion factor between the mass of a sample and the number of moles it contains.

• Units: grams per mole (g/mol)

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

• Example: Helium (He) has a molar mass of 4.003 g/mol; one atom of He = 4.003 amu.

Key Equation:

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

Relationship Between Mass, Moles, and Atoms

To convert between mass, moles, and number of atoms, use the molar mass and Avogadro's number as conversion factors.

• Mass (g) → Moles (mol) → Number of atoms

• Example: For aluminum (Al), $M_{Al} = 26.98$ g/mol

Conversion Example:

$16.2 \text{ g Al} \times \frac{1 \text{ mol Al}}{26.98 \text{ g Al}} \times \frac{6.022 \times 10^{23} \text{ atoms Al}}{1 \text{ mol Al}} = 3.62 \times 10^{23} \text{ atoms Al}$

Molecular Mass and Formula Mass

Definitions

• Molecular mass: The mass of one molecule of a molecular compound, calculated by summing the atomic masses of all atoms in the molecule according to its chemical formula.

• Formula mass: The mass of one formula unit of an ionic compound, calculated similarly by adding the atomic masses of the ions in the empirical formula.

Examples

• CO2 (Carbon dioxide): $12.01 + 2 \times 16.00 = 44.01$ amu/molecule

• NaCl (Sodium chloride): $22.99 + 35.45 = 58.44$ amu/formula unit

Practice Problems and Solutions

Calculating Molecular/Formula Mass

• KF (Potassium fluoride): $(1 \times 39.10) + (1 \times 19.00) = 58.10$ g/mol

• Glucose (C6H12O6): $(6 \times 12.01) + (12 \times 1.01) + (6 \times 16.00) = 180.18$ g/mol

• Fe2O3 (Iron(III) oxide): $(2 \times 55.85) + (3 \times 16.00) = 159.70$ g/mol

Summary Table: Conversions Between Mass, Moles, and Particles

Quantity	Conversion Factor	To
Mass (g)	1 mol / molar mass (g/mol)	Moles (mol)
Moles (mol)	Avogadro's number ($6.022 \times 10^{23}$) / 1 mol	Number of particles (atoms, molecules, ions)
Number of particles	1 mol / Avogadro's number ($6.022 \times 10^{23}$)	Moles (mol)

Key Terms

• Mole (mol): SI unit for amount of substance.

• Avogadro's number (NA): $6.022 \times 10^{23}$ particles/mol.

• Molar mass: Mass of one mole of a substance (g/mol).

• Molecular mass: Mass of one molecule (amu).

• Formula mass: Mass of one formula unit of an ionic compound (amu).

Additional info: The notes include a periodic table excerpt for reference atomic masses, which is essential for calculating molar and molecular masses.