What is Empirical Formula and How is it Calculated

Chemists use a variety of notations to explain compounds and their compositions. One of such notations is the empirical formula. Other basic notations include molecular and structural formulas. All these notations use chemical symbols of elements along with numbers to summarize atomic constituents in compounds.

What is Empirical Formula and How is it Calculated

The empirical formula is the most basic and initial whole number ratio of atoms, given by combustion analysis. Benzene for say, has an empirical formula of CH, a molecular formula of C6H6, and a structural formula in which all its atoms are shown, bonded to each other.

What is an empirical formula?

The empirical formula gives the simplest whole number ratio of atoms in a compound. Unlike molecular formula, it is not unique as many different compounds or isomers can have the same empirical formulas. So, this means that the empirical formula does not give any idea about the actual arrangement or number of atoms.

When the question is about the number of atoms in a molecule, the molecular formula comes to mind. It gives the exact number of each type of atom present in a molecule. The molecular formula is more commonly used and it is a multiple of the empirical formula. The structural formula, on the other hand, shows the arrangement of atoms in a molecule.

Examples of empirical formulae

Empirical formulas of common compounds are given below:

  • Glucose,  CH2O
  • Sulfur dioxide,  SO2
  • Water,  H2O
  • Acetic acid,  CH2O
  • Benzene,  CH

How to calculate empirical formula?

In order to calculate the empirical formula of a compound, the mass composition of its elements must be known. For this purpose, combustion analysis tests are performed to determine the percentages of specific elements in a sample of a compound. However, percentage compositions are provided when doing stoichiometric calculations.

These are the steps that summarize the calculation of the empirical formula:

  1. First of all, the percentage compositions are written as the masses, such that, they sum up to become the mass of the whole compound.
  2. These masses are then converted into the number of moles by the formula (number of moles = mass of element / Molar mass).
  3. Now, mole ratios are determined by dividing the number of moles of each element by the least number of moles.
  4. These mole ratios are then rounded off to the nearest whole numbers, which show the subscripts of elements in the empirical formula.

This is how empirical formulas are made, using data from combustion analysis and some stoichiometric calculations.

The above four step calculation of empirical formula is used in the examples given below.

EXAMPLE 1: A compound was found to contain 32.65% sulfur, 65.3% oxygen, and 2.04% hydrogen. What is the empirical formula of the compound?

Step 1: Write the percentage compositions in grams.

Sulfur = 32.65 g

Oxygen = 65.3 g

Hydrogen = 2.04 g

Step 2: Divide these grams by individual molar masses to get number of moles.

Moles of sulfur = 32.65 g / 32 gmol   = 1.0203 moles

Moles of oxygen = 65.3 g / 16 gmol   = 4.08 moles

Moles of hydrogen =2.04 g / 1.008 gmol   = 2.024 moles

Step 3: Determine mole ratios by dividing individual moles by the smallest number of moles.

Sulfur has the least number of moles, so, divide all the mole values by 1.0203

1.0203 moles of S / 1.0203 = 1

4.08 moles of O / 1.0203 = 3.998 ≈ 4

2.024 moles of H / 1.0203 = 1.984 ≈ 2

Step 4: This rounded-off data is now written with each element to get the empirical formula.

H2SO4 is the required empirical formula.

How to determine empirical formula from molecular formula?

Empirical formulas can be found out, even when molecular formulas are given. A chemist has to follow the steps given below to get such empirical formulas.

  1. Take all the subscripts from the molecular formula.
  2. Reduce them to the simplest whole number ratio by dividing with the smallest subscript.

For example, we can calculate the empirical formula of glucose from a known molecular formula (C6H12O6) using the above two steps.

Step 1: Take all the subscripts from the molecular formula of glucose

C-H-O

6-12-6

Step 2: Reducing all numbers to the least whole numbers, we get

C1H2O1 (we don’t write 1 in the formula, so, the empirical formula of glucose is CH2O)

How to find molecular formula from empirical formula?

If the empirical formula of a compound is known (by classical techniques, like combustion analysis), the molecular formula can be found provided that the molar mass of the compound is also known. Chemists use mass spectrometer to find out the molar mass of compounds.

These are three simple steps to follow when determining molecular formula from the empirical formula:

  1. Calculate the empirical formula mass.
  2. Divide given molar mass by empirical formula mass. The result will be a whole number or close to a whole number. Round it off if needed.
  3. Multiply the resulting whole number with the subscripts in the empirical formula. The result is the molecular formula.

This method of molecular formula determination has been applied in the example given below.

EXAMPLE: The empirical formula of a compound of boron and hydrogen is BH3. Its molar mass is 27.7g/mol. Determine the molecular formula of the compound.

Step 1: Calculate empirical formula mass (EFM)

E.F.M of BH3 = 13.84g/mol

Step 2: Divide molar mass of BH3 with the empirical formula mass.

molar mass / EFM = 27.7 gmol /  13.84gmol

= 2

Step 3: Multiply all the subscripts in the empirical formula with the obtained whole number i.e. 2

B2H6 is the molecular formula.

The generalized expression for the above calculations is:

Molecular formula = n × empirical formula

where n is the multiplication factor determined by dividing molar mass by the empirical formula mass.

Related topics

Key Takeaway(s)

  • An empirical formula is a formula of a compound containing the simplest whole number ratio of atoms present in it.
  • The empirical formula is the first step in the determination of the molecular formula of an unknown or newly discovered compound.
  • Determination of the empirical formula just requires the percentage elemental composition of a compound.
  • Whether it’s the empirical formula or the molecular formula, the relative ratios of elements in a  compound remain the same.
  • M.F = n (E.F)

Concepts Berg

How do molecular and empirical formulas differ?

The molecular formula gives the exact number of atoms present in a molecule whereas the empirical formula shows the simplest whole number of ratio of atoms present in a molecule.

Why is the empirical formula used in chemistry?

The empirical formula can be determined easily after the percent mass of each element is found with the help of combustion analysis. However, the molecular formula cannot be determined for an unknown compound experimentally. The empirical formula is therefore like a stepping stone to finding the molecular formula.

Can empirical formula of two compounds be the same?

The empirical formula of two different compounds can be the same. For example, glucose and acetic acid have the same empirical formula of CH2O, etc.

Can molecular formula of two compounds be the same?

Since the molecular formula is unique for every compound, so, it cannot be the same for two different compounds.

Can a molecular formula be the same as empirical formula for a molecule?

Yes, the molecular and empirical formula for a molecule can be the same. For example, H2O is both the empirical and molecular formula of water. NaCl, HF, CaCl2, etc are other examples of compounds having the same molecular and empirical formulas.

Reference Book(s)

  • Basic Principles of Inorganic Chemistry: Making the Connections, by Brian Murphy, Clair Murphy, Brian J. Hathaway (School of chemical sciences, Dublin City University, Dublin 9, Ireland) and (The Chemistry Department, University College, Cork, Ireland)

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