Laws, Atoms and the Mole: Quick Revision

A brief note on Laws, Atoms and the Mole. Read it before a test. Try each question at the end before you open its answer.

The laws of chemical combination

• Conservation of mass (Lavoisier): the mass of the products equals the mass of the reactants.
• Definite proportions (Proust): one compound always has the same make-up by mass.
• Multiple proportions (Dalton): when two elements form several compounds, the masses of one that join a fixed mass of the other are in a small whole-number ratio.
• Gaseous volumes (Gay Lussac): reacting gases have volumes in a small whole-number ratio, at the same temperature and pressure.
• Avogadro's law: equal volumes of gases, at the same temperature and pressure, hold equal numbers of molecules.

Atoms and their masses

• Dalton: atoms of fixed mass join in fixed ratios and are only rearranged in reactions. Today we know atoms can be divided and an element can have isotopes.
• $1\ \text{u}$ is one twelfth of the mass of a carbon-12 atom, $1.66056 \times 10^{-24}$ g.
• Average atomic mass, with $m_i$ the mass of each isotope and $p_i$ its share in percent:
  • $\bar{A} = \dfrac{\sum m_i p_i}{100}$
• Molecular mass is the sum of the atomic masses in a molecule. For an ionic solid it is called formula mass.

The mole

• One mole is $6.022 \times 10^{23}$ particles, the Avogadro constant $N_A$.
• Molar mass in g/mol has the same number as the molecular mass in u.
• The two formulas:
  • $n = \dfrac{m}{M}$
  • $N = n \times N_A$
• Multiply by the atoms in one molecule to count atoms. The mass of one particle is $\dfrac{M}{N_A}$.

A worked example

How many molecules and atoms are in $6.846$ g of sucrose, $\text{C}_{12}\text{H}_{22}\text{O}_{11}$, of molar mass $342.30\ \text{g mol}^{-1}$?

1. Moles. $n = \dfrac{6.846}{342.30} = 0.02000$ mol.
2. Molecules. $0.02000 \times 6.022 \times 10^{23} = 1.204 \times 10^{22}$.
3. Atoms in one molecule. $12 + 22 + 11 = 45$.
4. Atoms. $45 \times 1.204 \times 10^{22} = 5.420 \times 10^{23}$.

Practice with new numbers

A program to try

The program counts the moles and the atoms in three everyday samples.

Mistakes to avoid

• Adding volumes of gases. Masses are conserved in a reaction. Volumes of gases are not.
• A plain average of isotopes. Weight each isotope by its share.
• Atoms or molecules? One mole of $\text{O}_2$ holds two moles of oxygen atoms.
• The atomic mass for a gas of molecules. Nitrogen gas is $\text{N}_2$, $28.02\ \text{g mol}^{-1}$.
• Dividing the wrong way. Moles are grams divided by grams per mole.

Check yourself

1. A chemist finds $27.3\%$ carbon in one sample of carbon dioxide and $30\%$ in another. What should she suspect?

2. Why is the atomic mass of chlorine $35.45$ u, when no chlorine atom has that mass?

3. How many moles of hydrogen atoms are in $2.00$ mol of methane, $\text{CH}_4$?

4. Which has more molecules, $1$ g of water or $1$ g of carbon dioxide?

5. Three volumes of hydrogen react with one volume of nitrogen. Using Avogadro's law, what is the ratio of the numbers of molecules?