Chemical analysis shows that citric acid contains 37.51% C, 4.20% H, and 58.29% . What is the empirical formula for citric acid?
The correct answer and explanation is:
To find the empirical formula of citric acid, begin by converting the percent composition into moles of each element. Assume a 100 g sample of citric acid. This simplifies the percentages into grams:
- Carbon (C): 37.51 g
- Hydrogen (H): 4.20 g
- Oxygen (O): 58.29 g
Now, convert each mass into moles using the molar mass of each element:
- Carbon: 37.51 g ÷ 12.01 g/mol ≈ 3.125 mol
- Hydrogen: 4.20 g ÷ 1.008 g/mol ≈ 4.167 mol
- Oxygen: 58.29 g ÷ 16.00 g/mol ≈ 3.643 mol
Next, divide each mole value by the smallest number of moles to determine the simplest whole-number ratio:
- C: 3.125 ÷ 3.125 = 1.000
- H: 4.167 ÷ 3.125 ≈ 1.333
- O: 3.643 ÷ 3.125 ≈ 1.166
These are not whole numbers. Multiply each ratio by a common factor to make them whole numbers:
- Multiply all by 3:
- C: 1.000 × 3 = 3
- H: 1.333 × 3 = 4
- O: 1.166 × 3 = 3.5
Oxygen is still not whole. Multiply everything again by 2 to eliminate the fraction:
- C: 3 × 2 = 6
- H: 4 × 2 = 8
- O: 3.5 × 2 = 7
So, the empirical formula of citric acid is C₆H₈O₇.
The empirical formula represents the simplest whole-number ratio of atoms in a compound. In this case, the ratio 6:8:7 is already in its simplest form. This empirical formula also happens to be the molecular formula of citric acid, which is a naturally occurring weak organic acid found in citrus fruits.