1. Overview
This topic introduces how chemists measure the mass of atoms and molecules. Because individual atoms are far too small to weigh on a scale, we use a relative scale to compare their masses against a standard (Carbon-12). This allows us to calculate exactly how much of a substance is needed or produced in a chemical reaction.
Key Definitions
- Relative Atomic Mass ($A_r$): The average mass of the isotopes of an element compared to 1/12th of the mass of an atom of $^{12}C$.
- Relative Molecular Mass ($M_r$): The sum of the relative atomic masses of all atoms present in a covalent molecule.
- Relative Formula Mass ($M_r$): The sum of the relative atomic masses of all atoms in the formula of an ionic compound.
- Isotope: Atoms of the same element with the same number of protons but different numbers of neutrons.
Core Content
Understanding Relative Atomic Mass ($A_r$)
Atoms are compared to the Carbon-12 isotope, which is assigned a mass of exactly 12 units.
- An atom of Hydrogen is 1/12th the mass of Carbon-12, so its $A_r = 1$.
- An atom of Magnesium is twice as heavy as Carbon-12, so its $A_r = 24$.
- $A_r$ values are found on the Periodic Table (the larger number in the element box).
Calculating Relative Molecular/Formula Mass ($M_r$)
To find the $M_r$, you add up the $A_r$ values of every atom in the chemical formula.
- For Covalent Molecules ($M_r$):
- Example: Water ($H_2O$)
- Contains 2 x H ($A_r = 1$) and 1 x O ($A_r = 16$)
- $M_r = (2 \times 1) + 16 = 18$
- For Ionic Compounds ($M_r$):
- Example: Magnesium Chloride ($MgCl_2$)
- Contains 1 x Mg ($A_r = 24$) and 2 x Cl ($A_r = 35.5$)
- $M_r = 24 + (2 \times 35.5) = 95$
Calculating Reacting Masses in Simple Proportions
In a balanced equation, the ratio of the masses of reactants and products is constant. You can use the total $M_r$ of each part of the equation to predict masses.
Worked Example: Calculate the mass of Magnesium oxide ($MgO$) produced when $48g$ of Magnesium ($Mg$) is burned in excess oxygen.
Step 1: Write the balanced equation. Magnesium + Oxygen → Magnesium oxide $2Mg(s) + O_2(g) \rightarrow 2MgO(s)$
Step 2: Calculate the relative masses for the substances involved.
- $2 \times Mg = 2 \times 24 = 48$
- $2 \times MgO = 2 \times (24 + 16) = 2 \times 40 = 80$
Step 3: Use simple proportions. The equation shows that $48g$ of Magnesium will produce $80g$ of Magnesium oxide.
- Answer: $80g$ of $MgO(s)$
Extended Content (Extended Only)
There is no supplement curriculum for this specific sub-topic (3.2).
Key Equations
| Equation | Meaning | Units |
|---|---|---|
| $M_r = \sum A_r$ | $M_r$ is the sum of all Relative Atomic Masses in the formula. | No units (Relative) |
| $\text{Mass Ratio} = \frac{\text{Mass A}}{\text{Mass B}}$ | The ratio of masses in a reaction is constant. | Grams ($g$) |
Common Mistakes to Avoid
- ❌ Wrong: Giving $A_r$ or $M_r$ units like grams ($g$).
- ✓ Right: These are "relative" values; they have no units.
- ❌ Wrong: Using the Atomic Number (the smaller number on the Periodic Table) instead of the Mass Number ($A_r$) for calculations.
- ✓ Right: Always use the larger number (the mass number) from the Periodic Table.
- ❌ Wrong: Forgetting to multiply by the subscript in a formula (e.g., saying $M_r$ of $O_2$ is 16).
- ✓ Right: Multiply the $A_r$ by the number of atoms (e.g., $M_r$ of $O_2$ is $16 \times 2 = 32$).
Exam Tips
- Command Words: If asked to "Calculate," always show your addition steps (e.g., $12 + (16 \times 2)$). This earns marks even if your final answer is wrong.
- Expected Questions: You will often be asked to find the $M_r$ of a compound containing brackets, such as Calcium hydroxide, $Ca(OH)_2$.
- Tip: Everything inside the bracket is multiplied by the small number outside.
- $M_r$ of $Ca(OH)_2 = 40 + [2 \times (16 + 1)] = 74$.
- Real-World Contexts: Questions often use the thermal decomposition of limestone ($CaCO_3$) to ask about reacting masses.
- $CaCO_3(s) \rightarrow CaO(s) + CO_2(g)$
- Remember that if a gas ($CO_2$) is produced, the mass of the solid will appear to decrease as the gas escapes.
- Periodic Table: You don't need to memorize $A_r$ values; they are always provided in the Periodic Table at the back of the exam paper. Use the specific values provided there (e.g., $Cl = 35.5$).