Percent to moles to the smallest whole ratio
Treat the percentages as grams (assume 100 g), divide each by the element's atomic mass to get moles, then divide every mole value by the smallest one. The results are the subscripts. If any come out fractional, multiply them all up to whole numbers.
Worked example: 40.0% C, 6.7% H, 53.3% O
This is the composition of glucose. The four steps below give CH2O, its empirical formula.
| Element | Grams | ÷ atomic mass | Moles | ÷ smallest |
|---|---|---|---|---|
| Carbon | 40.0 | ÷ 12.01 | 3.33 | 1.00 |
| Hydrogen | 6.7 | ÷ 1.008 | 6.65 | 2.00 |
| Oxygen | 53.3 | ÷ 16.00 | 3.33 | 1.00 |
The smallest mole value is 3.33, so every column is divided by 3.33. The ratio 1 : 2 : 1 reads straight off as CH2O.
Turning a fractional ratio into whole numbers
A subscript that lands on a clear fraction is real, not a rounding error. Multiply the whole set by the number that clears it.
| Decimal ends in | Multiply all by | Example |
|---|---|---|
| .5 | 2 | 1 : 2.5 → 2 : 5 |
| .33 or .67 | 3 | 1 : 1.33 → 3 : 4 |
| .25 or .75 | 4 | 1 : 1.25 → 4 : 5 |
| .2, .4, .6, .8 | 5 | 1 : 1.2 → 5 : 6 |
Common atomic masses
- Use these values. C 12.01, H 1.008, O 16.00, N 14.01, S 32.06, Cl 35.45, Na 22.99, P 30.97, Fe 55.85. Small differences between sources are why a subscript can read 2.98 instead of 3.
- Check the percentages add up. They should total about 100%. If a compound lists only some elements, the remainder is usually oxygen.
- Watch the two easy mistakes. Rounding a real fraction (2.5) down to a whole number, and dividing by the wrong element in step three. Always divide by the smallest mole value, not the smallest mass.
Common questions
Why assume a 100 gram sample?
It makes each percentage equal a number of grams directly. 40% carbon becomes 40 grams, so you skip a conversion step. The final ratio is the same whatever sample size you pick.
What if the ratio comes out as 1 to 1.5?
Multiply every number by the same small whole number until they are all whole. A 1 to 1.5 ratio becomes 2 to 3 when you multiply by 2. Common cases: multiply .5 by 2, .33 or .67 by 3, .25 by 4.
Is the empirical formula the same as the molecular formula?
Not always. The empirical formula is the simplest whole-number ratio; the molecular formula is the real count of atoms and is always a whole multiple of it. Glucose is C6H12O6 but its empirical formula is CH2O. To find the molecular formula you also need the molar mass.
How close to a whole number is close enough to round?
Values like 2.98 or 3.03 come from rounding in the atomic masses and should be rounded to the whole number. But 2.5 or 2.33 are real fractions, not rounding noise, and must be cleared by multiplying.
