To find a molecular formula from an empirical formula, divide the compound’s molar mass by the empirical formula’s molar mass, then multiply every subscript in the empirical formula by the resulting whole number. The empirical formula shows the simplest whole-number ratio of atoms in a compound, while the molecular formula shows the actual number of atoms of each element in a molecule.
For example, the empirical formula of glucose is CH₂O, but its molecular formula is C₆H₁₂O₆. Both formulas describe the same relative proportions of carbon, hydrogen, and oxygen, but the molecular formula contains six times as many atoms of each element as the empirical formula.
The key to finding a molecular formula is knowing the compound’s molar mass in addition to its empirical formula. The empirical formula alone cannot determine the molecular formula because several compounds can share the same simplest atomic ratio while containing different numbers of atoms per molecule.
Understand the difference between empirical and molecular formulas
An empirical formula represents the simplest whole-number ratio of elements in a compound. It does not necessarily indicate the actual number of atoms present in an individual molecule.
For example, hydrogen peroxide has the molecular formula H₂O₂. Its empirical formula is HO because the ratio of hydrogen atoms to oxygen atoms, 2:2, simplifies to 1:1.
Similarly, benzene has the molecular formula C₆H₆, while its empirical formula is CH. The molecular formula indicates that each benzene molecule contains six carbon atoms and six hydrogen atoms. The empirical formula expresses the same composition as a simplified ratio of one carbon atom for every hydrogen atom.
A molecular formula, by contrast, gives the actual number of atoms of each element in a molecule. Its subscripts are whole numbers that specify the number of atoms present.
The relationship between the two formulas is straightforward: the molecular formula is always an integer multiple of the empirical formula for a compound with a defined molecular formula.
This relationship can be expressed as:
Molecular formula = (Empirical formula)ₙ
Here, n is a positive whole number. Finding the molecular formula means determining the value of n.
Find the molar mass of the empirical formula
Before calculating the multiplier, determine the molar mass of the empirical formula. Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol).
To calculate it, add the atomic masses of all the atoms represented in the empirical formula. Use the periodic table to obtain the atomic mass of each element.
For example, consider the empirical formula CH₂O. Its molar mass is calculated using the approximate atomic masses of carbon, hydrogen, and oxygen:
- Carbon: 1 × 12.01 = 12.01 g/mol
- Hydrogen: 2 × 1.008 = 2.016 g/mol
- Oxygen: 1 × 16.00 = 16.00 g/mol
Adding these values gives:
Empirical formula molar mass = 12.01 + 2.016 + 16.00 = 30.026 g/mol
The empirical formula CH₂O therefore has a molar mass of approximately 30.03 g/mol.
This value represents the molar mass of the simplest formula unit represented by the empirical formula. It is not necessarily the actual molar mass of the compound’s molecules.
Divide the molecular molar mass by the empirical formula molar mass
Once the empirical formula’s molar mass is known, divide the compound’s actual molar mass by that value.
The equation is:
n = Molecular molar mass ÷ Empirical formula molar mass
The result tells you how many times the empirical formula must be multiplied to produce the molecular formula.
For instance, suppose a compound has the empirical formula CH₂O and a measured molar mass of approximately 180.16 g/mol.
The empirical formula molar mass is approximately 30.03 g/mol. Therefore:
n = 180.16 ÷ 30.03 ≈ 6
Because the result is a whole number, the molecular formula contains six times as many atoms of each element as the empirical formula.
If the quotient is not close to a whole number, check the arithmetic, atomic masses, and measured molar mass. Experimental uncertainty and rounding can cause small deviations, but a valid molecular formula requires an integer multiplier.
Multiply every subscript by the whole-number multiplier
After determining n, multiply every subscript in the empirical formula by that number. If an element has no written subscript, its subscript is understood to be 1.
For the example above, the empirical formula is CH₂O and the multiplier is 6.
Apply the multiplier to each element:
- Carbon: 1 × 6 = 6
- Hydrogen: 2 × 6 = 12
- Oxygen: 1 × 6 = 6
The molecular formula is therefore C₆H₁₂O₆.
This is the molecular formula of glucose, a sugar found in living organisms and used by cells as an energy source.
Notice that every subscript must be multiplied by the same number. Multiplying only one element’s subscript or adding the multiplier to the subscripts would produce an incorrect formula.
Work through a complete example
Consider a compound with the empirical formula NO₂ and a molar mass of approximately 92.02 g/mol. The goal is to determine its molecular formula.
Step 1: Calculate the empirical formula molar mass.
The empirical formula contains one nitrogen atom and two oxygen atoms.
Using approximate atomic masses:
Nitrogen: 14.01 g/mol
Oxygen: 2 × 16.00 = 32.00 g/mol
Total empirical formula molar mass = 14.01 + 32.00 = 46.01 g/mol
Step 2: Calculate the multiplier.
Divide the compound’s molar mass by the empirical formula molar mass:
n = 92.02 ÷ 46.01 = 2
The multiplier is 2.
Step 3: Multiply each subscript by 2.
The empirical formula is NO₂.
Nitrogen: 1 × 2 = 2
Oxygen: 2 × 2 = 4
The molecular formula is N₂O₄.
This example demonstrates why an empirical formula does not always provide enough information to identify the actual molecular composition. The formula NO₂ expresses the simplest nitrogen-to-oxygen ratio, but N₂O₄ represents a molecule containing two nitrogen atoms and four oxygen atoms.
What if the empirical formula and molecular formula are the same?
Sometimes the multiplier is 1. This happens when the compound’s molar mass equals the empirical formula molar mass, within the precision of the measurements.
For example, water has the molecular formula H₂O. The subscripts cannot be reduced to a simpler whole-number ratio, so its empirical formula is also H₂O.
The empirical formula molar mass of H₂O is approximately 18.02 g/mol, which matches the molar mass of water. Dividing the two values gives a multiplier of approximately 1.
Therefore, the empirical formula and molecular formula are identical.
This outcome is entirely valid. Finding the molecular formula does not always mean increasing the subscripts.
What if the quotient is not a whole number?
The multiplier must be a positive whole number because a molecular formula represents a whole number of atoms in a molecule. A quotient such as 2.5 or 3.7 cannot be used directly as the multiplier.
If the quotient is not close to an integer, first check that the empirical formula is correct and fully simplified. Next, recalculate the empirical formula molar mass and verify that the compound’s molar mass is expressed in the appropriate units.
Also consider the precision of the given data. A measured molar mass may be rounded, so a quotient such as 2.99 may reasonably indicate a multiplier of 3.
If the quotient remains substantially different from a whole number, the supplied information may be inconsistent or insufficiently precise. Do not arbitrarily round a large discrepancy to the nearest integer.
In some cases, the empirical formula itself may have been incorrectly determined from experimental composition data. Revisiting the original calculation may resolve the problem.
Why the empirical formula alone is not enough
An empirical formula establishes the relative proportions of elements but does not reveal the total number of atoms in a molecule.
Consider the empirical formula CH. It could correspond to a molecular formula such as C₂H₂ or C₆H₆. Both formulas have a carbon-to-hydrogen ratio of 1:1, but their molecules contain different numbers of atoms and have different molar masses.
The empirical formula cannot distinguish between these possibilities because simplifying either molecular formula produces CH.
A molar mass provides the additional information needed to identify the appropriate multiplier. When the molar mass is known, the empirical formula and molar mass together generally allow the molecular formula to be determined.
However, not every substance is best described by a molecular formula. Ionic compounds, such as sodium chloride (NaCl), are typically represented by formula units that express the simplest ratio of ions in the solid rather than discrete molecules. For such substances, the empirical formula is generally the appropriate representation.
A reliable method to remember
Finding a molecular formula from an empirical formula requires three calculations:
- Calculate the empirical formula molar mass by adding the atomic masses of all the atoms represented in the formula.
- Divide the compound’s molar mass by the empirical formula molar mass to determine the whole-number multiplier.
- Multiply every subscript in the empirical formula by that multiplier to obtain the molecular formula.
The central principle is that the empirical formula gives the simplest atomic ratio, while the molar mass reveals how many times that ratio occurs in a molecule.
When both pieces of information are available and consistent, converting an empirical formula into a molecular formula is a straightforward process of calculating a molar mass, finding an integer multiplier, and applying it to every element in the formula.
