# 1.9.1 Empirical Formula for Molecular Formula

An empirical formula represents the simplest whole number ratio of various atoms present in a compound, whereas, the molecular formula shows the exact number of different types of atoms present in a molecule of a compound.

If the mass per cent of various elements present in a compound is known, its empirical formula can be determined. Molecular formula can further be obtained if the molar mass is known. The following example illustrates this sequence.

A compound contains 4.07% hydrogen, 24.27% carbon and 71.65% chlorine. Its molar mass is 98.96 g. What are its empirical and molecular formulas?

Step 1. Conversion of mass per cent to grams

Since we are having mass per cent, it is convenient to use 100 g of the compound as the starting material. Thus, in the 100 g sample of the above compound, 4.07g hydrogen, 24.27g carbon and 71.65g chlorine are present.

Step 2. Convert into number moles of each element Divide the masses obtained above by respective atomic masses of various elements. This gives the number of moles of constituent elements in the compound

Moles of hydrogen = 4.07 g / 1.008g = 4.04

Moles of carbon = 24.27g / 12.01g= 2.021

Moles of chlorine = 71.65g / 35.453g =2.021

Step 3. Divide each of the mole values obtained above by the smallest number amongst them

Since 2.021 is smallest value, division by it gives a ratio of 2:1:1 for H:C:Cl . In case the ratios are not whole numbers, then they may be converted into whole number by multiplying by the suitable coefficient.

Step 4. Write down the empirical formula by mentioning the numbers after writing the symbols of respective elements

CH2Cl is, thus, the empirical formula of the above compound.

Step 5. Writing molecular formula

• Determine empirical formula mass by adding the atomic masses of various atoms present in the empirical formula. For CH2Cl, empirical formula mass is 12.01 + (2 × 1.008) + 35.453 = 49.48 g
• Divide Molar mass by empirical formula mass = 98.96g / 49.48g = 2 = (n)
• Multiply empirical formula by n obtained above to get the molecular formula

Empirical formula = CH2Cl, n = 2. Hence molecular formula is C2H4Cl2.