Calculation of Formula of Crystalline Salt Na2So4. XH2O on Heating

Given: The crystalline salt Na2So4. XH2O on heating loses 55.9% of its weight.

To find: The formula of the crystalline salt.

Solution:
Let us assume that the initial mass of the crystalline salt is 100 g.
After heating, the salt loses 55.9% of its weight, which means it loses 55.9 g.

Therefore, the mass of the salt after heating is 100 - 55.9 = 44.1 g.

Let us assume that the number of moles of water lost during heating is 'y'.
Then, the number of moles of Na2SO4 in the salt before heating is:

n(Na2SO4) = (44.1 g / 142 g/mol) - y

Similarly, the number of moles of Na2SO4 in the salt after heating is:

n(Na2SO4) = 44.1 g / 142 g/mol

Equating both the expressions, we get:

(44.1 g / 142 g/mol) - y = 44.1 g / 142 g/mol

Solving for 'y', we get:

y = 0.311 mol

This means that the crystalline salt contains 0.311 moles of water.

Now, we can calculate the formula of the crystalline salt as follows:

The mass of Na2SO4 in the salt before heating is:

m(Na2SO4) = n(Na2SO4) x M(Na2SO4)
= (44.1 g / 142 g/mol - 0.311 mol) x 142 g/mol
= 30.9 g

Therefore, the mass of water in the salt is:

m(H2O) = 44.1 g - 30.9 g
= 13.2 g

The formula of the crystalline salt can be written as:

Na2SO4 . xH2O

where x is the number of moles of water per mole of Na2SO4.

The molar mass of Na2SO4 is 142 g/mol, and the molar mass of H2O is 18 g/mol.

Therefore, the number of moles of water per mole of Na2SO4 can be calculated as:

x = 13.2 g / (18 g/mol) / (30.9 g / 142 g/mol)
= 10

Hence, the formula of the crystalline salt is:

Na2SO4 . 10H2O

Conclusion: The formula of the crystalline salt Na2SO4. XH2O on heating is Na2SO4. 10H2O.