Stoichiometry – The Mole and the Avogadro Constant 🧪
What is a mole? 🔬
Think of a mole as a super‑big bag of marbles. Just as a bag might hold 12 marbles, a mole always holds exactly
\$6.022 \times 10^{23}\$ entities (atoms, molecules, ions, etc.). This number is called the Avogadro constant and is the same for every substance.
Molar Mass – The Weight of One Mole 📏
The molar mass is the mass of one mole of a substance. It is measured in grams per mole (g mol⁻¹). For example, the molar mass of water (H₂O) is:
\$M_{\ce{H2O}} = 2(1.008) + 15.999 \approx 18.015\ \text{g mol}^{-1}\$
The Core Formula – From Mass to Moles ➡️
The relationship between mass, molar mass and amount of substance is:
\$n = \frac{m}{M}\$
where:
- \$n\$ = number of moles (mol)
- \$m\$ = mass of the sample (g)
- \$M\$ = molar mass (g mol⁻¹)
Step‑by‑Step Example 🚀
How many moles of sodium chloride (NaCl) are in 58.44 g?
- Find the molar mass of NaCl:
- \$M_{\ce{Na}} = 22.99\$ g mol⁻¹
- \$M_{\ce{Cl}} = 35.45\$ g mol⁻¹
- \$M_{\ce{NaCl}} = 22.99 + 35.45 = 58.44\$ g mol⁻¹
- Apply the formula:
\$n = \frac{m}{M} = \frac{58.44\ \text{g}}{58.44\ \text{g mol}^{-1}} = 1.00\ \text{mol}\$
- Interpretation: 58.44 g of NaCl contains exactly one mole of NaCl, i.e., \$6.022 \times 10^{23}\$ NaCl formula units.
From Moles to Atoms – Using Avogadro's Number 🔢
To find the number of atoms or molecules:
\$N = n \times N_A\$
where \$N_A = 6.022 \times 10^{23}\ \text{mol}^{-1}\$.
Example: How many atoms of carbon are in 2.00 g of CO₂?
- Find \$M_{\ce{CO2}} = 12.01 + 2(15.999) = 44.01\$ g mol⁻¹.
- Calculate moles of CO₂:
\$n = \frac{2.00}{44.01} = 0.0455\ \text{mol}\$
- Each CO₂ molecule contains 1 carbon atom, so:
\$N_{\ce{C}} = 0.0455\ \text{mol} \times 6.022 \times 10^{23}\ \text{mol}^{-1} \approx 2.74 \times 10^{22}\ \text{atoms}\$
Exam Tips & Tricks 📚
- Always check units – the answer must be in moles, grams, or number of entities as required.
- Use the exact molar mass from the periodic table (not rounded) to avoid cumulative errors.
- Remember that \$N_A\$ is a constant – you can use \$6.02 \times 10^{23}\$ for quick estimates.
- When converting between mass and moles, keep the equation \$n = m/M\$ in mind; it’s the “backbone” of stoichiometry.
- Practice with real‑world examples (e.g., fuel consumption, battery capacity) to see how moles appear outside the lab.
Quick Reference Table 📊
| Quantity | Symbol | Units |
|---|
| Amount of substance | \$n\$ | mol |
| Mass | \$m\$ | g |
| Molar mass | \$M\$ | g mol⁻¹ |
| Avogadro constant | \$N_A\$ | mol⁻¹ |