Question

How can you determine the formula of a hydrate?

Answer 1

Hint:To determine the formula of a hydrate, a known mass of hydrate is first dehydrated, then the mass of compounds before and after dehydration were compared. Then, the number of water molecules (x) attached to the hydrated substance can be calculated as:
$$\text{x}={\displaystyle \frac{{\text{n}}_{\text{water}}}{{\text{n}}_{\text{anhydrous solid}}}}$$
Where ‘n’ represents the number of moles.

Complete step-by-step answer:Water molecules are present as water vapors in the atmosphere and some elements when left in open, form complexes with these water molecules which are called hydrated compounds. The water present in such compounds is known as the water of hydration or water of crystallization. On strong heating, these compounds lose water of crystallization and become anhydrous.
Such type of compound is then represented in following manner: $\text{(Anhydrous solid)}\text{.x}{\text{H}}_2\text{O}$
Examples of hydrates: Gypsum $\left(\text{CaS}{\text{O}}_4.2{\text{H}}_2\text{O}\right)$, Borax $\left(\text{N}{\text{a}}_3{\text{B}}_4{\text{O}}_7.10{\text{H}}_2\text{O}\right)$ etc.
Now, let us learn how to determine the formula of a hydrate. To find the formula of hydrate of a compound, we need to find the value of ‘x’, that is, the number of moles of water molecules per mole of anhydrous compound.
To find the value of ‘x’, first we need to take a known mass of hydrate. Then, it is completely dehydrated by heating and the mass of dehydrated or anhydrous solid is noted. The mass of water evaporated can then be find out as follows:
$$\text{(Anhydrous solid)}\text{.x}{\text{H}}_2\text{O}\stackrel{\mathrm{\Delta }}{\to }\text{Anhydrous solid}+\text{x}{\text{H}}_2\text{O}$$
$${\text{m}}_{{\text{H}}_2\text{O(evaporated)}}={\text{m}}_{\text{hydrate}}-{\text{m}}_{\text{anhydrous solid}}$$
Since we know the molar mass of anhydrous solid, we can calculate the number of moles.
$$\begin{gathered} {\text{n}}_{\text{anhydrous solid}}={\displaystyle \frac{{\text{m}}_{\text{anhydrous solid}}}{{\text{M}}_{\text{anhydrous solid}}}} \\ {\text{n}}_{{\text{H}}_2\text{O}}={\displaystyle \frac{{\text{m}}_{{\text{H}}_2\text{O(evaporated)}}}{{\text{M}}_{{\text{H}}_2\text{O}}}} \end{gathered}$$
Where ‘M’ represents molar mass.
By dividing the number of moles of water evaporated by the number of moles of anhydrous solid, we will get the number of moles of water per mole of anhydrous solid (x).
$$\text{x}={\displaystyle \frac{{\text{n}}_{{\text{H}}_2\text{O}}}{{\text{n}}_{\text{anhydrous solid}}}}$$
Hence, the formula of hydrate will be - $(\text{Anhydrous solid)}\text{.x}{\text{H}}_2\text{O}$.

Note:The hydrates which lose water of crystallization on standing in the atmosphere are known as efflorescent and the compounds which can easily absorb water from the surrounding are known as hygroscopic compounds. While compounds or elements which absorb a large amount of water from the surrounding so that they become soluble in it are known as deliquescent.