In Finding an Empirical Formula you weighed a strip of magnesium, burned it in a crucible, and weighed what was left. Two masses, a balance, and a burner — and out of that comes the formula of a compound you never saw made. That is worth stopping on. You did not look at the atoms. You counted them, indirectly, by weighing.
Empirical means the ratio, molecular means the molecule
Two different questions, two different answers, and they are often not the same answer.
The empirical formula is the simplest whole-number ratio of atoms in the compound. The molecular formula is the actual number of each kind of atom in one molecule.
Glucose is . Its atoms are in the ratio 1 : 2 : 1, so its empirical formula is — which is also the empirical formula of methanal, of ethanoic acid, and of several sugars that are not glucose. An empirical formula alone does not identify a compound, and that is not a flaw in the idea; it is the honest limit of what a mass measurement can tell you.
Two cases where the distinction disappears:
- Ionic compounds have no molecular formula at all, because they have no molecules. and are empirical formulas describing a lattice ratio, as Ionic and Covalent Bonding set out. There is nothing more to find.
- Some molecules are already at their simplest ratio. Water is both ways; there is no to reduce to.
The procedure
Everything below is one idea repeated: masses tell you nothing about ratios, and moles tell you everything. Sixteen grams of oxygen and sixteen grams of sulfur are not equal numbers of atoms. One mole of each is.
- Start with masses in grams. If you were given percentages instead, assume a 100 g sample — then every percentage is a mass in grams, and you have lost nothing, because the ratio does not depend on how much you have.
- Divide each element’s mass by that element’s molar mass. You now have moles of each.
- Divide every one of those mole values by the smallest of them. The smallest becomes 1 and the others become ratios to it.
- If any result is not close to a whole number, multiply all of them by the smallest factor that clears the fraction: 2 for a .5, 3 for a .33 or .67, 4 for a .25 or .75.
- Write the whole numbers as subscripts. That is the empirical formula.
- Given a molar mass for the real compound, divide it by the empirical formula mass and multiply every subscript by the whole number you get. That is the molecular formula.
Your magnesium result runs through it in four lines. Suppose 0.243 g of magnesium gave 0.403 g of oxide. The oxygen was not weighed directly — it came out of the air — so you get it by subtraction: 0.160 g.
Divide both by the smaller and you get 1 : 1. The formula is — which is also what the charges predict, with , so two completely independent methods agree. When that happens, believe the result.
A percentage example, for the more usual case. A compound is 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. Take 100 g:
Divide by 3.33 and you get 1 : 1.99 : 1, which is 1 : 2 : 1, so the empirical formula is .
From empirical to molecular
The empirical formula gives you the shape of the ratio. To get the real molecule you need one more piece of information from outside the mass data — the molar mass of the compound, which comes from a separate measurement.
For the compound above, has a molar mass of 30.03 g/mol. If a separate experiment says the compound’s molar mass is 180.16 g/mol, then
and the molecular formula is — glucose. Had the measured molar mass been 60.05, the multiplier would be 2 and the compound would be ethanoic acid instead. Same empirical formula, same percentage composition, different substance.
The multiplier is always a whole number, because a molecule contains a whole number of atoms. If you calculate 3.4, something is wrong with an input, and no amount of rounding will fix it honestly.
When the numbers are not whole
This is where the method gets a reputation for being fiddly, and the fiddliness is real. After dividing by the smallest, you will get something like 1.00, 1.33, 2.51. Deciding what those mean is a judgement call, so here is how to make it defensibly.
Round when you are within about 0.02. A ratio of 1.99 is 2. A ratio of 3.01 is 3. Measurement noise of that size is expected, and pretending otherwise produces absurd formulas like .
Multiply when you are near a familiar fraction. 1.50 is not 2 and must never be rounded to 2 — it is , so multiply everything by 2. Likewise 1.33 means multiply by 3, and 2.25 means multiply by 4. The check is that every value must become whole, not just the awkward one.
Stop and think when you are in between. A value of 1.6 is not near anything simple. That is the number telling you something went wrong upstream: a mass recorded incorrectly, an incomplete reaction, a product that absorbed water before it was weighed, or a sample that was not pure. Chasing it with a multiplier of 5 to force is how you end up defending a formula that does not exist.
Say what the data cannot support
If your magnesium oxide comes out at , the useful sentence is not “so the formula is ” and it is certainly not "". It is: “the ratio came out at 1 : 1.3, higher in oxygen than requires, which is consistent with some magnesium nitride forming as well since the crucible was open to the air.” That sentence gets full marks. The other two do not.
Drill the procedure in Empirical Formula Practice until the five steps run without you looking them up. Then Stoichiometry takes the formula you now trust and puts it through a balanced equation.
Curriculum connection
D3.3
explain the relationship between the empirical formula and the molecular formula of a chemical compound
Link to original
D2.4
determine the empirical formulae and molecular formulae of various chemical compounds, given molar masses and percentage composition or mass data [AI]
Link to original