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Empirical Formula
Solving Empirical Formula Problems There are two common types of empirical formula problems. Luckily, the steps to solve either are almost exactly the same. Example #1: Given mass % of elements in a compound.

A compound was found to contain 32.65% Sulfur, 65.3% Oxygen and 2.04% Hydrogen. What is the empirical formula of the compound?

1) The first step in this problem is to change the % to grams.
32.65%→32.65g of S
65.3%→65.3g of O
2.04%→2.04g of H

2) Next divide all the given masses by their molar mass.
32.65g of S/ 32gm-1 = 1.0203 moles of S
65.3g of O/ 16gm-1 = 4.08 moles of O
2.04g of H/ 1.008gm-1 = 2.024 moles of H

3) Then, pick the smallest answer in moles from the previous step and divide all the answers by that. Remember that if you calculate a number that is x0.9 round to the nearest whole number
1.0203 moles of S/ 1.0203 = 1
4.08 moles of O/1.0203 = 3.998 ≈ 4
2.024 moles of H/1.0203 = 1.984 ≈ 2

4) Lastly, the coefficients calculated in the previous step will become the subscripts in the chemical formula.
S = 1
O = 4
H = 2

H2SO4

Example#2: Given the mass of a reactant before a chemical reaction and the mass of a product after a reaction.

When 0.273g of Mg is heated in a Nitrogen (N2) environment a chemical reaction occurs. The product of the reaction is 0.378g . Calculate the empirical formula.

1) In any empirical formula problem you must first find the mass % of the elements in the compound. Since the total mass of the final product was 0.378 we find that:

0.378g total-0.273g magnesium = 0.105g nitrogen

0.105g nitrogen/0.378g total (100) = 27.77%

0.273g magnesium/0.378g total (100) =72.23%

2) Then change the % to grams
27.77%→27.77g of N
72.23%→72.23g of Mg

3) Next, divide all the masses by their respective molar masses.
27.77g/14gm-1 = 1.98 moles N
72.23g/24.31gm-1 = 2.97 moles Mg

4) Pick the smallest answer of moles and divide all figures by that.
1.98 moles N/ 1.98 = 1
2.97 moles Mg/ 1.98 = 1.5

Since our answer for magnesium is not close enough to round to the nearest whole number we must choose a factor to multiply all the figures by that will yield us whole numbers
1*2= 2 N
1.5*2= 3 Mg

5) Lastly, the coefficients calculated in the previous step will become the subscripts in the chemical formula.
1.98 moles N/ 1.98 = 1
1.98 moles N/ 1.98 = 1
N = 2
1.98 moles N/ 1.98 = 1
Mg = 3

Mg3N2