Empirical Formula- Practice and Examples
What Is an Empirical Formula?
An empirical formula shows the simplest whole-number ratio of atoms in a compound. That's it. Nothing more, nothing less.
It doesn't tell you how many atoms are actually in a molecule. It tells you the ratio. If you want the actual molecular formula, you'll need the molar mass too—but that's a different problem.
For example:
- Benzene (C₆H₆) has empirical formula CH
- Glucose (C₆H₁₂O₆) has empirical formula CH₂O
- Water (H₂O) is already in its simplest form, so empirical formula = molecular formula
How to Find Empirical Formula: The Method
Here's the process, step by step. Memorize this.
Step 1: Get Mass Percent or Grams
If you're given percent composition, assume you have 100 grams of the compound. The percentages become grams directly.
Step 2: Convert Grams to Moles
Divide each mass by the element's atomic mass. Use:
Moles = Grams ÷ Atomic Mass
Step 3: Divide by the Smallest Number of Moles
Find which element has the fewest moles. Divide all mole values by that number.
Step 4: Round to Nearest Whole Number
If you get 1.9, round to 2. If you get 1.5, multiply everything by 2. If you get 1.25, multiply by 4.
Practice Problems with Solutions
Example 1: Finding Empirical Formula from Percent Composition
Problem: A compound is 40.0% C, 6.7% H, and 53.3% O. What is its empirical formula?
Step 1: Convert to grams (assume 100 g sample)
- C: 40.0 g
- H: 6.7 g
- O: 53.3 g
Step 2: Convert to moles
- C: 40.0 ÷ 12.01 = 3.33 mol
- H: 6.7 ÷ 1.008 = 6.65 mol
- O: 53.3 ÷ 16.00 = 3.33 mol
Step 3: Divide by smallest (3.33)
- C: 3.33 ÷ 3.33 = 1
- H: 6.65 ÷ 3.33 = 2
- O: 3.33 ÷ 3.33 = 1
Answer: C₁H₂O₁ or simply CH₂O
Example 2: Finding Empirical Formula from Combustion Analysis
Problem: Combustion of 0.255 g of a compound containing C, H, and O produces 0.561 g CO₂ and 0.306 g H₂O. Find the empirical formula.
Step 1: Find mass of C in CO₂
0.561 g CO₂ × (12.01 ÷ 44.01) = 0.153 g C
Step 2: Find mass of H in H₂O
0.306 g H₂O × (2.016 ÷ 18.02) = 0.0342 g H
Step 3: Find mass of O
0.255 g compound - 0.153 g C - 0.0342 g H = 0.0678 g O
Step 4: Convert to moles
- C: 0.153 ÷ 12.01 = 0.0127 mol
- H: 0.0342 ÷ 1.008 = 0.0339 mol
- O: 0.0678 ÷ 16.00 = 0.00424 mol
Step 5: Divide by smallest (0.00424)
- C: 0.0127 ÷ 0.00424 = 3
- H: 0.0339 ÷ 0.00424 = 8
- O: 0.00424 ÷ 0.00424 = 1
Answer: C₃H₈O
Example 3: Handling Decimals
Problem: A compound contains 48.8% C, 13.5% H, and 37.7% N. Find the empirical formula.
Converting to moles:
- C: 48.8 ÷ 12.01 = 4.06
- H: 13.5 ÷ 1.008 = 13.4
- N: 37.7 ÷ 14.01 = 2.69
Dividing by smallest (2.69):
- C: 4.06 ÷ 2.69 = 1.51
- H: 13.4 ÷ 2.69 = 4.98
- N: 2.69 ÷ 2.69 = 1
The 1.51 is close to 1.5, which means multiply everything by 2:
- C: 1.51 × 2 = 3.02 ≈ 3
- H: 4.98 × 2 = 9.96 ≈ 10
- N: 1 × 2 = 2
Answer: C₃H₁₀N₂
Empirical vs Molecular Formula
People mix these up constantly. Here's the difference:
| Feature | Empirical Formula | Molecular Formula |
|---|---|---|
| Definition | Simplest ratio | Actual number of atoms |
| Example (H₂O₂) | HO | H₂O₂ |
| Example (Benzene) | CH | C₆H₆ |
| Uses | Determining ratios | Knowing exact composition |
To find the molecular formula, you need the molar mass. Divide the molar mass by the empirical formula mass, then multiply all subscripts by that number.
Common Mistakes to Avoid
- Rounding too early: Wait until the very end. Rounding mid-calculation compounds errors.
- Forgetting to divide by smallest: Some students stop after finding moles. You must normalize the ratio.
- Atomic mass errors: Know your periodic table. Using wrong atomic masses gives wrong answers every time.
- Not checking if answer makes sense: Subscripts should be whole numbers. If you get 2.5, multiply by 2. If you get 1.33, multiply by 3.
- Confusing mass percent with mass: If given 25% and 75%, that's 25 g and 75 g in a 100 g sample—not 25 g and 75 g total.
Quick Reference: Atomic Masses
| Element | Atomic Mass | Common Element | Atomic Mass |
|---|---|---|---|
| H | 1.01 | O | 16.00 |
| C | 12.01 | N | 14.01 |
| S | 32.07 | Cl | 35.45 |
Getting Started: Your Turn to Practice
Work through these without looking at the answers first:
- A compound is 72.2% Fe and 27.8% O. Find the empirical formula. (Answer: Fe₂O₃)
- A compound with 85.7% C and 14.3% H. Find the empirical formula. (Answer: CH₂)
- A compound contains 43.6% P and 56.4% O. Find the empirical formula. (Answer: P₂O₅)
If you got those wrong, go back and check your division by the smallest mole value. That's where most errors happen.
Bottom Line
Finding empirical formulas is a three-step process: grams → moles → divide by smallest → round. That's the whole game. Get the moles right, divide correctly, and round only at the end. The problems vary in complexity, but the method never changes.