3.3 Mass Percents and Empirical and Molecular Formulas

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How to Find the Empirical Formula from Mass Percent (3-Step Method)

General Chemistry 3.3

Lesson Overview

Empirical and molecular formulas represent two ways of expressing a compound's composition—one as the simplest whole-number ratio of atoms, the other as the exact count per molecule. Mass percent composition can be calculated from a known formula using a one-mole sample, or the process can be reversed to determine an empirical formula from mass percent data by assuming a 100-gram sample, converting to moles, and finding the lowest whole-number ratio. The molecular formula is then obtained by comparing the compound's molecular weight to the empirical formula weight.

2 Types of Chemical Formulas: Molecular vs. Empirical

Before diving into mass percent calculations, it helps to understand the distinction between a compound's molecular formula and its empirical formula.

TermDefinition
Mass PercentThe percentage by mass of each element in a compound
Molecular FormulaThe actual number of atoms of each element per molecule (e.g., P4O10)
Empirical FormulaThe most reduced whole-number ratio of atoms in a compound (e.g., P2O5)

The molecular formula tells you exactly how many of each type of atom appear in a single molecule. For tetraphosphorus decoxide, the molecular formula P4O10 indicates four phosphorus atoms and ten oxygen atoms per molecule.

The empirical formula, by contrast, gives the most reduced whole-number ratio between the atoms. Since 4 and 10 are both divisible by two, the empirical formula reduces to P2O5.

They're Often the Same

For many compounds, the molecular formula already is the lowest whole-number ratio. Propane (C3H8) is a good example: the 3:8 ratio cannot be reduced further, so the empirical and molecular formulas are identical.

CompoundMolecular FormulaEmpirical FormulaSame?
Tetraphosphorus decoxideP4O10P2O5No
PropaneC3H8C3H8Yes
GlucoseC6H12O6CH2ONo

Calculating Mass Percent from a Chemical Formula

Mass percent composition tells you what fraction of a compound's total mass comes from a particular element. The general formula is straightforward:

% Element = (grams of element / total mass) × 100

Consider a 300-gram sample of calcium carbonate (CaCO3). To find the percent carbon, you need to know how many of those 300 grams are actually carbon atoms. That requires some calculation—but there is a much easier approach.

Why a One-Mole Sample Size Works

Mass percent is an intensive property, meaning it does not depend on sample size. Whether you have 5 grams or 5 million grams of calcium carbonate, the mass percent of each element remains the same. This means you can choose any convenient sample size for your calculation.

The One-Mole Shortcut

When you know a compound's formula, choose a one-mole sample. One mole of CaCO3 weighs 100 g (Ca ≈ 40, C ≈ 12, O3 ≈ 48). That one mole contains exactly one mole of carbon (12 g), making the math trivially simple.

Example: Percent Carbon in CaCO3

Using a one-mole sample (100 g total):

% C = (12 g / 100 g) × 100 = 12%

One mole of CaCO3 contains one mole of carbon, which weighs 12 g. Divide by the molar mass (100 g) and multiply by 100.

Example: Percent Oxygen in CaCO3

One mole of CaCO3 contains three moles of oxygen (3 × 16 = 48 g):

% O = (48 g / 100 g) × 100 = 48%

The remaining 40% must be calcium, which you can verify: (40 g / 100 g) × 100 = 40%.

Quick Check

The mass percents of all elements in a compound must add up to 100%. For CaCO3: 40% (Ca) + 12% (C) + 48% (O) = 100%. If your percentages don't sum to 100, go back and check your work.

3-Step Method: Empirical Formula from Mass Percent

Now for the reverse process—and it is considerably more involved. Given mass percent data, you can determine a compound's empirical formula by working through three systematic steps.

Suppose a compound is 80% carbon and 20% hydrogen by mass. What is its empirical formula?

1 Assume a 100-Gram Sample

Since mass percent is an intensive property, you can pick any sample size. When converting from a formula to mass percents, a one-mole sample was ideal. But here you don't know the formula yet, so you can't predict what one mole weighs.

Instead, assume you have 100 grams of the compound. This makes the arithmetic trivial: 80% of 100 g is simply 80 g, and 20% of 100 g is simply 20 g.

Applying Step 1

80% carbon → 80 g of carbon

20% hydrogen → 20 g of hydrogen

2 Convert Grams to Moles

A chemical formula represents a mole-to-mole ratio, not a gram-to-gram ratio. You cannot simply look at 80 g of carbon and 20 g of hydrogen and call it a 4:1 ratio—that would be wrong.

Common Mistake

Students often skip this step, treating the gram ratio as the formula ratio. An 80:20 gram ratio (4:1) is not the same as C4H. You must convert to moles first because atoms of different elements have different masses.

Convert each element's mass to moles using its molar mass from the periodic table:

Applying Step 2

80 g C × (1 mol C / 12 g C) = 6.67 mol C


20 g H × (1 mol H / 1 g H) = 20 mol H

Now you have an actual mole-to-mole ratio: 6.67 mol carbon to 20 mol hydrogen.

3 Find the Lowest Whole-Number Ratio

The empirical formula requires whole-number subscripts, and 6.67 is clearly not a whole number. To fix this, divide both values by the smaller of the two numbers. This guarantees at least one subscript becomes 1.

Applying Step 3

C: 6.67 / 6.67 = 1


H: 20 / 6.67 = 3

Both values are whole numbers, giving the empirical formula CH3.

What If You Don't Get Whole Numbers?

Dividing by the smallest value guarantees one subscript equals 1, but the other might land on a fraction. In that case, do not round—multiply the entire ratio by the appropriate integer:

  • If you get a subscript of 0.5 (a half), multiply everything by 2
  • If you get 0.33 (a third), multiply everything by 3
  • If you get 0.25 (a quarter), multiply everything by 4

Example: Handling Non-Integer Results

If dividing produced C1H2.5, you would recognize the 0.5 as a half and multiply everything by 2, yielding C2H5.

If dividing produced C1H1.33, you would recognize the 0.33 as a third and multiply everything by 3, yielding C3H4.

Finding the Molecular Formula from the Empirical Formula

Mass percent data alone yields only the empirical formula. To determine the molecular formula, you need one additional piece of information: the compound's molecular weight (or molar mass).

The molecular formula is always a whole-number multiple of the empirical formula. To find that multiple, divide the actual molecular weight by the empirical formula weight.

Example: From CH3 to the Molecular Formula

The empirical formula CH3 has a formula weight of:

12 + 3(1) = 15 amu

If the molecular weight is 30 amu:

Multiplier = 30 / 15 = 2

Multiply every subscript by 2: CH3 × 2 = C2H6 (ethane).

The Multiplier Must Be a Whole Number

When you divide the molecular weight by the empirical formula weight, the result must come out to an integer (1, 2, 3, etc.). If it doesn't, double-check your empirical formula—something went wrong in a previous step.

Molecular Weight (amu)Multiplier (MW / 15)Molecular Formula
151CH3
302C2H6
453C3H9
604C4H12

Every possible molecular formula preserves that fundamental 1:3 carbon-to-hydrogen ratio from the empirical formula. The molecular weight simply tells you which multiple applies.

7 Key Takeaways

  1. The molecular formula gives the exact atom count per molecule; the empirical formula gives the lowest whole-number ratio. They are sometimes identical.
  2. Mass percent composition is an intensive property—it does not change with sample size. Use a one-mole sample when calculating mass percent from a known formula.
  3. To find the percent of an element: divide the element's mass contribution (in one mole) by the molar mass and multiply by 100.
  4. To find the empirical formula from mass percent: assume 100 g, convert grams to moles, then divide by the smallest mole value to get whole-number subscripts.
  5. If dividing produces a fractional subscript, do not round—multiply the entire ratio by the appropriate integer (2 for halves, 3 for thirds, etc.).
  6. To find the molecular formula, divide the molecular weight by the empirical formula weight. Multiply all empirical subscripts by that whole-number result.
  7. Always verify: mass percents should sum to 100%, and the molecular-to-empirical weight ratio should be a whole number.

3.2 Calculations with Moles

3.4 Limiting Reactant Calculations