Question

The hydrated salt $N{a}_{2}S{O}_4.n{H}_{2}O$ undergoes $55\mathrm{\%}$ loss in weight on heating and becomes anhydrous. The value of $n$ will be:
A. $5$
B. $3$
C. $7$
D. $10$

Answer 1

Hint: Sodium sulphate is an inorganic compound and it is also called sulphate of soda. Sodium sulphate’s all forms are white solids. They are highly soluble in water. Decahydrate is the major commodity chemical product. And mostly it is used for the manufacture of detergents and also in the kraft process.

Complete Step by Step Solution
According to the question, we have to find the number of moles of water molecule that is $n$ :
Now, the molecular mass of the hydrated salt $N{a}_{2}S{O}_4.n{H}_{2}O$ :
 $$\begin{gathered} [23\times 2+32+16\times 4+n(2\times 1+16)]g \\ \Rightarrow (46+32+64+18n)g \\ \Rightarrow (142+18n)g \end{gathered}$$
On heating it becomes anhydrous that means the water molecules get separated from the salt.
Now, the molecular mass of $n$ water molecules will be: $18n$
After heating it undergoes $55\mathrm{\%}$ loss in weight. So, mathematically comparison:
We can write,
 $\Rightarrow (142+18n)={\displaystyle \frac{18n}{55}}\times 100$
By solving this we will get $n=10$ . The hydrated salt was $N{a}_{2}S{O}_4.10H_{2}O$ .
So, option D is correct.

Note
Sodium sulphate is used as a thermal storage. The high heat storage capacity in the phase changes from solid to liquid, and the advantageous phase change temperature of ${32}^{0}C$ which makes this material for storing low grade solar heat for later release in space heating applications. It is also used for the incorporation into thermal tiles that are placed in an attic space and also it is incorporated into cells surrounded by solar–heated water. The phase change allows a substantial reduction in the mass of the material required for effective heat storage (the heat of fusion of sodium sulphate decahydrate is $82kJ/mol$ with the further advantage of a consistency of temperature as long as sufficient material in the appropriate phase is available.
For cooling applications, a mixture with common salt that is sodium chloride lowers the melting point to ${18}^{0}C$ . The heat of fusion of $NaCl.N{a}_{2}S{O}_4.10H_{2}O$ , is actually increased slightly to $286kJ/kg$ .