Step 1: Understanding the Concept:
The empirical formula shows the simplest whole-number ratio of the different atoms present in a chemical compound.
We determine this ratio by converting mass percentages into relative moles for each element.
Step 2: Key Formula or Approach:
The number of moles for each element is calculated as \(\frac{\text{Percentage by mass}}{\text{Atomic mass}}\).
Then, we divide each mole value by the smallest calculated mole value to find the simplest ratio.
Step 3: Detailed Explanation:
Let us assume we have a 100 g sample, which means the percentages translate directly to grams.
Mass of C = 38.71 g.
Mass of H = 9.67 g.
Mass of O = 51.67 g.
We calculate the moles using standard atomic masses (C = 12 g/mol, H = 1 g/mol, O = 16 g/mol):
Moles of C = \(\frac{38.71}{12} \approx 3.22 \text{ mol}\).
Moles of H = \(\frac{9.67}{1} = 9.67 \text{ mol}\).
Moles of O = \(\frac{51.67}{16} \approx 3.22 \text{ mol}\).
Next, we divide each by the smallest mole value (3.22) to get the atomic ratio:
C ratio = \(\frac{3.22}{3.22} = 1\).
H ratio = \(\frac{9.67}{3.22} \approx 3\).
O ratio = \(\frac{3.22}{3.22} = 1\).
This results in a simple whole-number ratio of 1:3:1 for C:H:O.
Step 4: Final Answer:
The empirical formula of the given compound is CH\(_{3}\)O.