Hydrates: Determining the Chemical Formula From Empirical Data

Lesson Transcript
Instructor
Elizabeth (Nikki) Wyman

Nikki has a master's degree in teaching chemistry and has taught high school chemistry, biology and astronomy.

Expert Contributor
Dawn Mills

Dawn has taught chemistry and forensic courses at the college level for 9 years. She has a PhD in Chemistry and is an author of peer reviewed publications in chemistry.

Hydrates are compounds that contain water molecules which are chemically bonded to an element or compound. Learn about hydrates, anhydrates, and how to use the five-step process to determine the chemical formula of hydrates from empirical data. Updated: 08/25/2021

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 nH2 O for a magnesium sulfate hydrate or Na2 CO3 nH2 O for a sodium carbonate hydrate. Luckily for us, this is an easy determination. Finding 'n' is fun!

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  • 0:01 Hydrates
  • 1:12 Steps to Finding the…
  • 4:45 Example One
  • 6:36 Example Two
  • 9:18 Lesson Summary
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Steps to Finding the Formula of a Hydrate

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

  1. 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.

  2. 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.

  3. 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.

  4. 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).

  5. 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 nH2 O was heated up, the water was released, and the final anhydrate mass was 120.4 g. What is the formula of this hydrate?

  1. 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 nH2 O - 120.4 g MgSO4 = 90 g H2 O.
  2. 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.
  3. 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.
  4. 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.
  5. 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 nH2 O, originally contains 17.70 g. After heating, its final weight is 15.10 g. What is its formula?

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Additional Activities

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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