Moles, Avogadro’s Number, and Molar Mass in General Chemistry

Moles and Avogadro’s Number

Definition and Importance

The concept of the mole is central to chemical quantification, allowing chemists to count atoms, molecules, or ions by weighing them. The mole links the atomic scale to the macroscopic scale.

• 1 mole = $6.02 \times 10^{23}$ particles (Avogadro’s number)

• This number applies to atoms, molecules, ions, or formula units.

Examples

• 1 mole of Al contains $6.02 \times 10^{23}$ Al atoms.

• 1 mole of NaCl contains $6.02 \times 10^{23}$ NaCl molecules.

Moles of Elements in a Chemical Formula

Stoichiometry in Compounds

When dealing with compounds, the number of moles of each element can be determined from the chemical formula.

• Example: $1$mole of$$C_3H_4O_4$ molecules of $C_3H_4O_4$.

• Each mole of $C_3H_4O_4$ contains:

  • 3 moles of C

  • 4 moles of H

  • 4 moles of O

• General formula: $1 \text{ mole of compound} \times \frac{\text{number of moles of element}}{1 \text{ mole of compound}} = \text{moles of element}$

Molar Mass and Atomic Mass

Definition and Calculation

The molar mass of a substance is the mass of one mole of that substance, expressed in grams per mole (g/mol). For elements, it is numerically equal to the atomic mass listed in the periodic table.

• Molar mass of Ag: $107.9$ g/mol (from periodic table)

• Calculation: $\text{Molar mass} = \frac{\text{Total mass of sample}}{\text{Number of moles}}$

Calculating Number of Atoms from Moles

Conversion Process

To find the number of atoms in a given amount of substance, use Avogadro’s number as a conversion factor.

• Example: How many atoms of C are present in 0.448 mol C?

• Given: $12.01$ g $= 1$ mol C $= 6.02 \times 10^{23}$ C atoms

• Calculation: $0.448 \text{ mol C} \times \frac{6.02 \times 10^{23} \text{ C atoms}}{1 \text{ mol C}} = 2.70 \times 10^{23} \text{ C atoms}$

Summary Table: Key Quantities in Chemical Calculations

Quantity	Definition	Conversion Factor
Mole	Amount containing $6.02 \times 10^{23}$ entities	$1 \text{ mol} = 6.02 \times 10^{23}$ particles
Molar Mass	Mass of 1 mole of substance	From periodic table (g/mol)
Atoms/Molecules	Entities in a sample	$\text{mol} \times 6.02 \times 10^{23}$

Additional info:

• Atomic mass units (amu) are used for single atoms, while molar mass (g/mol) is used for bulk quantities.

• Stoichiometry allows calculation of the number of atoms, molecules, or ions in a given mass of substance.