How is molecular formula determined from empirical formula?

Short Answer

The molecular formula is determined from the empirical formula by comparing the molar mass of the compound with the empirical formula mass. First, the empirical formula mass is calculated. Then, the molar mass of the compound is divided by this value to find a whole number. Finally, the subscripts in the empirical formula are multiplied by this whole number to get the molecular formula.

This method helps chemists find the actual number of atoms present in a molecule. While the empirical formula gives only the simplest ratio, the molecular formula gives the complete and true composition of the compound.

Detailed Explanation

Determining Molecular Formula from Empirical Formula

The molecular formula provides the actual number of atoms of each element in a molecule. However, many compounds share the same empirical formula but have different molecular formulas. To determine the molecular formula, we must use the empirical formula along with the molar mass of the compound. This process allows chemists to move from a basic ratio of elements to the full chemical identity of a substance.

Step 1: Find the empirical formula

The empirical formula represents the simplest whole-number ratio of atoms in a compound. For example:

  • Empirical formula of glucose → CH₂O
  • Empirical formula of benzene → CH
  • Empirical formula of water → H₂O

The molecular formula is always a whole-number multiple of the empirical formula.

Step 2: Calculate empirical formula mass

To determine the molecular formula, the first required value is the empirical formula mass. This is found by adding the atomic masses of all atoms in the empirical formula.

Example: CH₂O

  • Carbon = 12
  • Hydrogen = 1 × 2 = 2
  • Oxygen = 16
    Empirical formula mass = 12 + 2 + 16 = 30 g

This mass is essential for comparing with the molar mass.

Step 3: Obtain the molar mass of the compound

The molar mass (molecular mass in grams per mole) is usually determined experimentally or given in the problem. It tells us how heavy one mole of the compound is.

For example, glucose has a molar mass of 180 g mol⁻¹.

Step 4: Divide molar mass by empirical formula mass

To find how many times the empirical formula is repeated in the molecular formula, we divide:

n = Molar mass ÷ Empirical formula mass

Where n must always be a whole number such as 1, 2, 3, 4, etc.

Example for glucose:

  • Molar mass = 180
  • Empirical formula mass = 30

n = 180 ÷ 30 = 6

This shows that the molecular formula contains 6 empirical units.

Step 5: Multiply the empirical formula by n

Finally, every subscript in the empirical formula is multiplied by the number n.

For glucose:

Empirical formula = CH₂O
n = 6

Molecular formula = C₆H₁₂O₆

This provides the actual number of atoms present in one molecule.

Worked Example

Suppose a compound has an empirical formula CH₃ and a molar mass of 30 g mol⁻¹.

Step 1: Calculate empirical formula mass
C = 12
H₃ = 1 × 3 = 3
Total = 15

Step 2: Divide molar mass by empirical mass
n = 30 ÷ 15 = 2

Step 3: Multiply empirical formula by n
(CH₃)₂ → C₂H₆

Thus, the molecular formula is C₂H₆, which is ethane.

Why this method works

An empirical formula only gives the simplest ratio of atoms. The real molecule could contain one, two, or more multiples of this ratio. The molar mass helps reveal how many empirical units fit inside one actual molecule. That is why dividing the molar mass by the empirical formula mass gives a whole number that completes the molecular formula.

Importance of determining molecular formula

Knowing the molecular formula is important because it:

  • Provides the actual number of atoms in a molecule
  • Helps calculate molecular mass accurately
  • Allows identification of the correct chemical structure
  • Helps in understanding the behaviour and properties of the compound
  • Distinguishes between compounds with similar empirical formulas but different molecular formulas

For example, CH₂O is the empirical formula for both glucose and formaldehyde, but glucose is C₆H₁₂O₆ and formaldehyde is CH₂O. Their properties are very different, so knowing the molecular formula is essential.

Applications in real chemistry

This method is used in:

  • Organic chemistry
  • Drug formulation
  • Chemical analysis
  • Forensic science
  • Environmental testing

Anytime chemists need the true molecular composition, they use empirical and molar mass data together.

Conclusion

The molecular formula is determined from the empirical formula by calculating the empirical formula mass, comparing it with the molar mass, and multiplying the subscripts of the empirical formula by the resulting whole number. This process gives the actual number of atoms in a molecule. It is a vital method that connects experimental data with the true chemical identity of a compound.