Empirical Formula and Molecular Formula

Empirical Formula shows the simplest whole-number ratio of the elements in a compound. Molecular Formula indicates the exact number of each type of atom in a molecule. It may be the same as the empirical formula or a multiple of it.

1.0Molecular Formula

• Represents the actual number of each type of atom present in a molecule.
• Uses subscripts to indicate the exact count of each atom in a molecule.
• Reflects the true composition of a compound, not simplified.
• The molecular mass (or molar mass) of a compound corresponds to a whole-number multiple of the empirical formula mass.
• Example: The molecular formula for glucose is C₆H₁₂O₆​, showing that each molecule contains 6 carbon, 12 hydrogen, and 6 oxygen atoms.

2.0Empirical Formula

The empirical formula of a compound represents the simplest whole-number ratio of atoms of each element present in the compound. It gives the relative number of atoms rather than the actual number in a molecule.

• Represents the simplest whole-number ratio of the elements in a compound.
• Provides a reduced or simplified version of the formula, focusing on the ratio, not the exact count.
• Known as the "simplest formula" because it only shows the basic proportional relationship between elements.
• The empirical formula is derived directly from the per cent composition of the compound.
• Example: The empirical formula for glucose is CH₂O, indicating the simplest ratio of carbon, hydrogen, and oxygen is 1:2:1.

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3.0Steps to Calculate the Empirical Formula

1. Determine the Mass of Each Element: Use the given data or assume a 100 g sample if percentages are provided.
2. Convert Mass to Moles: Use the formula: Moles of an element=Mass of the element (g)Atomic mass of the element (g/mol)$\text{Moles of an element}=\frac{\text{Mass of the element (g)}}{\text{Atomic mass of the element (g/mol)}}$Moles of an element=Atomic mass of the element (g/mol)Mass of the element (g)​
3. Find the Simplest Whole-Number Ratio: Divide all mole values by the smallest number of moles calculated.
4. Write the Empirical Formula: Use the ratio of moles as subscripts in the formula. If the ratios are not whole numbers, multiply by the smallest integer that converts them to whole number

Example

Glucose:

• Percent composition: C: 40%, H: 6.7%, O: 53.3%
• Empirical formula: CH₂O

Hydrogen Peroxide:

• Simplest ratio: HO

Solved Example 

1. Calculation of the Empirical Formula of Phosphoric Acid

Given Composition:

• Hydrogen (H): 3.06%
• Phosphorus (P): 31.63%
• Oxygen (O): 65.31%

Solution:

Assume 100 g of the compound:

• • This simplifies the percentages directly into masses:
  • • Mass of H = 3.06 g
    • Mass of P = 31.63 
    • Mass of O = 65.31 g

Calculate the number of moles for each element:

• Using the formula: $Moles=\frac{Mass}{AtomicMass}$
• • For H, Moles of H = (3.06)/1 =3.06
  • For P. Moles of P = (31.63)/31 = 1.02
  • For O, Moles of O = (65.31)/16 =4.08

Find the simplest ratio of moles:

• • Divide all the mole values by the smallest number of moles, 1.02
  • • Ratio of H = $\frac{3.06}{1.02}=3$
    • Ratio of P = $\frac{31.63}{1.02}=1$
    • Ratio of O = $\frac{65.31}{1.02}=4$

Write the empirical formula:

• Use these ratios as subscripts for the elements:
• • Empirical formula = H₃PO₄

Solved Example

1. Glucose:

Empirical formula: CH₂O

Empirical formula mass: 12+2(1)+16=30 g/mol

Molar mass: 180 g

n = 180/30 = 6

Molecular formula: C₆H₁₂O₆​

2. Hydrogen Peroxide:

Empirical formula: HO

Empirical formula mass: 1+16=17 g/mol

Molar mass: 34 g/mol

n = 34/17 = 2 

Molecular formula: H₂O₂

4.0Process to Determine the Molecular Formula from the Empirical Formula

Determine the Empirical Formula:

• Start with the per cent composition or the masses of each element in the compound.
• Convert these masses to moles.
• Find the simplest whole-number ratio of the elements, which gives you the empirical formula.

Calculate the Empirical Formula Mass:

• Add up the atomic masses of all the elements in the empirical formula. This gives you the empirical formula mass.

Determine the Molecular Weight (Molar Mass) of the Compound:

• The molar mass (usually given in the problem) is the actual mass of one mole of the compound.
• This value is needed to relate the empirical formula to the molecular formula.

Find the Integer Multiple (n):

• Use the formula: $n=\frac{MolecularWeight}{EmpiricalFormulaMass}$
• This integer n tells you how many times the empirical formula must be multiplied to obtain the molecular formula.

Calculate the Molecular Formula:

• Multiply each subscript in the empirical formula by the integer n.
• The result gives the molecular formula.

Solved Example

Empirical formula: CH₂

The molar mass of the compound: is 84 g/mol

Steps:

1. Empirical Formula Mass:

Carbon (C): 12 g/mol

Hydrogen (H): 2×1 g/mol = 2 g/mol

Empirical formula mass = 12+2 = 14 g/mol

2. Find the Integer Multiple n:
   $n=\frac{MolecularWeight}{EmpiricalFormulaMass}$

   n = 8414 = 6

3. Determine the Molecular Formula:

Multiply each subscript in CH₂ by 6.

Molecular formula: C₆H₁₂​.

5.0Differences Between Empirical and Molecular Formulas