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.

The empirical formula gives us the simplest form of the ratio of atoms in a compound. For example, in glucose (C6H12O6), the empirical formula is CH2O, which indicates that for every carbon atom, there are two hydrogen atoms and one oxygen atom. The molecular formula, however, tells us the actual number of atoms in a molecule, which in the example of glucose is six carbons, twelve hydrogens, and six oxygens.

Think of a recipe for a cake. The empirical formula is like saying you need 1 cup of flour, 2 eggs, and 1 cup of sugar to make the cake (to get the simplest version). The molecular formula gives the exact amounts required for a specific cake, such as 3 cups of flour, 6 eggs, and 3 cups of sugar to serve a large gathering.

If the mass per cent of various elements present in a compound is known, its empirical formula can be determined.

To find the empirical formula from mass percentages, you first convert those percentages into grams (assuming 100 g of the compound). Then, divide the mass of each element by its atomic mass to get the number of moles. Once you have the number of moles for each element, divide each by the smallest number of moles to obtain the simplest ratio. Finally, use those ratios to write the empirical formula.

Imagine you are trying to create a new smoothie. If you have 40 g of strawberries, 20 g of bananas, and 40 g of yogurt, you would first determine how many 'parts' you have based on the smallest ingredient. Here, the banana is lowest (20 g), so you have a 2:1:2 ratio of strawberries to bananas to yogurt. Therefore, the smoothie recipe would be 2 parts strawberries, 1 part banana, and 2 parts yogurt.

Molecular formula can further be obtained if the molar mass is known.

Once the empirical formula is established, the next step is to calculate its empirical formula mass by adding up the atomic masses of the atoms in the empirical formula. Then, divide the compound's molar mass (the mass of one mole of the compound) by the empirical formula mass to find a whole number 'n'. Multiply the subscripts in the empirical formula by this number to get the molecular formula.

Imagine that after determining the smoothie recipe for a regular serving (one cup), you find that to serve a whole batch (12 cups), you need 12 times the amount of each ingredient. If your empirical recipe says 2 strawberries, 1 banana, 2 yogurts, by multiplying 2 by 12, 1 by 12, and 2 by 12, you find you'll need 24 strawberries, 12 bananas, and 24 yogurts for your party.

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?

To solve the problem, we first treat the percentages as grams. We then calculate moles: for hydrogen, 4.07 g / 1.008 g/mol = 4.04 moles; for carbon, 24.27 g / 12.01 g/mol = 2.02 moles; for chlorine, 71.65 g / 35.453 g/mol = 2.02 moles. Dividing all by the smallest (2.02) gives us a ratio of 2:1:2. Thus, the empirical formula is C1H2Cl2. Next, we find the empirical formula mass (49.48 g), divide the molar mass (98.96 g) by the empirical formula mass to get n = 2, giving us C2H4Cl2 as the molecular formula.

Consider making a fruit salad with a mix of fruits. The percentages you started with tell you how much fruit to use; when you mix it all together in larger quantities for a party, you're applying the same ratios on a larger scale, just like finding the molecular formula after establishing the empirical ratio.

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