How to Find Molecular Formula From Empirical Formula

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The empirical formula for a chemical compound is an expression of the relative abundances of the elements that form it. It isn't the same as the molecular formula, which tells you the actual number of atoms of each element present in a molecule of the compound. Different compounds with very different properties may have the same empirical formula. You can derive the molecular formula of a compound from its empirical formula only if you know the molar mass of the compound.

TL;DR (Too Long; Didn't Read)

If you know the empirical formula of a compound, you know the elements present in the compound and their relative proportions. Calculate the molar mass based on the formula and divide this into the mass of the actual compound. The division gives you a whole number. Multiply the subscript of each element in the empirical formula by this number to get the molecular formula for the compound.

How to Find the Empirical Formula

Chemists can determine the elements in a compound and their relative percentages by a chemical reaction with a known compound that produces products that they can collect and weigh. After doing so, they divide the mass of each element by its molar mass to determine the number of moles present in a particular amount – usually 100 grams. The number of moles of each element produces the empirical formula, which is the simplest expression of the elements present in a single molecule of the compound and their relative proportions.

Determining the Molecular Formula

The first step in determining the molecular formula of a compound is to calculate the empirical mass from its empirical formula. To do this, look up the mass of each element present in the compound, and then multiply that number by the subscript that appears after its symbol in the formula. Sum the masses to determine the molar mass represented by the formula.

The next step is to weigh a sample, then divide the empirical mass into the actual mass of the compound. This division produces a whole number. Multiply the subscripts in the empirical formula by this number to determine the molecular formula.

Examples

1. Analysis of a compound reveals it contains 72 g carbon (C), 12 g hydrogen (H) and 96 g oxygen (O). What is its empirical formula?

    Start by dividing the mass of each element present in the compound by the molar mass of that element to find the number of moles. The periodic table tells you the molar mass of carbon is 12 grams (ignoring fractions), that of hydrogen is 1 gram and that of oxygen is 16 grams. The compound therefore contains 72/12 = 6 moles carbon, 12/1 = 12 moles hydrogen and 96/16 = 6 moles oxygen.

    There are 12 moles of hydrogen but only 6 moles of carbon and oxygen, so divide by 6.

    The ratios of carbon to hydrogen to oxygen are 1 : 2 : 1, so the empirical formula is CH2O, which happens to be the chemical formula for formaldehyde.

    2. Calculate the molecular formula for this compound, given that the sample weighs 180g.

    Compare the recorded mass to that of the molar mass expressed by the empirical formula. CH2O has one carbon atom (12g), two hydrogen atoms (2g) and one oxygen atom (16g). Its total mass is thus 30 grams. However, the sample weighs 180 grams, which is 180/30 = 6 times as much. You therefore have to multiply the subscript of each element in the formula by 6 to get C6H12O6, which is the molecular formula for the compound.

    This is the molecular formula for glucose, which has very different properties than formaldehyde, even though they have the same empirical formula. Don't mistake one for the other. Glucose tastes good in your coffee, but putting formaldehyde in your coffee is likely to give you a very unpleasant experience.

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