Question

What‌ ‌is‌ ‌the‌ ‌number‌ ‌of‌ ‌molecules‌ ‌of‌ ‌water‌ ‌of‌ ‌crystallizationin‌ ‌‌$CuS{O_4}$‌‌ ‌?‌ ‌
E.$3$‌ ‌ ‌
F.$4$‌ ‌ ‌
G.$5$‌ ‌ ‌
H.$6$‌ ‌

Answer 1

Hint: Here, we need the concepts of water of crystallization. We need to remember that the water of crystallization is termed as the part of water that is available in the crystalline structure of a metallic salt or complex substance which cannot bind directly with a metallic cation.

Complete step by step answer:
We must have to know that when the process of water crystallization occurs then moist solvents, compounds or molecules incorporate with the water molecules in a crystalline framework. Here, we will consider that if $10g$ of hydrous copper sulfate gives $6.4g$ of anhydrous $CuS{O_4}$ on heating. First we need to note the mass of all elements:
$Cu = 64$ , $S = 32$ , $O = 16$
Let’s consider that n is the number of water molecules in one molecule of hydrous copper sulphate
Now, let’s first write all the given quantities:
Mass of hydrous $CuS{O_4} = 10g$
Mass of anhydrous $CuS{O_4} = 6.4g$
After water crystallization now the mass of both the substances have changed:
Mass of hydrous $CuS{O_4} = 160 + 18n$
Mass of anhydrous $CuS{O_4} = 160$
To find the value of n we will equalize both the values of hydrous and anhydrous $CuS{O_4}$ and do cross-multiplication:
$\dfrac{{6.4g}}{{10g}} = \dfrac{{160}}{{(160 + 18n)}}$
$ \Rightarrow \dfrac{{(160 + 18n)6.4}}{{10}} = 160$
On simplification we get,
$ \Rightarrow n = \dfrac{{576}}{{115.2}}$
Thus, the value of $n = 5$ (option C).
Therefore, the option C is correct.

Note:
We must know that the water of crystallization is equal to the total number of water molecules that are present in one unit of a salt.Here, the anhydrous copper sulfate which is used it is used as a drying agent that is formed by the combination of sulfur and copper for fertilizers, leathers, food items, and textile. For example if we consider $CaS{O_4}.2{H_2}O$ then it has 2 molecules of water of crystallization.