## Empirical Formulas

The empirical formula of a compound is the formula which expresses only the relative number of atoms of each element in the compound. Empirical formulas are sometimes called ‘the simplest formulas’ , but because they are obtained from experimental data, they are usually called empirical formulas, and are useful to:

1. Determine the molecular mass (or weight) of compounds whose molecular masses have not been known.

2. Determine the molecular masses of compounds whose molecular masses are variable, even though they have a definite percentage composition (i.e., for different compounds formed from the same elements).

### To Determine Empirical Formula

To determine the empirical formula of a compound, we need to know:

1. The chemical composition of the compound - this is derived from experimental procedure, and can be expressed as percentage.

2. The relative atomic masses of the constituent elements.

Procedure: 1. From the chemical composition of the compound, and the relative atomic masses of the constituent elements given, convert the composition of each constituent element to number of moles.

2. Derive the mole ratio of the constituent elements.

3. Finally, express the mole ratio as the subscripts of the symbols of their respective element. The simplest formula obtained is the empirical formula.

Example: Analysis of carbon monoxide shows that it is 42.9% carbon and 57.1% oxygen. What is its empirical formula? (C=12, O=16) Solution: 1. Convert the percentage composition of each element to number of moles (consider each percentage as the mass).

Number of moles = mass (or % composition)/relative atomic mass

For carbon, 42.9/12 = 3.58

For oxygen, 57.1/16 = 3.58

2. Take the ratio of their moles:

C : O

3.58 3.58 = 1 : 1 3.

Express the above ratio as subscripts of the symbols of their respective element, we have C1O1 which is better expressed as CO - this is the empirical formula.

### To Determine Molecular Formula

The molecular formula of a compound is the formula expressing one mole of the compound. It can be derived from its empirical formula if the molecular mass (or weight) is known. The product of the mass of a compound from its empirical formula and a factor equals the molecular mass of the compound. From this equation, its molecular formula can be deduced.

Example: Determine the molecular formula of a compound of molecular weight 30 amu whose empirical formula is CH3 (C=12, H=1)

Solution: mass of the compound from its empirical formula = CH3 = 12+3(1) = 15

Product of mass of compound from empirical formula and a factor (x) equals the molecular weight.

xCH3 = 30

15x = 30

x = 30/15 = 2

Thus, 2CH3

Therefore, molecular formula = C2H6

Note: - Many compounds have empirical formulas that are the same as their molecular formulas, for example, CO2 is both the empirical and molecular formula for carbon(IV)oxide. Others have their empirical formulas different from their molecular formulas, example, when you see a formula like H2O2, C2H6 and C6H12O6, you are looking at a molecular formula, the empirical formula is HO, CH3 and CH2O respectively. - Different compounds can have the same empirical formula.

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