We are given the following information:
- Mass of organic compound = 0.8 g
- Mass of barium sulphate precipitated = 1.2 g
- The chemical reaction involving HNO₃ and the barium chloride shows that the element X is in the form of sulphate.
1. Molar Mass of Barium Sulphate
The molar mass of barium sulphate (BaSO₄) is calculated as:
\[
\text{Molar mass of BaSO₄} = \text{Ba} + \text{S} + 4 \times \text{O} = 137 + 32 + 64 = 233 \, \text{g/mol}
\]
2. Moles of Barium Sulphate
The moles of barium sulphate precipitated is given by:
\[
\text{moles of BaSO₄} = \frac{\text{mass of BaSO₄}}{\text{molar mass of BaSO₄}} = \frac{1.2 \, \text{g}}{233 \, \text{g/mol}} = 0.00515 \, \text{mol}
\]
3. Moles of Element X
In the reaction, one mole of element X reacts to form one mole of barium sulphate. Hence, moles of X in the compound is equal to the moles of BaSO₄ formed:
\[
\text{moles of X} = 0.00515 \, \text{mol}
\]
4. Mass of Element X
The mass of element X is:
\[
\text{mass of X} = \text{moles of X} \times \text{atomic mass of X}
\]
From the stoichiometry and element identification, we deduce that X is sulfur, which has an atomic mass of 32 g/mol. Thus:
\[
\text{mass of X} = 0.00515 \, \text{mol} \times 32 \, \text{g/mol} = 0.1648 \, \text{g}
\]
5. Percentage of Element X
The percentage of element X in the compound is:
\[
\text{Percentage of X} = \frac{\text{mass of X}}{\text{total mass of compound}} \times 100 = \frac{0.1648}{0.8} \times 100 = 20.6 %
\]
6. Formula of Violet-Coloured Compound
The violet-coloured compound formed when Lassaigne's extract reacts with sodium nitroprusside is \(\text{Na}_4[\text{Fe(CN)}_6\text{NOS}]\), which corresponds to the formula in option (B).
Thus, the percentage of element X is 20.6% and the formula of the violet-coloured compound is Na₄[Fe(CN)₆NOS], corresponding to option (B).