Question

How do you calculate the empirical formula of a hydrate?

Answer 1

Hint Hydrates are the types of compounds in which water in definite mass is present in the form of ${{H}_{2}}O$ along with the compound in its formula. These molecules of water can be removed by heating the crystal in the form of steam. The remaining part of the compound is known as an anhydrate.

Complete step by step solution:
Let us study about the hydrates in detail;
The water present along with the compound in its empirical form is known as water of hydration or water of crystallisation in the hydrates. The hydrates contain water in the stoichiometric amounts.
The hydrate formula is represented as $Anhydrous-solid.x{{H}_{2}}O$ , where x is the ratio of ${{H}_{2}}O$ moles per mole of anhydrous component.
The empirical formula can be determined by the following steps;
Step I – Determine the mass of the water that has been removed.
As we would know the total mass of a hydrate, by subtracting the mass of anhydrate we can calculate the mass of water.
Step II – Calculate the number of moles of water by using the determined mass of the same.
We need to divide the mass of water with the molar mass of water to calculate the number of moles of water.
Step III – Calculate the number of moles of anhydrate.
Similarly, we need to find the number of moles of anhydrate as we found for water.
Step IV – Calculate the water-anhydrate mole ratio and use this in the formula.
Divide the moles of water by the moles of anhydrate to get the mole ratio to be written in the hydrate formula.
For example-
Let us assume that you have to determine the formula for the hydrate of barium chloride;
Sample of hydrate weighs = 4.13 gm
Anhydrate weight after heating the sample = 3.52 gm
Step I- Mass of water = (4.13 – 3.52) = 0.61 gm
Step II- Moles of water = $0.61gm\times \dfrac{1mole}{18gm}=0.034moles$
Step III- Moles of anhydrate = $3.52gm\times \dfrac{1mole}{208.2gm}=0.017moles$ ; since molar mass of $BaC{{l}_{2}}=208.2gm/mole$
Step IV- Mole ratio = $\dfrac{0.034}{0.017}=2$
Thus, we need 2 moles of water for each mole of $BaC{{l}_{2}}$ . Thus, the hydrate formula of barium chloride is $BaC{{l}_{2}}.2{{H}_{2}}O$ .

Note: Do note that we would have more water than the anhydrate thus, we divide the moles of water by the moles of anhydrate to get the mole ratio in the final step.
If the mole ratio is close to the whole integer, try to round off and write the formula. But if the mole ratio is in decimals, find the lowest common multiple in the form of the whole number and modify the entire formula.