# Hydrates: Determining the Chemical Formula From Empirical Data

## Hydrates

'Ah, I need to hydrate!' Everyone knows what it means to hydrate. To hydrate means to drink, but it can also mean to 'combine chemically with water.' Although we use the word hydrate in our everyday lives, it's actually a chemistry term.

A **hydrate** is a compound that contains water with a definite mass in the form of H2 O. Hydrates are often in the form of a crystal that can be heated, and the water can be 'burned off' by turning it into steam. This usually causes the hydrate to lose its crystalline structure. The substance that is left over after the hydrate has lost its water is called an **anhydrate**. By measuring the compound before heating and after, the amount of water in the original hydrate can be determined and the formula discovered.

Unknown hydrates are written with their base form; then an *'n*' is placed before the H2 O. The *'n*' before the H2 O means there is a number there, but we don't know what it is yet, such as in MgSO4 *n*H2 O for a magnesium sulfate hydrate or Na2 CO3 *n*H2 O for a sodium carbonate hydrate. Luckily for us, this is an easy determination. Finding *'n*' is fun!

## Steps to Finding the Formula of a Hydrate

Here are the steps to finding the formula of a hydrate:

- Determine the mass of the water that has left the compound. This allows us to determine the mass of water that was in the hydrate and the mass of the anhydrate. We do this by subtracting the mass of the anhydrate from the mass of the hydrate. This equals the mass of water.

- Convert the mass of water to moles. To do this, we divide mass of water by the molar mass of water to get moles of water. Remember that the units for molar mass are g/mol. When we divide mass (in g) by molar mass (g/mol), grams will cancel out and we will be left with moles.

- Convert the mass of anhydrate that is left over to moles. To do this, we divide the mass of anhydrate by the molar mass of anhydrate to get the moles of anhydrate.

- Find the water-to-anhydrate mole ratio. Generally, you will have more waters than anhydrate, so divide the moles of water by the moles of anhydrate. This gives you your mole ratio (a note about this step: if your calculations give you a number that is very close to a whole integer, it's generally safe to round to the nearest whole one. If your number has a decimal that is close to 0.33, 0.5, or 0.66, you need to find the lowest common multiple of that number that is a whole number and apply it to the entire formula).

- Use the mole ratio to write the formula.

Let's see how these steps work with a sample problem:

A 210.4 g hydrate of Epsom salt, MgSO4 *n*H2 O was heated up, the water was released, and the final anhydrate mass was 120.4 g. What is the formula of this hydrate?

- Determine the mass of the water that has left the compound. Take the mass of the hydrate and subtract the mass of anhydrate from that to get the mass of water. 210.4 g MgSO4
*n*H2 O - 120.4 g MgSO4 = 90 g H2 O. - Convert the mass of water to moles. Mass of water / molar mass of water = moles of water. 90 g H2 O / (18 g/mol H2 O) = 5 moles H2 O.
- Convert the mass of anhydrate that is left over to moles. Mass of anhydrate / molar mass of anhydrate = moles of anhydrate. 120.4 g MgSO4 / (120.4 g/mol MgSO4) = 1 mole MgSO4.
- Find the water-to-anhydrate mole ratio. Divide moles of water by moles of anhydrate to get the mole ratio. 5 moles H2O / 1 mole MgSO4 = 5:1.
- Use the mole ratio to write the formula. Since there are 5 moles of H2O for every 1 mole of MgSO4, the formula is MgSO4 5H2

## Example One

Are you ready for another example? Feel free to pause at any point to do your own calculations:

A hydrate of sodium carbonate, Na2 CO3 *n*H2 O, originally contains 17.70 g. After heating, its final weight is 15.10 g. What is its formula?

- Take the mass of the hydrate and subtract the mass of the anhydrate to get the mass of water. 17.70 g Na2 CO3
*n*H2 O - 15.10 g Na2 CO3 = 2.60 g H2 O. - Divide the mass of water by the molar mass of water to get moles of water. 2.60 g H2 O / (18.00 g/mol H2 O) = 0.144 moles H2 O.
- Divide the mass of anhydrate by the molar mass of anhydrate to get moles of anhydrate. 15.1 g Na2 CO3 / (106 g/mol Na2 CO3) = 0.142 moles Na2 CO3.
- Divide moles of water by the moles of anhydrate to get the mole ratio. 0.144 moles H2 O / 0.142 moles Na2 CO3 = 1.01:1. It is safe to round this to a 1:1 ratio.
- Use the mole ratio to write the formula. Since there is only 1 mole of H2 O for every 1 mole of Na2 CO3, the mole ratio is 1:1 and the formula is Na2 CO3 H2 O.

## Example Two

Let's try an example that you might encounter in a lab setting. Here we are in the lab after dehydrating some iron (III) chloride salts. Now it's time for data analysis. We want to determine the formula for a hydrate of iron (III) chloride, FeCl3 *n*H2 O. Let's look at our data:

- Mass of the empty dish used for weighing = 2.5 g
- Mass of dish and sample before heating = 7.4 g
- Mass of dish and sample after heating = 5.4 g

What's the formula for our hydrate? To solve this, we can use the same steps we used in the previous example. This time, however, we must subtract the mass of our weighing dish from the mass of our sample before and after heating.

The mass of the hydrate = the mass of the dish and sample before heating - the mass of the empty dish. 7.4 g - 2.5 g = 4.9 g, the mass of our hydrate.

The mass of the anhydrate = the mass of the dish and sample after heating - the mass of the empty dish. 5.4 g - 2.5 g = 2.9 g, the mass of the anhydrate.

The mass of water = the mass of the hydrate - the mass of the anhydrate. 4.9 g - 2.9 g = 2.0 g of water.

Moles of water = the mass of water / the molar mass of water. 2.0 g H2O / (18 g/mol H2 O) = 0.11 moles H2 O.

Moles of anhydrate = mass of anhydrate / molar mass of anhydrate. 2.9 g FeCl3 / (162 g/mol FeCl3) = 0.018 moles FeCl3.

The mole ratio is all we have left to determine. Mole ratio = moles of water / moles of anhydrate. 0.11 moles H2 O / 0.018 moles FeCl3 = 6.1:1. 6.1 is very close to 6, so it is safe to round down. We'll call this 6. Since there are 6 waters to every 1 iron (III) chloride, the ratio is 6:1. The formula for our hydrate is FeCl3 6H2 O.

## Lesson Summary

A **hydrate** is a compound that contains water with a definite mass in the form of H2 O. An **anhydrate** is a hydrate that has lost its water molecules. Determining the formula for a hydrate means discovering the number of water molecules that the substance contains. The steps to determining the formula for experimental data are easy:

- Determine the mass of water that has been removed from the compound
- Convert the mass of water to moles
- Convert the mass of anhydrate that is left over to moles
- Find the water-to-anhydrate mole ratio
- Use the mole ratio to write the formula

## Learning Outcomes

Once you've completed this lesson, take a few moments to:

- Compare hydrate and anhydrate
- Enumerate the steps for determining the formula for a hydrate
- Analyze two related examples

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## Determining the Chemical Formula of a Hydrate

The exercises below will provide additional practice in determining the chemical formula of a hydrate based on experimental data. This is practical knowledge that can be applied after an experiment has been completed. There are a couple of questions below including their corresponding solutions in order to check your work.

## Exercises

1. A chemist weighs a sample of Na2 CO3 at 5.84 grams before it is heated. After the sample was heated it is weighed again at 2.42 g. Determine the formula of the hydrate.

2. A 15.67 g hydrate sample of magnesium carbonate weighed in at 7.58 g after heating. What is the formula of the hydrate?

## Solutions

The first solution is step by step to assist you in solving the second problem.

1. Start by determining the mass of water that evaporated.

mass water = 5.84 - 2.42 = 3.42 g

Determine the moles of Na2 CO3 and water.

Na2 CO3 : 2.42 ÷ 105.988 = 0.023 mol

H2 O : 3.42 ÷ 18.01 = 0.19 mol

Find the closest whole number molar ratio.

Na2 CO3 : 0.023 ÷ 0.023 = 1

H2 O : 0.19 ÷ 0.023 = 8

The formula is Na2 CO3 * 8H2 O

2. MgCO3 * 5H2 O

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