Question

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

Answer 1

Step 1. Given information

• A compound of X and Y has the empirical formula ${\mathrm{XY}}_2$.
• The vapor density of this compound is equal to the empirical formula weight.

Step 2. Relationship between molecular weight and vapor density, and molecular weight and empirical formula weight

$\text{Molecular weight}=2\times \text{vapor density}\left(\text{V.D}\right)$ … (1)

$\text{Molecular weight}=n\times \text{Empirical formula weight}$ … (2)

Step 3. Equate equations (1), and (2)

From equations, (1) and (2), one can conclude that,

$2\times \text{vapor density}=n\times \text{Empirical formula weight}$

Or,

$n=\frac{2\times \text{vapor density}}{\text{Empirical formula weight}}$ … (3)

• However, it is given that

$\text{Empirical formula weight}=\text{vapor density}$

• Therefore,

$n=\frac{2\times \text{V.D}}{\text{V.D}}=2$

Step 4. Relationship between molecular formula and empirical formula

$\text{Molecular formula}={\left[\text{Empirical formula}\right]}_n$

Step 5. Determination of the molecular formula

$$\begin{gathered} \text{Molecular formula}={\left[{\text{XY}}_2\right]}_2 \\ ={\text{X}}_2{\text{Y}}_4 \end{gathered}$$

Hence, the molecular formula is ${\text{X}}_2{\text{Y}}_4$.