To find out how many water molecules are in a hydrate, you need to determine the value of 'x' in the hydrate's chemical formula, which is typically written as Anhydrous Solid⋅xH₂O. This value 'x' represents the number of moles of water molecules per mole of the anhydrous solid compound.
Understanding Hydrates and Their Formulas
A hydrate is an ionic compound that has water molecules loosely attached to its crystal structure. When a hydrate is heated, the water molecules are driven off, leaving behind the anhydrous (without water) solid.
The formula of a hydrate, Anhydrous Solid⋅xH₂O, signifies that for every one mole of the anhydrous solid, there are 'x' moles of water molecules incorporated into the crystal lattice. Determining 'x' is key to finding the exact number of water molecules associated with the compound.
The Method to Calculate 'x'
According to the provided reference on the Formula of a Hydrate, the number of moles of water per mole of anhydrous solid (x) is calculated by dividing the number of moles of water by the number of moles of the anhydrous solid.
This means the core calculation is:
x = (Moles of H₂O) / (Moles of Anhydrous Solid)
Practical Steps to Determine 'x'
In a laboratory setting, determining 'x' typically involves experimentally removing the water from a known mass of the hydrate. Here's a general outline of the process:
- Weigh the Hydrate: Accurately measure the mass of the hydrated sample.
- Heat the Hydrate: Carefully heat the hydrate to drive off the water molecules. Heating is usually done until a constant mass is achieved, ensuring all the water has evaporated.
- Weigh the Anhydrous Solid: Measure the mass of the remaining anhydrous solid.
- Calculate the Mass of Water Lost: Subtract the mass of the anhydrous solid from the initial mass of the hydrate. This difference is the mass of water that was present in the hydrate.
- Convert Masses to Moles:
- Use the molar mass of water (approximately 18.015 g/mol) to convert the mass of water lost into moles of water.
- Use the molar mass of the specific anhydrous solid to convert its mass into moles of anhydrous solid.
- Calculate 'x': Divide the moles of water (calculated in step 5) by the moles of the anhydrous solid (calculated in step 5).
Here's a summary table of the key quantities needed:
| Quantity | How to Obtain It | Unit |
|---|---|---|
| Mass of Hydrate | Experimental measurement | grams |
| Mass of Anhydrous Solid | Experimental measurement (after heating) | grams |
| Mass of Water | Mass of Hydrate - Mass of Anhydrous Solid | grams |
| Moles of Water | Mass of Water / Molar Mass of H₂O | moles |
| Moles of Anhydrous Solid | Mass of Anhydrous Solid / Molar Mass of Solid | moles |
| x (Moles H₂O / Moles Solid) | Moles of Water / Moles of Anhydrous Solid | unitless |
The calculated value of 'x' will often be a whole number or a simple fraction that can be rounded to the nearest whole number to represent the stoichiometric ratio of water molecules in the hydrate's formula.
Example:
Suppose you heat a sample of hydrated copper(II) sulfate (CuSO₄⋅xH₂O).
- Initial mass of hydrate = 5.00 g
- Mass of anhydrous CuSO₄ after heating = 3.20 g
- Mass of water lost = 5.00 g - 3.20 g = 1.80 g
Now, convert to moles:
-
Molar mass of H₂O ≈ 18.015 g/mol
-
Molar mass of CuSO₄ ≈ 159.61 g/mol
-
Moles of H₂O = 1.80 g / 18.015 g/mol ≈ 0.0999 mol
-
Moles of CuSO₄ = 3.20 g / 159.61 g/mol ≈ 0.0201 mol
Finally, calculate 'x':
- x = (Moles of H₂O) / (Moles of Anhydrous CuSO₄)
- x = 0.0999 mol / 0.0201 mol ≈ 4.97
This value is very close to 5. Therefore, the value of 'x' is 5, and the formula of the hydrate is CuSO₄⋅5H₂O (copper(II) sulfate pentahydrate), meaning there are 5 water molecules per formula unit of CuSO₄.
This method allows you to experimentally determine the exact number of water molecules associated with a hydrate sample and write its correct chemical formula.
