Learn the difference between the empirical formula and chemical formula. Learn how to calculate the percent composition of an element in a compound. Learn how, if given a percent composition, to determine the empirical formula for a compound.

## Empirical Formula

This lesson will cover how to start with an empirical formula and determine the chemical formula. There are several steps to get to the empirical formula.

I’m going to break it into two halves. In the first half, you learn how to determine the percent of elements in a compound. In the second part, you learn how to take those percentages and determine the empirical formula.First though, you need to understand what I mean when I say ’empirical formula.’ The** empirical formula** shows the kind and proportions of atoms in a substance in its simplest form.

The** chemical formula**, on the other hand, is the shorthand way of writing a substance by using chemical symbols and number subscripts with the exact numbers of atoms.It’s like saying the word family. I can tell you that my family consists of a mother, father and some kids. This is like the empirical formula: 1M 1F 2SD (one mother, one father, two sons and daughters).

But, to be more specific, my family consists of a mother, a father, seven sons and three daughters. This is like the chemical formula: 1M 1F 7S 3D (one mother, one father, seven sons, three daughters).It sounds a bit confusing, but let’s look at a few examples. Consider hydrogen peroxide. The chemical formula is H2O2.

In one molecule of hydrogen peroxide, there are two hydrogens and two oxygens. The empirical formula is HO. This is how you would write hydrogen peroxide, H2O2, in its simplest form.

The chemical formula, as you can tell, gives a more exact representation of the substance.

Look at glucose and formaldehyde. Glucose’s chemical formula is C6H12O6. Formaldehyde’s chemical formula is CH2O.

Both of them have the same empirical formula of CH2O.

## Determining the Percent Composition of Compounds

First, let’s practice finding the percent composition of compounds. To find the percent composition, you need the formula, from which you find the molar mass (from which you find the mass percentage) of each element.

- Write the formula.
- Use the formula to determine molar mass.
- Use the molar mass to determine the mass percentage of each element.

If you have a compound that has the formula C2H5OH, first determine the mass of each element.

- mass of C = (2 moles C / 1) * (12 g C / 1 mole) = 24 g C
- mass of H = (6 moles H / 1) * (1 g H / 1 mole) = 6 g H

When you are counting the number of hydrogens, don’t forget to count the one at the end of the formula!

- mass of O = (1 mole O / 1) * (16 g O / 1 mole) = 16 g O
- Total mass = 24 g + 6 g + 16 g = 46 g

Next, determine the percent of each element in the total compound.

- C = (24 / 46) * 100% = 52%
- H = (6 / 46) * 100% = 13%
- O = (16 / 46) * 100% = 35%

## Determining the Empirical Formula

Now, let’s practice determining the empirical formula of a compound. To do this, you need the percent composition (which you use to determine the mass composition), then the composition in moles and finally, the smallest whole number mole ratio of atoms.

- Find the percent composition.
- Use the percent composition to determine the mass composition.
- Use the mass composition to determine the composition in moles.
- Use the composition in moles to find the smallest whole number ratio of atoms.

For this example, our compound has 72% Cl, 24% C and 4% H. First, determine the mass of each of the elements in 100 g of the substance.

- 72 g Cl
- 24 g C
- 4 g H

Next, determine how many moles there are of each element in 100 g of the substance by using the molar mass of each element.

- (72 g Cl / 1) * (1 mole Cl / 35.5 g Cl) = 2 moles
- (24 g C / 1) * (1 mole C / 12 g C) = 2 moles
- (4 g H / 1) * (1 mole H / 1 g H) = 4 moles

Divide each one by the smallest number of moles.

- Cl = 2 / 2 = 1
- C = 2 / 2 = 1
- H = 4 / 2 = 2

So, the empirical formula is CH2Cl.

## Practice

Now, let’s put it all together.

So, pretend you have made something in the lab. You know you reacted 0.35 g of a compound containing carbon, hydrogen and nitrogen with some oxygen, and you made 0.50 g of carbon dioxide and 0.

50 g of water. You want to know how many of each atom is in the compound that you started with. In other words, you want to know the empirical formula.Givens:

- C + H + N + O ;==; CO2 + H2O
- 0.35 g = C + H + N
- 0.50 g = CO2
- 0.50 g = H2O

To do this, you need to make a few assumptions.

Assume that all of the carbon was used to make the CO2. You have the mass of CO2 (0.50 g). This is how you do it:

- (Mass of carbon / molar mass of CO2) * (mass of CO2 made / 1) = amount of carbon in CO2

I always like to put my whole numbers over a denominator of one to keep everything as a fraction and make it easier to see what crosses out.

- (12.0 g C / 44.0 g CO2) * (0.50 g CO2 / 1) = 0.14 g C

The amount of carbon that you just determined is the carbon from the unknown compound.

Now you can determine the percentage of carbon in that compound.

- (0.14 g C / 0.35 g compound) * 100% = 40% of the compound is carbon

So, now we know that 40% of our compound is made of carbon. But, what about the other 60%? Let’s determine what percent of the compound is hydrogen by using the same kind of equations.

- (Molar Mass of H / molar mass of H2O) * (amount of H2O / 1) = amount of hydrogen in H2O
- (2.0 g H / 18.0 g H2O) * (0.50 g H2O / 1) = 0.056 g H

The mass is 2 g because, in water, hydrogen travels in pairs, and each of the hydrogens is 1 g.The percentage of hydrogen in the compound is:

- (0.056 g H / 0.
35 g compound) * 100% = 16%

So, 16% of the unknown compound is hydrogen. You know that 16% is hydrogen and 40% is carbon, so 44% is nitrogen (100% – 16% – 40%). Now that you have the percentages of each kind of atom in your unknown compound, you can determine the formula. Now, pretend that you have 100 g of your unknown compound. From the percentages you determined, you know that 16 g is hydrogen, 40 g is carbon and 44 g is nitrogen.

Convert these numbers to moles.

- (16 g H / 1) * (1 mole H / 1 g H) = 16 moles H
- (40 g C / 1) * (1 mole C / 12 g C) = 3.3 moles C
- (44 g N / 1) * (1 mole N / 14 g N) = 3.1 moles N

Now that you know your moles, you can find the ratio of each of the atoms in the compound. You do this by dividing each of the mole values by the smallest of the mole values.

- For hydrogen, this is 16 / 3.1 = 5.2
- For carbon, this is 3.3 / 3.
1 = 1.1

- For nitrogen, this is 3.1 / 3.1 = 1

Round these to whole numbers and you know that the compound has five H, one C and one N.

So, its empirical formula is CH5N.

## Lesson Summary

Whew. That was quite a bit of work. Let me see if I can summarize it a bit for you. This lesson taught you the meaning of **empirical formula**, which shows the kind and proportions of atoms in a substance in its simplest form. This is different from the **chemical formula**, which gives a more exact representation of the substance because it is the shorthand way of writing a substance by using chemical symbols and number subscripts with the exact numbers of atoms.

If you have determined the percentage of each element in a compound, you can determine the empirical formula.

- You determine the percent of the elements in the unknown compound.
- You determine the number of moles of each element in the unknown compound.
- You determine the mole ratio of each of the elements.
- You write the empirical formula.

## Learning Outcomes

Once you have finished this lesson, you might be able to:

- Define empirical formula and chemical formula and explain the differences between them
- List the steps involved in determining the percent composition of elements in a compound
- Determine the empirical formula for a compound after calculating the percent composition of each element in the compound