3.1 Relative Atomic Mass and Relative Molecular Mass
Since individual atoms are extremely small and light, scientists measure atomic mass relative to a standard atom: Carbon-12.
Relative Atomic Mass ($A_r$)
The average mass of one atom of an element compared to $\frac{1}{12}$ of the mass of one atom of carbon-12.
$$A_r = \frac{\text{Average mass of one atom of the element}}{\frac{1}{12} \times \text{Mass of one atom of Carbon-12}}$$
Relative Molecular Mass ($M_r$) and Relative Formula Mass ($F_r$)
- Relative Molecular Mass ($M_r$): Sum of relative atomic masses of all atoms present in a covalent molecule (e.g., $M_r$ of $\text{H}_2\text{O} = (2 \times 1) + 16 = 18$).
- Relative Formula Mass ($F_r$): Sum of relative atomic masses of all atoms present in an ionic compound unit (e.g., $F_r$ of $\text{NaCl} = 23 + 35.5 = 58.5$).
3.2 The Mole Concept
A mole is the amount of substance that contains $6.02 \times 10^{23}$ elementary entities (atoms, molecules, or ions). This constant number is called the Avogadro Constant ($N_A$).
Relationships and Formulae
- Number of Particles:
$$\text{Number of particles} = \text{Number of moles } (n) \times N_A$$
- Molar Mass ($M$): Mass of one mole of a substance ($\text{g mol}^{-1}$), numerically equal to its $A_r$ or $M_r$.
$$\text{Mass (g)} = \text{Number of moles } (n) \times \text{Molar Mass}$$
- Molar Volume ($V_m$): Volume occupied by one mole of any gas at a specific condition.
- At Room Conditions (RTP): $24\text{ dm}^3\text{ mol}^{-1}$ ($24,000\text{ cm}^3\text{ mol}^{-1}$)
- At Standard Temperature and Pressure (STP): $22.4\text{ dm}^3\text{ mol}^{-1}$ ($22,400\text{ cm}^3\text{ mol}^{-1}$)
$$\text{Volume of gas } (\text{dm}^3) = \text{Number of moles } (n) \times \text{Molar Volume}$$
3.3 Chemical Formulae
A chemical formula represents the composition of elements in a compound.
Empirical Formula vs Molecular Formula
- Empirical Formula: The chemical formula that shows the simplest whole-number ratio of atoms of each element in a compound.
- Molecular Formula: The chemical formula that shows the actual number of atoms of each element present in a molecule of a compound.
$$\text{Molecular Formula} = (\text{Empirical Formula})_n, \quad \text{where } n = \frac{\text{Molar Mass}}{\text{Empirical Mass}}$$
Determining Empirical Formulae experimentally
- Method 1 (Combustion of reactive metals like Magnesium): Magnesium is heated strongly in a crucible with a lid. The lid is lifted periodically to let oxygen in while preventing white magnesium oxide smoke from escaping.
- Method 2 (Reduction of metal oxides like Copper(II) oxide): Dry hydrogen gas is passed over heated copper(II) oxide inside a glass tube. Suitable for unreactive metals below hydrogen in the reactivity series (e.g., CuO, PbO, FeO).
3.4 Chemical Equations
A chemical equation uses chemical symbols and formulae to represent a reaction, satisfying the Law of Conservation of Mass (atoms are neither created nor destroyed).
Steps for Stoichiometric Calculations
- Write a balanced chemical equation with correct state symbols: $(s)$, $(l)$, $(g)$, $(aq)$.
- Convert given quantitative values (mass, volume, or particle count) into moles ($n$).
- Use mole ratios derived from the coefficients in the balanced equation to find moles of the required substance.
- Convert the calculated mole value into the final requested unit (g, $\text{dm}^3$, or particle count).