Q.In the estimation of sulphur by the Carius method, 0.468 g of an organic sulphur compound gave 0.668 g of barium sulphate. Find out the percentage of sulphur in the given compound.

Empirical Formula Calculation: From Intuition to Precision

Imagine you have a jar of marbles — some red, some blue. You don't know how many marbles are in the jar, but you know that for every 2 red marbles, there are 3 blue ones. That ratio — 2:3 — is the simplest description of the mixture. It doesn't tell you the total count, but it captures the essential relationship between the two types.

That's exactly what an empirical formula does for a chemical compound. It tells you the simplest whole-number ratio of atoms of each element present in the compound.

The Core Idea

When a new compound is discovered, chemists first find out what elements are in it and in what proportions by mass. But mass alone doesn't tell you the atomic ratio — because different atoms have different masses. A gram of hydrogen contains far more atoms than a gram of carbon.

The empirical formula is the bridge from "how much mass of each element" to "how many atoms of each element, in the simplest ratio."

The Step-by-Step Process

Let's work through a concrete example. Suppose a compound is found to contain 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass.

Step 1: Assume 100 g of the compound. This converts percentages directly into grams. So we have:

• Carbon: 40.0 g
• Hydrogen: 6.7 g
• Oxygen: 53.3 g

Step 2: Convert each mass to moles. Use the atomic masses from the periodic table:

• Moles of C = $\frac{40.0 \text{ g}}{12.0 \text{ g/mol}} = 3.33 \text{ mol}$
• Moles of H = $\frac{6.7 \text{ g}}{1.0 \text{ g/mol}} = 6.7 \text{ mol}$
• Moles of O = $\frac{53.3 \text{ g}}{16.0 \text{ g/mol}} = 3.33 \text{ mol}$

Step 3: Divide each mole value by the smallest mole value. This normalises the ratio:

• C: $\frac{3.33}{3.33} = 1$
• H: $\frac{6.7}{3.33} \approx 2$
• O: $\frac{3.33}{3.33} = 1$

Step 4: If needed, multiply to get whole numbers. Here we already have 1:2:1, so the empirical formula is $CH_2O$.

Why This Works

The key insight is that moles directly count atoms. One mole of any element contains the same number of atoms ($6.022 \times 10^{23}$). So when you find the mole ratio, you're finding the atom ratio. Dividing by the smallest number just reduces that ratio to its simplest form.

Common Pitfalls …