Question

If the percentage of water of crystallization in $MgS{O_4}.x{H_2}O$ is 13%, then what is the value of x?
(A) 1
(B) 5
(C) 7
(D) 4

Answer 1

Magnesium sulphate is mostly used in agriculture to treat magnesium deficiency in soils (an essential plant nutrient). This application favours monohydrate, which was producing 2.3 million tonnes per year by the mid-1970s. The salt is a substantial component of the water from several springs, and the anhydrous form and various hydrates occur in nature as minerals.

Complete answer:
Water molecules contained inside crystals are known as water(s) of crystallisation or water(s) of hydration in chemistry. In the production of crystals from aqueous solutions, water is frequently present. The entire mass of water in a substance at a particular temperature is sometimes referred to as water of crystallisation, and it is usually present in a definite (stoichiometric) ratio. Water contained in the crystalline framework of a metal complex or a salt that is not directly bound to the metal cation is known as "water of crystallisation."
The molar mass of ${\text{MgS}}{{\text{O}}_4}$ is $120.4\;{\text{g mo}}{{\text{l}}^{ - 1}}$
The molar mass of ${\text{MgS}}{{\text{O}}_4} \cdot {\text{x}}{{\text{H}}_2}{\text{O}}$ is $120.4 + 18 \times {\text{g mo}}{{\text{l}}^{ - 1}}$
Thus, 1 mole of ${\text{MgS}}{{\text{O}}_4} \cdot {\text{x}}{{\text{H}}_2}{\text{O}}$ weighs $120.4 + 18{\text{x g}}$ and contains 18 x g water.
But, the percentage of water of crystallization in ${\text{MgS}}{{\text{O}}_4} \cdot {\text{x}}{{\text{H}}_2}{\text{O}}$ is 13 %.
Hence, $\dfrac{{13 \times (120.4 + 18{\text{x}})}}{{100}} = 18{\text{x}}$
or, $120.4 + 18{\text{x}} = 138.4{\text{x}}$
or, $120.4{\text{x}} = 120.4$
$\Rightarrow {\text{x}} = 1$
Thus, the value of x is 1 .
Hence, the correct option is A.

Note :
A hydrate is a salt with accompanying water of crystallisation. Because of the presence of hydrogen bonds that form polymeric structures, the structure of hydrates may be extremely complex. Many hydrates' structures were unknown in the past, thus the dot in the formula was used to describe the composition without stating how the water was bound.