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

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