Question

Hydrated Calcium Sulfate $\left[ {CaS{O_4}.x{H_2}O} \right]$ contains $21\% $ (by mass)of water of crystallization. The number of molecules of water of crystallization, i.e., 'x' in the hydrate compound is:
\[\left( {Ca = 40,{\text{ }}S = 32,{\text{ }}O = 16,{\text{ }}H = 1} \right)\]
A. $1$
B. $2$
C. $4$
D. $5$

Answer 1

Hint: We realize that when certain substances are presented to water present in the air. They either adsorb it on their surface or have it in their structure delivering an intricate where water bonds with the cation in ionic substances. The water present in the last case is known as water of crystallization (or) water of hydration.

Complete step by step answer:
We can characterize hydrates are inorganic salts involving atoms of water joined in a fixed proportion as a necessary piece of the crystal which are either appended to focus of metal or that has solidified with the metal complex. Such hydrates are likewise said to have water of crystallization or water of hydration.
Given data contains,
The water of crystallization as $21\% $.
The mass of calcium is $40g/mol$.
The mass of sulfur is $32g/mol$.
The mass of oxygen is $16g/mol$.
The mass of hydrogen is $1g/mol$.
From the mass of elements the total molar mass of hydrated calcium sulfate is $CaS{O_4}.x{H_2}O = 136 + 18x$.
Since the water of crystallization is $21\% $, the value of x is calculated as,
$\dfrac{{18x}}{{136 + 18x}} = \dfrac{{21}}{{100}}$
On simplification we get,
$x = 2$
Solving the above equation, we get the value of x as two. So the number of molecules of water of crystallization in hydrated calcium sulfate $\left[ {CaS{O_4}.x{H_2}O} \right]$ is $2$.

So, the correct answer is Option B.

Note: We have to know that a hydrate which has lost atoms of water is known as an anhydride. We could eliminate the excess water with solid warming. Anhydrous is the substance that doesn't contain any water particles. Scarcely any anhydrous mixes are hydrated effectively that they are hygroscopic in nature. We can utilize them as drying specialists or desiccants.