The Mole and Avogadro’s Number - Chemistry

1. Fundamental Concepts

Mole (mol): One mole contains $6.022 \times 10^{23}$ particles (atoms, molecules, ions, etc.).

Avogadro’s Number ((N_A)): $6.022 \times 10^{23}, \text{mol}^{-1}$ , the number of particles in one mole of substance.

Molar Mass (M): The mass of one mole of a substance, in g/mol. It equals the relative atomic or molecular mass.

Relationship between amount of substance and number of particles:

$n = \frac{N}{N_A} \quad \text{or} \quad N = n \times N_A$
where (n) = moles, (N) = number of particles, (N_A) = Avogadro’s number.

Relationship between moles and mass:

$n = \frac{m}{M} \quad \text{or} \quad m = n \times M$ where (m) = mass in grams, (M) = molar mass in g/mol.

Combined usage: You can calculate number of particles, moles, or mass using these formulas.

Easy

1. Calculate the number of molecules in 2 mol of oxygen $O_2$ :

$N = n \times N_A = 2 \times 6.022 \times 10^{23} = 1.204 \times 10^{24} \text{ molecules}$

Medium

2. Calculate the number of atoms in 12 g of carbon $C$ :

$n = \frac{m}{M} = \frac{12}{12} = 1,\text{mol}$
$N = n \times N_A = 1 \times 6.022 \times 10^{23} = 6.022 \times 10^{23} \text{ atoms}$

Hard
3. Calculate the number of hydrogen atoms in 18 g of water $H_2O$ :

Moles of water: $n = \frac{18}{18} = 1 \text{ mol H}_2\text{O}$
Each molecule has 2 H atoms:

$N_H = 2 \times n \times N_A = 2 \times 1 \times 6.022 \times 10^{23} = 1.204 \times 10^{24} \text{ H atoms}$

1. Identify what is given: mass, moles, or number of particles.

2. Choose the right formula:

Moles → number of particles: $N = n \cdot N_A$

Mass → moles: $n = \frac{m}{M}$

Number of particles → moles: $n = \frac{N}{N_A}$

3. Check units: mass in grams, molar mass in g/mol.

4. Verify logic: particle numbers must be positive and reasonable.

5. Use chemical formula: multiply by the number of atoms in each molecule if needed.