Question

A compound of X and Y has the empirical formula ${\mathrm{XY}}_2$. Its vapour density is equal to its empirical formula weight. Determine its molecular formula.

Answer 1

Step 1: Given data:

Vapour density = empirical formula weight

Empirical formula of X and Y is ${\mathrm{XY}}_2$

Step 2: Finding the molecular weight:

Since,

$$\begin{gathered} \mathrm{molecular}\mathrm{weight}=2\times \mathrm{vapour}\mathrm{density} \\ \Rightarrow \mathrm{molecular}\mathrm{weight}=2\times \mathrm{empirical}\mathrm{formula}\mathrm{weight} \end{gathered}$$($\because \mathrm{Vapour}\mathrm{density}=\mathrm{empirical}\mathrm{formula}\mathrm{weight}$)

Step 3: Finding the value of n:-

Since,

$$\begin{gathered} \mathrm{molecular}\mathrm{weight}=\mathrm{n}\times \mathrm{empirical}\mathrm{formula}\mathrm{weight} \\ \Rightarrow 2\times \mathrm{empirical}\mathrm{formula}\mathrm{weight}=\mathrm{n}\times \mathrm{empirical}\mathrm{formula}\mathrm{weight} \\ \Rightarrow \mathrm{n}=2 \end{gathered}$$ ($\mathrm{from}\mathrm{step}1$)

Step 4: Finding the molecular formula:-

The molecular formula of the compound is $={(\mathrm{Empirical}\mathrm{formula})}_{\mathrm{n}}={\left({\mathrm{XY}}_2\right)}_2={\mathrm{X}}_2{\mathrm{Y}}_4$

Therefore, the molecular weight of the compound is ${\mathrm{X}}_2{\mathrm{Y}}_4$