**Imperial Formula**

The empirical formula is a representation of a molecule or compound that shows the simplest whole-number ratio of atoms present in the compound. It does not provide information about the actual number of atoms or the arrangement of atoms in the molecule. The empirical formula is determined through experimental data and can be derived from the percent composition of the compound or from the masses of the elements in the compound.

**Molecular Formula**

On the other hand, the molecular formula represents the actual number and types of atoms present in a molecule. It provides the exact composition and structure of the molecule. The molecular formula is derived from the empirical formula by determining the actual number of atoms in a molecule. It is either the same as or a multiple of the empirical formula.

**Difference between Empirical and Molecular Formula**

1. **Information Provided**
- Empirical Formula: It provides the simplest whole-number ratio of atoms in a compound.
- Molecular Formula: It provides the actual number and types of atoms in a molecule.

2. **Composition**
- Empirical Formula: It represents the relative ratios of different elements in a compound.
- Molecular Formula: It provides the exact composition of a molecule.

3. **Derivation**
- Empirical Formula: It is determined experimentally from the percent composition or by analyzing the masses of elements in the compound.
- Molecular Formula: It is derived from the empirical formula by determining the actual number of atoms present in a molecule.

4. **Multiple Forms**
- Empirical Formula: Different compounds can have the same empirical formula.
- Molecular Formula: Each compound has a unique molecular formula.

5. **Simplification**
- Empirical Formula: It represents the simplest form of a compound.
- Molecular Formula: It can be the same as the empirical formula or a multiple of it.

6. **Examples**
- Empirical Formula: The empirical formula of hydrogen peroxide is HO.
- Molecular Formula: The molecular formula of hydrogen peroxide is H2O2.

In conclusion, the empirical formula provides the simplest ratio of atoms in a compound, while the molecular formula gives the exact composition of a molecule. The empirical formula is derived from experimental data, while the molecular formula is derived from the empirical formula by determining the actual number of atoms in a molecule.