Moles [Higher Tier]

The mole

• Chemical amounts are measured in moles, symbol mol
• The mass of one mole of a substance in grams is numerically equal to its relative formula mass: one mole of water, $M_r = 18$, has a mass of 18 g
• One mole of any substance contains the same number of particles as one mole of any other: the Avogadro constant, $6.02 \times 10^{23}$ per mole
• Moles can count anything: atoms, molecules, ions, electrons, or the formula units in an equation. One mole of carbon has the same number of atoms as one mole of carbon dioxide has molecules

$$\text{moles} = \frac{\text{mass (g)}}{M_r} \qquad \text{mass} = \text{moles} \times M_r$$

• Worked example: moles in 11 g of carbon dioxide ($M_r = 44$): $\frac{11}{44} = 0.25$ mol
• Worked example: mass of 0.5 mol of sodium hydroxide ($M_r = 40$): $0.5 \times 40 = 20$ g
• Number of particles $=$ moles $\times \, 6.02 \times 10^{23}$. In 0.25 mol of $\text{CO}_2$ there are $1.5 \times 10^{23}$ molecules, and three times that many atoms