Empirical and Molecular Formula

The empirical formula can be defined as the simplest ratio of the number of atoms involved in the formation of the compound. The chemical formula of any compound can be defined on the basis of two types of formula which include molecular formulas and empirical formulas. Both the empirical formula and a molecular formula represent the number and the identity of the atom. The molecular formula can be defined as the formula that gives the actual number of atoms involved in the compound. To have a clear understanding of the concept of empirical formula and molecular formula an example is mentioned below.

Example 

The molecular formula of glucose is C6H12O6, representing the actual number of atoms

The empirical formula for the compound is CH2O. It is because the simplest ratio of the atoms involved (carbon: hydrogen: oxygen) is 1: 2: 1. Thus making up the formula.

The general relationship between the molecular formula and empirical formula is defined as follows

Molecular Formula  = n × Empirical Formula

The empirical formula definition is “ formula representing the simplest ratio of the atoms of the compound”. The empirical formula of the compound gives us an idea about the percent composition of the atoms that make up the compound.

Calculation of Empirical Formula

Finding the empirical formula of a compound is based on the number of atoms involved in the formation of the compound. 

Example 1

Calculate the empirical formula of water.

Solution 

The molecular formula of water is H2O, the ratio of the atoms involved is calculated as 2:1. The empirical formula, in this case, is the same as the molecular formula H2O.

Example 2

Calculate the empirical formula of ethene

Solution-

The molecular formula of ethene is C2H4. the ratio of the atoms involved in the compound is 1:2. Thus the empirical formula is CH2.

Steps for Empirical Formula Calculation 

There are the following steps in the experimental calculation of the empirical formula.

1. Calculate the mass of each compound

2. Calculate the number of moles

3. Calculate the ratio of moles.

To have a better understanding of the calculation of empirical formula from mass following examples are mentioned below.

Example 1

The empirical formula of aluminium oxide, which has 1.08 g of aluminium combines chemically with 0. 96 g of oxygen.

Solution-

Mass of aluminium 1.08g

Mass of oxygen 0.96

Number of moles of = mass / atomic mass

No. of moles of aluminum = 1.08/ 27 

No. of moles = 0.04

Number of moles of oxygen = 0.96/ 16= 0.06

Ratio of Al moles = 0.04 / 0.04 = 1

Ratio of oxygen moles = 0.06 / 0.04 = 1.5

Since the ratio must contain the simplest whole number the ratio is 2:3, thus the empirical formula is Al2O3.

Calculation of Empirical Formula From the Percentage

Example- Calculate the Empirical Formula of the Phosphoric Acid with Composition Given as H, 3.06%; P, 31.63%; O, 65.31%

Solution- 

Mass of H= 3.06, the mass of P= 31.63, the mass of O= 65.31

The number of mole of H= 3.06 / 1 = 3.06

Number of moles of P= 31.63 / 31 = 1.02

Number of moles of O = 65.31 / 16 = 4.08

Ratio of moles H = 3.06 / 1.06 = 3

Ratio of mole of P = 1.06 / 1.06 = 1

Ratio of mole of O = 4.08 / 1.06 = 4

Thus the empirical formula of phosphoric acid is H3PO4

Calculation of Molecular Formulas from the Empirical Formula

As mentioned earlier there is a general relationship between the empirical and molecular formula represented by,

Molecular Formula  = n × Empirical Formula

The following example will help develop a better understanding of the relationship between empirical and molecular formula

Example 

Calculate the molecular formula of boron hydride. The empirical formula of the compound is BH3 and the molecular mass is 27.66

Solutions- 

The molecular mass = 27.66

The empirical formula mass = atomic mass of boron + 3 (atomic mass of hydrogen) 

 B + 3(H) = 10.81 + 3(1) = 13.81u

Since Molecular Formula  = n × Empirical Formula

n =  molecular formula mass / empirical formula mass = 27.66 / 13.81 = 2

Substituting the value in the general relation

Molecular formula = 2 ( BH3)

Molecular formula = B2H6

Difference between Empirical and Molecular Formula

The major difference between the empirical formula and the molecular formula is that the empirical formula represents the simplest ratio of atoms involved in the compound, whereas the empirical molecular formula represents the total number of atoms of an element present in the compound. The empirical formula represents the percentage of an element in the compound. 

Conclusion

The empirical formula is the type of chemical formula representing the simplest ratio of atoms that are involved in the chemical formula.  The general relation between both the empirical and molecular formula is, (Molecular Formula  = n × Empirical Formula). This can be used for finding both the empirical formula and the molecular m\formula of the compound. n in the relation represents the ratio of molecular mass and empirical mass of the compound. The main role of the empirical formula is in experimental chemistry it allows statisticians to determine the probable outcome when the complete data is not available.