Molecular Formula

A chemical formula is a way of describing the information about the chemical proportions of atoms that make up a certain chemical compound or molecule. It uses the symbols of the chemical element and numbers, and also occasionally uses other symbols such as brackets, dashes, square brackets, commas, plus (+), and minus (-) signs. There are different types of chemical formulae like empirical formula, molecular formula, structural formula, and condensed formula. Let’s discuss the molecular formula and its calculation with examples in detail in this article.

What is Molecular Formula?

The molecular formula specifies the actual number of each type of atom in a molecule. For example, the molecular formula of benzene is C₆H₆, i.e., it is composed of six carbon and six hydrogen atoms. The molecular formula helps in determining whether a chemical compound is a binary compound, ternary compound, quaternary compound, or has even more elements depending upon the number of elements in a molecule. A molecular formula is always a multiple of the empirical formula, where an empirical formula for a chemical compound is defined as a simple expression that represents the ratio of the elements in the compound. For example, the molecular formula of hydrogen peroxide is H₂O₂, whereas its empirical formula is HO. We need the molar mass of a compound to find the molecular formula of a compound, and it is often derived after obtaining the empirical formula. Though molecular formulae are simple and easy to understand, they lack the knowledge concerning the atomic arrangement and bonding that is presented in a molecular formula. A molecular formula gives more information about a molecule than its empirical formula, however, it is more difficult to establish. 

Relation between Molecular Formula and Empirical Formula

The molecular formula specifies the actual number of each type of atom in a molecule, whereas an empirical formula for a chemical compound is a simple expression that represents the ratio of the elements in the compound. For example, the molecular formula of hydrogen peroxide is H₂O₂, whereas its empirical formula is HO. Here, the n-factor is 2. The empirical formula might be the same for different chemical compounds. For example, glucose, formaldehyde, and acetic acid have the same empirical formula, CH₂O, but their molecular formulae are different. For some chemical compounds, both formulae are the same, like water (H₂O), hypochlorous acid (HClO), formaldehyde (CH₂O), methane (CH₄), etc.

M = n × E

where,
M is the molecular formula
n is the ratio of molar mass and empirical formula mass
E is the empirical formula

How to Calculate Molecular Formula?

The molecular formula of a chemical compound can be found in the following ways:

Using Composition and Molecular Weight

Step 1: Multiply the molecular weight with the given component percentage. 

Step 2: Divide each value obtained by the atomic weight of that atom.

Step 3: Round off the obtained values to the closest whole number. Finally, write the molecular formula.

Example: A compound is composed of 82.78% nitrogen and 17.22% hydrogen. If its molecular weight is 17.031 g/mol, then find its molecular formula.

Solution:

Given data:

The molecular weight of a compound = 17.031 g/mol

Nitrogen percentage in the given compound = 82.78%

Hydrogen percentage in the given compound = 17.22%

Step 1: Multiply the molecular weight with the given component percentage.

Nitrogen = 17.031 × (82.78/100) = 14.0982

Hydrogen = 17.031 × (17.22/100) = 2.9327

Step 2: Divide each value obtained by the atomic weight of that atom.

Nitrogen: 14.0982/14.0067 = 1.00654

Hydrogen: 2.9327/1.00794 = 2.90960

Step 3: Round off the obtained values to the closest whole number.

Nitrogen: 1

Hydrogen: 3

Thus, the molecular formula of the given compound is NH₃.

Using Empirical Formula and Molecular Weight

Step 1: Calculate the empirical formula mass from the given empirical formula.

Step 2: Find the n-factor by using its formula. n = Molar Mass/Empirical Formula Mass

Step 3: Now, multiply all the subscripts in the empirical formula by n and the resultant formula is the required molecular formula.

Example: The empirical formula of a compound of carbon, hydrogen, and oxygen is HO. If its molar mass is 34.014 g/mol, then determine the molecular formula of the compound.

Solution:

Given data:

The empirical formula of a compound = CH2O

The molar mass of the compound = 60.052 g/mol

Step 1: First, let’s calculate the empirical formula molar mass.

Empirical formula molar mass (EFM) = 1.00794 + 15.9994

= 2.01588 + 31.9988

= 17.007 g/mol

Step 2: Now, divide the molar mass of the given compound by the empirical formula mass.

n = Molar mass/EMF = 60.052/17.007 = 2

Step 3: Molecular Formula = n × (Empirical formula)

So, the molecular Formula of the given compound = 2 × (HO) = H₂O₂

Hence, the molecular formula of the compound is H₂O₂.

Solved Examples on Molecular Formula

Example 1: A compound is composed of 68.29% carbon, 12.02% hydrogen, and 21.69% oxygen. If its molecular weight is 86.136 g/mol, then find its molecular formula.

Solution:

Given data:

The molecular weight of a compound = 86.136 g/mol

Carbon percentage in the given compound = 68.29%

Hydrogen percentage in the given compound = 12.02%

Oxygen percentage in the given compound = 21.69%

Step 1: Multiply the molecular weight with the given component percentage. 

Carbon = 86.136 × (68.29/100) = 58.8223

Hydrogen =86.136 × (12.02/100) = 10.3535

Oxygen = 86.136 × (21.69/100) = 18.6828

Step 2: Divide each value obtained by the atomic weight of that atom.

Carbon: 58.8223 /12.0107 = 4.8973 

Hydrogen: 10.3535/1.00794 = 10.2719

Oxygen: 18.6828/15.9994 = 1.1677

Step 3: Round off the obtained values to the closest whole number.

Carbon: 5

Hydrogen: 10

Oxygen: 1

Thus, the molecular formula of the given compound is C₅H₁₀O.

Example 2: Oxalic acid is composed of 27.42% carbon, 2.33% hydrogen, and 70.25% oxygen. If its molecular weight is 90.035 g/mol, then find its molecular formula.

Solution:

Given data:

The molecular weight of oxalic acid = 90.035 g/mol

Carbon percentage in oxalic acid = 27.42%

Hydrogen percentage in oxalic acid = 2.33%

Oxygen percentage in oxalic acid = 70.25%

Step 1: Multiply the molecular weight with the given component percentage.

Carbon = 90.035 × (27.42/100) = 24.6875

Hydrogen = 90.035 × (2.33/100) = 2.0978

Oxygen = 90.035 × (70.25/100) = 63.2496

Step 2: Divide each value obtained by the atomic weight of that atom.

Carbon = 24.6875/12.0107 = 2.0554

Hydrogen: 10.3535/1.00794 = 2.08127

Oxygen: 63.2496/15.9994 = 3.9532

Step 3: Round off the obtained values to the closest whole number.

Carbon: 2

Hydrogen: 2

Oxygen: 4

Thus, the molecular formula of the given compound is C₂H₂O₄.

Example 3: The empirical formula of a compound of carbon, hydrogen, and oxygen is CH₂O. If its molar mass is 60.052 g/mol, then determine the molecular formula of the compound.

Solution: 

Given data:

The empirical formula of a compound = CH₂O

The molar mass of the compound = 60.052 g/mol

First, let’s calculate the empirical formula molar mass.

Empirical formula molar mass (EFM) = 12.0107 + 2 × 1.00794 + 15.9994

= 30.026 g/mol

Now, divide the molar mass of the given compound by the empirical formula mass.

n = Molar mass/EMF = 60.052/30.026 = 2

Molecular Formula = n × (Empirical formula)

So, the molecular Formula of the given compound = 2 × (CH₂O) = C₂H₄O₂

Hence, the molecular formula of the compound is C₂H₄O₂.

Example 4: Boric acid is composed of 21.14% boron, 4.65% hydrogen, and 74.21% oxygen. If its molecular weight is 61.83 g/mol, then find its molecular formula.

Solution:

Given data:

The molecular weight of boric acid = 61.83 g/mol

Boron percentage in boric acid = 27.42%

Hydrogen percentage in boric acid = 4.65%

Oxygen percentage in boric acid = 68.79%

Step 1: Multiply the molecular weight with the given component percentage.

Boron = 61.83 × (21.14/100) = 13.0709

Hydrogen = 61.83 × (4.65/100) = 2.8750

Oxygen = 61.83 × (74.21/100) = 45.8840

Step 2: Divide each value obtained by the atomic weight of that atom.

Boron: 13.6891/10.811 = 1.209

Hydrogen: 2.2568/1.00794 = 2.8524

Oxygen: 32.2320/15.9994 = 2.8679

Step 3: Round off the obtained values to the closest whole number.

Boron: 1

Hydrogen: 3

Oxygen: 3

Thus, the molecular formula of the given compound is H₃BO₃.

Example 5: The empirical formula of a compound that is composed of hydrogen, chlorine, and oxygen is HClO. If its molar mass is 52.46 g/mol, then determine the molecular formula of the compound.

Solution:

Given data:

The empirical formula of a compound = HClO

The molar mass of the compound = 52.46 g/mol

First, let’s calculate the empirical formula molar mass.

Empirical formula molar mass (EFM) = 1.00794 + 35.453 + 15.9994

= 52.460 g/mol

Now, divide the molar mass of the given compound by the empirical formula mass.

n = Molar mass/EMF = 52.460/52.46 = 1

Molecular Formula = n × (Empirical formula)

So, the molecular Formula of the given compound = 1 × (HClO) = HClO

Here, the empirical formula and the molecular formula of the given compound are the same.

Hence, the molecular formula of the compound is HClO.

FAQs on Molecular Formula

Question 1: What is meant by a chemical formula?

Answer:

A chemical formula is a way of describing the information about the chemical proportions of atoms that make up a certain chemical compound or molecule. It uses the symbols of the chemical element and numbers, and also occasionally uses other symbols such as brackets, dashes, square brackets, commas, plus (+), and minus (-) signs. There are different types of chemical formulae like the empirical formula, molecular formula, structural formula, and condensed formula.

Question 2: Define molecular formula and give an example.

Answer:

The Molecular Formula specifies the actual number of each type of atom in a molecule. For example, the molecular formula of benzene is C₆H₆, i.e., it is composed of six carbon and six hydrogen atoms. We need the molar mass of a compound to find the molecular formula of a compound, and it is often derived after obtaining the empirical formula.

Question 3: What is the difference between the empirical formula and the molecular formula?

Answer:

• The molecular formula specifies the actual number of each type of atom in a molecule, whereas an empirical formula for a chemical compound is a simple expression that represents the ratio of the elements in the compound. 
• For example, the molecular formula of hydrogen peroxide is H₂O₂, whereas its empirical formula is HO. 
• The empirical formula might be the same for different chemical compounds. For example, glucose, formaldehyde, and acetic acid have the same empirical formula, CH₂O, but their molecular formulae are different. 
• For some chemical compounds, both formulae are the same, like water (H₂O), hypochlorous acid (HClO), formaldehyde (CH₂O), methane (CH₄), etc.

Question 4: What is the relationship between the empirical formula and the molecular formula?

Answer:

A molecular formula is always a multiple of the empirical formula and the relationship between the empirical formula and the molecular formula is given as follows:

Molecular Formula = n × (Empirical formula) (where n is a positive integer)

where “n” is the ratio of molar mass and empirical formula mass.

n = Molar Mass/Empirical Formula Mass

Question 5: What are the molecular formulae of glucose, dichlorine hexoxide, and dimethyl ether?

Answer:

Molecular formula of glucose = C₆H₁₂O₆

Molecular formula of dichlorine hexoxide = Cl₂O₆

Molecular formula of dimethyl ether = C₂H₆O.

Related Resources

• Molecular Weight
• Chemical Formula of Common Compounds
• Molar Mass