Determine the empirical formula of an oxide of sulphur containing 60% of oxygen  [S = 32, O = 16 ]

Analysis

To find the empirical formula, we need to determine the simplest whole-number ratio of the atoms (Sulfur and Oxygen) present in the compound.

Concept

The empirical formula represents the ratio of elements in a compound by moles.

1. Assume a sample mass of 100g (this makes percentages equal to grams).
2. Calculate the number of moles for each element using the formula: $n = \frac{\text{mass}}{\text{molar mass}}$.
3. Divide each mole value by the smallest mole value obtained to get the simplest ratio.

Step-by-Step Solution

Step 1: Determine the mass of each element

• Total mass = 100g
• Oxygen (O) = 60% of 100g = 60g
• Sulfur (S) = 100% - 60% = 40% of 100g = 40g

Step 2: Calculate the number of moles

• Molar mass of S = 32 g/mol
• Molar mass of O = 16 g/mol

• Moles of S = $\frac{40}{32} = 1.25 \text{ mol}$
• Moles of O = $\frac{60}{16} = 3.75 \text{ mol}$

Step 3: Find the simplest ratio Divide both values by the smallest number (1.25):

• Ratio of S = $\frac{1.25}{1.25} = 1$
• Ratio of O = $\frac{3.75}{1.25} = 3$

The ratio of S to O is 1:3. Therefore, the empirical formula is SO$_3$.

Conclusion

The calculation confirms that for every 1 atom of Sulfur, there are 3 atoms of Oxygen.

Exam Tip: When calculating empirical formulas, if you get a decimal like 0.5, multiply the whole ratio by 2. If you get 0.33, multiply by 3. In this case, the division resulted in whole numbers, which is a great sign that your calculation is correct!