Empirical formula is the formula where atoms of elements are in their smallest whole number ratios.
For example, is C3H6 an empirical formula? Since both 3 and 6 can be divided further by 3, C3H6 is not an empirical formula. Instead, C1H2 is an empirical formula.
Let's look at an example and do a step by step calculation to determine empirical formula:
What is an empirical formula for a compound that contains 15.8% carbon and 84.2% sulfur?
Calculating Empirical Formula from percents or grams given:
1. Assume 100 g. Percents given will become grams. If grams are given, no need to assume anything.
C = 15.8g
S = 84.2 g
2. Divide the mass of each element by the molar mass (found in the Periodic Table) to find the number of moles.
C = 15.8g *1 mol = 1.315 mol
12.011g
S = 84.2 g* 1mol = 2.626 mol
32.06g
3. Divide all moles by the smallest mole number. If you get close to the whole numbers, these are your subscripts. If not, multiply by a number to get to whole numbers.
C = 1.315 mol = 1
1.315 mol
S = 2.626 mol = 2
1.315 mol
We got whole number or close to whole numbers, so no need to multiple further!
The empirical formula is CS2
Let's try another problem:
What is the empirical formula of a compound containing C, H and O that is 59.9%C and 8.06%H.
First, lets find % O. All the percents must add up to 100%
%O = 100% - (59.9% + 8.06%) = 32.0%O
1. Assume 100 g. Percents given will become grams. If grams are given, no need to assume anything.
C = 59.9g
H = 8.06g
O = 32.0g
2. Divide the mass of each element by the molar mass (found in the Periodic Table) to find the number of moles.
C = 59.9g *1 mol = 4.987 mol
12.011g
H = 8.06g *1 mol = 7.996 mol
1.008g
O = 32.0g *1 mol = 2.000 mol
15.999g
3. Divide all moles by the smallest mole number. If you get close to the whole numbers, these are your subscripts. If not, multiply by a number to get to whole numbers.
C = 4.987 mol = 2.49
2.000 mol
H = 7.996 mol = 3.998
2.000 mol
O = 2.000 mol = 1
2.000 mol
Since, 2.49 is not close to a whole number we now need to multiply all numbers by a number that would make 2.49 close to a whole number. Let's try multiplying by 2, we get
C = 2.49*2 = 4.987
H = 3.998*2 = 7.996
O = 1*2 =2
Therefore, empirical formula is C5H8O2
Calculating Molecular Formula
Example: What is the molecular formula of a compound if the empirical formula is CH2O and the molar mass is 90g/mol?
1.Find empirical formula if it is not given.
In this case, empirical formula is given so we can move to step number 2. Otherwise, we would find empirical formula using the method above.
2. Find the molar mass of the empirical formula
CH2O
C = 1 *12.011g/mol = 12.011 g/mol
H = 2 * 1.008g/mol = 2.016 g/mol
O = 1 * 15.999g/mol = 15.999 g/mol
12.011 g/mol + 2.016 g/mol + 15.999 g/mol = 30.031 g/mol
3. Divide the molar mass given by the mass of the empirical formula to see how many times it goes in. You should get a whole number (or very close to it).
90g/mol = 2.9969 = 3
30.031 g/mol
4. Multiply the subscripts in the empirical formula by the number you get.
C1*3H2*3O1*3 = C3H6O3