Quick Summary
- RMM = sum of all atomic masses in a compound
- Uses carbon-12 as the standard (assigned value of 12)
- No unit because it is a ratio
- Used to find molar mass and perform stoichiometric calculations
- Essential for WAEC Chemistry calculations
Understanding Relative Molecular Mass
Relative molecular mass is one of the most important concepts in Chemistry. You use it in almost every calculation question in WAEC and NECO exams. It helps you convert between mass and moles, balance equations, and find percentage composition.
Think of relative molecular mass as a way to compare how heavy molecules are. Scientists needed a standard, so they chose carbon-12. They said one carbon-12 atom has a mass of exactly 12 units. Every other atom is compared to this standard.
For example, water is H₂O. To find its relative molecular mass, you add up the masses of all its atoms:
- Hydrogen has a relative atomic mass of 1
- Oxygen has a relative atomic mass of 16
- Water has 2 hydrogen atoms and 1 oxygen atom
- RMM of water = (2 × 1) + (1 × 16) = 18
Notice there is no unit. We do not say “18 grams” or “18 kilograms”. We just say 18. This is because relative molecular mass is a ratio. It compares one mass to another mass.
The Carbon-12 Standard
Why did scientists pick carbon-12? Carbon is common in nature and stable. It has 6 protons and 6 neutrons, giving it a mass number of 12. Scientists agreed to assign it a value of exactly 12 atomic mass units.
When we say hydrogen has a relative atomic mass of 1, we mean one hydrogen atom is about one-twelfth the mass of one carbon-12 atom. When we say oxygen has a relative atomic mass of 16, we mean one oxygen atom is about 16/12 times the mass of one carbon-12 atom.
This standard makes calculations easier. Everyone in the world uses the same reference point.
How to Calculate Relative Molecular Mass
Follow these simple steps:
Step 1: Write down the molecular formula of the compound.
Step 2: List each element and how many atoms of that element are in the formula.
Step 3: Look up the relative atomic mass of each element (you can find this on the periodic table or in your exam data sheet).
Step 4: Multiply the number of atoms by the relative atomic mass for each element.
Step 5: Add all the values together.
Example 1: Find the RMM of sulfuric acid (H₂SO₄)
- Hydrogen (H): 2 atoms × 1 = 2
- Sulfur (S): 1 atom × 32 = 32
- Oxygen (O): 4 atoms × 16 = 64
- RMM = 2 + 32 + 64 = 98
Example 2: Find the RMM of calcium carbonate (CaCO₃)
- Calcium (Ca): 1 atom × 40 = 40
- Carbon (C): 1 atom × 12 = 12
- Oxygen (O): 3 atoms × 16 = 48
- RMM = 40 + 12 + 48 = 100
Example 3: Find the RMM of ammonium sulfate ((NH₄)₂SO₄)
Be careful with brackets. The subscript outside the bracket applies to everything inside.
- Nitrogen (N): 2 atoms × 14 = 28
- Hydrogen (H): 8 atoms × 1 = 8
- Sulfur (S): 1 atom × 32 = 32
- Oxygen (O): 4 atoms × 16 = 64
- RMM = 28 + 8 + 32 + 64 = 132
Comparison: Relative Atomic Mass vs Relative Molecular Mass
| Feature | Relative Atomic Mass (RAM) | Relative Molecular Mass (RMM) |
|---|---|---|
| Applies to | Individual atoms | Molecules or compounds |
| Symbol | Ar | Mr |
| Example | Oxygen atom = 16 | Oxygen molecule (O₂) = 32 |
| Calculation | Read from periodic table | Sum of all atomic masses in formula |
| Unit | No unit (it is a ratio) | No unit (it is a ratio) |
Why Relative Molecular Mass Matters
You need RMM for many calculations in Chemistry:
1. Finding Molar Mass: The molar mass in grams per mole is numerically equal to the RMM. If water has RMM of 18, then one mole of water has a mass of 18 grams.
2. Converting Mass to Moles: Number of moles = mass ÷ molar mass. You cannot do this without knowing the RMM.
3. Percentage Composition: To find what percentage of a compound is a certain element, you need the RMM.
4. Stoichiometry: Balancing equations and finding how much product you get from reactants requires RMM calculations.
5. Empirical and Molecular Formulas: You need RMM to work out the actual formula of a compound from its empirical formula.
Common Exam Mistakes
WAEC examiners report these common errors year after year:
Mistake 1: Forgetting atoms in brackets. Students see (NH₄)₂ and only count one nitrogen and four hydrogens. The correct count is two nitrogens and eight hydrogens.
Mistake 2: Using wrong atomic masses. Always check your data sheet. Do not memorize atomic masses because exam questions may use slightly different values.
Mistake 3: Adding units. Students write “RMM = 98 g” or “98 amu”. This is wrong. RMM has no unit. It is just a number.
Mistake 4: Confusing relative atomic mass with relative molecular mass. Oxygen atom has RAM of 16. Oxygen molecule (O₂) has RMM of 32. Know the difference.
Mistake 5: Poor arithmetic. Simple addition errors cost marks. Double-check your calculations.
Practice Questions
Multiple Choice Questions
1. What is the relative molecular mass of calcium hydroxide, Ca(OH)₂? [Ca = 40, O = 16, H = 1]
- a) 57
- b) 58
- c) 74 ✓
- d) 114
Tip: Ca = 40, O = 16×2 = 32, H = 1×2 = 2. Total = 40 + 32 + 2 = 74
2. The relative molecular mass of a compound is 180. If the empirical formula is CH₂O, what is the molecular formula? [C = 12, H = 1, O = 16]
- a) CH₂O
- b) C₃H₆O₃
- c) C₆H₁₂O₆ ✓
- d) C₉H₁₈O₉
Tip: Empirical formula mass = 12 + 2 + 16 = 30. Molecular formula = 180 ÷ 30 = 6 times the empirical formula.
3. Which of the following has the highest relative molecular mass? [N = 14, H = 1, S = 32, O = 16, Cl = 35.5]
- a) NH₃
- b) H₂SO₄
- c) HCl
- d) H₂O
Answer: b) H₂SO₄ = 98 ✓
4. Relative molecular mass has no unit because it is:
- a) Too small to measure
- b) A ratio of two masses ✓
- c) Always equal to 12
- d) An arbitrary number
Essay Questions
1. (a) Define relative molecular mass. (2 marks)
(b) Calculate the relative molecular mass of the following compounds: (i) Sodium carbonate, Na₂CO₃ (ii) Ammonium nitrate, NH₄NO₃ [Na = 23, C = 12, O = 16, N = 14, H = 1] (4 marks)
(c) Explain why relative molecular mass has no unit. (2 marks)
Tips: For part (a), mention carbon-12 standard and sum of atomic masses. For part (b), show your working clearly. For part (c), explain it is a ratio.
2. (a) Distinguish between relative atomic mass and relative molecular mass. (4 marks)
(b) A compound has the empirical formula CH and a relative molecular mass of 78. Determine its molecular formula. [C = 12, H = 1] (3 marks)
(c) State two uses of relative molecular mass in Chemistry calculations. (2 marks)
Tips: For part (a), use a table format. For part (b), find empirical formula mass first (13), then divide 78 by 13 to get 6. Molecular formula = C₆H₆.
3. The relative molecular mass of hydrated copper(II) sulfate is 250. If the formula is CuSO₄.xH₂O, calculate the value of x. [Cu = 64, S = 32, O = 16, H = 1] (5 marks)
Tips: CuSO₄ = 64 + 32 + 64 = 160. Water molecules = 250 – 160 = 90. Each H₂O = 18. So x = 90 ÷ 18 = 5. Answer: x = 5 (the compound is CuSO₄.5H₂O).
Memory Aids
RMM Calculation Mnemonic: “Write List Look Multiply Add”
- Write the formula
- List each element and count atoms
- Look up atomic masses
- Multiply atoms by atomic mass
- Add everything together
Remember: RMM has NO UNIT because it is a RATIO.
Carbon-12: Think “C12” like a vitamin. It is the standard that keeps everything healthy in Chemistry calculations.
Related Topics
To deepen your understanding of relative molecular mass, explore these related Chemistry topics:
- Relative Atomic Mass: Learn how individual atoms are weighted against carbon-12
- The Mole Concept: Understand how RMM connects to molar mass and Avogadro’s number
- Empirical and Molecular Formulas: Use RMM to find actual molecular formulas
- Stoichiometry: Apply RMM in balancing equations and calculating yields
- Percentage Composition: Calculate what fraction of a compound is each element using RMM