Experimenting for the formula of simple compounds

A chemical formula tells you the ratio of atoms in a compound. The empirical formula is that ratio written in its simplest whole-number form. For example, magnesium oxide is MgO — one magnesium atom for every one oxygen atom.

We cannot count atoms directly, but we can weigh them. By measuring the mass of each element in a compound and converting those masses to moles, we can work out the ratio of atoms — because moles are a way of counting particles.

The route every experiment follows:

1. Measure the mass of each element that combines.
2. Convert each mass to moles using $n = m / A_r$.
3. Divide both mole values by the smaller one to get the simplest ratio.
4. Round to whole numbers and write the formula.

Why "empirical"? It means "found by experiment". The formula comes from masses you measured at the bench, not from a textbook.

The standard experiment is to burn magnesium ribbon in a crucible so it reacts with oxygen from the air to form magnesium oxide:

$2\text{Mg} + \text{O}_2 \rightarrow 2\text{MgO}$

You cannot weigh the oxygen directly — it comes from the air. So you weigh the magnesium before and the magnesium oxide after, and find the oxygen by subtraction:

$\text{mass of oxygen} = \text{mass of magnesium oxide} - \text{mass of magnesium}$

The method, step by step.

1. Weigh the empty crucible and lid.
2. Add a coil of cleaned magnesium ribbon and weigh again → mass of Mg = (crucible + Mg) − (empty crucible).
3. Heat strongly with the lid on. Lift the lid occasionally with tongs to let more air (oxygen) reach the metal.
4. Keep heating until the magnesium has fully reacted (no more bright glow).
5. Allow to cool, then weigh the crucible + contents → mass of MgO.
6. Heat to constant mass: reheat, cool and reweigh; repeat until the mass no longer changes. This proves all the magnesium has reacted.

The two key practical points the lid solves at once:

• Lid down stops the white magnesium-oxide smoke escaping (which would lose product and make the mass too low).
• Lid lifted occasionally lets in fresh oxygen so the reaction can complete.

Once you have the masses, the calculation is always the same. Lay it out as a table — examiners reward clear working.

Worked example. A student burns 0.240 g of magnesium. The magnesium oxide formed has a mass of 0.400 g. Find the empirical formula. ($A_r$: Mg = 24, O = 16.)

Step 1 — find the mass of each element.

• Mass of Mg = 0.240 g.
• Mass of O = 0.400 − 0.240 = 0.160 g.

Step 2 — convert to moles ($n = m / A_r$).

	Magnesium	Oxygen
Mass (g)	0.240	0.160
$A_r$	24	16
Moles	0.240 / 24 = 0.010	0.160 / 16 = 0.010

Step 3 — divide both by the smaller value (0.010).

• Mg: 0.010 / 0.010 = 1.
• O: 0.010 / 0.010 = 1.

Step 4 — write the ratio and formula. Mg : O = 1 : 1 → empirical formula = MgO. ✓

What if the ratio isn't whole? Sometimes dividing gives values like 1 : 1.5 or 1 : 2.33. Multiply both numbers by a small whole number to clear the decimal:

• 1 : 1.5 → ×2 → 2 : 3.
• 1 : 2.33 → ×3 → 3 : 7.

Never round 1.5 down to 1 — that changes the compound.

Examiners love to ask why a result might be inaccurate, and whether the error makes the calculated mass of oxygen (and so the ratio) too high or too low. Be ready to reason in that direction.

Error	What happens	Effect on result
Lid lifted too much / off	White MgO smoke escapes	Mass of MgO too low → mass of O too low
Not heated to constant mass	Some Mg unreacted	Mass of MgO too low → too little oxygen
Magnesium not cleaned	Surface MgO already present, or oil	Starting mass wrong
Crucible cracks / spits	Product lost	Mass of MgO too low
Some Mg reacts with nitrogen in air	Forms magnesium nitride too	Not all mass gain is oxygen

Improving accuracy:

• Use an accurate balance (e.g. to two or three decimal places).
• Heat to constant mass so you know the reaction is complete.
• Keep the lid mostly on, lifting only briefly, to balance "let oxygen in" against "keep the smoke in".

A clean trick for the exam: if asked "why might the calculated mass of oxygen be lower than the true value?", the answer is usually "some magnesium oxide smoke escaped" or "not all the magnesium reacted".