Chemistry 9701/12 — October/November 2021

Background Concept

An empirical formula gives the simplest whole-number ratio of atoms of each element in a compound. It is found by converting the mass (or percentage) of each element into moles, then dividing by the smallest number of moles to obtain integer ratios.

Understanding the Question

The question gives the percentage composition of compound X by mass: 40.0% carbon, 6.7% hydrogen and 53.3% oxygen. We are asked to determine the empirical formula, not the molecular formula. This means we only need the simplest ratio of C, H and O atoms.

Approach

Because percentages are relative masses, we can assume a convenient sample size, such as 100 g. Then the percentage of each element becomes its mass in grams. Convert each mass to moles by dividing by the relative atomic mass, and then simplify the mole ratio.

Step-by-Step Reasoning

1. Assume 100 g of compound X.

   • Mass of C = 40.0 g
   • Mass of H = 6.7 g
   • Mass of O = 53.3 g

2. Convert to moles using Ar values: C = 12, H = 1, O = 16.

   • Moles of C = 40.0 / 12 = 3.33
   • Moles of H = 6.7 / 1 = 6.7
   • Moles of O = 53.3 / 16 = 3.33

3. Divide each by the smallest value, 3.33.

   • C: 3.33 / 3.33 = 1
   • H: 6.7 / 3.33 = 2
   • O: 3.33 / 3.33 = 1

4. The simplest whole-number ratio is C : H : O = 1 : 2 : 1, so the empirical formula is CH2O.

Key Takeaways

• Percentages can be treated as masses by assuming a 100 g sample.
• The empirical formula is always the simplest whole-number ratio of atoms.
• The molecular formula is a whole-number multiple of the empirical formula, but it is not asked for here.

Common Mistakes

• Using the percentage values directly as mole ratios without dividing by relative atomic mass.
• Rounding 6.7 to 6 instead of recognising that 6.7 / 3.33 = 2 exactly.
• Choosing CH2O but then thinking the molecular formula is needed; the question only asks for the empirical formula.

Things to Be Careful About

• Always divide by the smallest number of moles, not by the smallest percentage.
• Check that the final ratio consists of whole numbers; if not, multiply all values by a common factor.
• Use the correct relative atomic masses: C = 12, H = 1, O = 16.