A compound of X and Y has the empirical formula $X Y_{2}$ .Its vapor density is equal to its empirical formula weight. Determine its molecular formula.

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Solution

Part one: Introduction to molecular formula, empirical formula and vapor density
The number of atoms of each element in single molecule is given by molecular formula.
The empirical formula is the simplest the ratio of atoms of each element of the compound.
Vapor density is ratio of molar mass of gas and molar of Hydrogen $(H_{2})$ .
Part two: Determination of molecular formula
The molar mass of the compound will be
$m o l a r m a s s = V . D \times m o l a r m a s s o f H y d r o g e n (H_{2}) m o l a r m a s s = V . D \times 2$
Here the vapor density is equal to the empirical formula weight.
$\begin{array}{rcl} M o l a r m a s s & = & e m p i r i c a l f o r m u l a w e i g h t \times 2 \\ E m p i r i c a l f o r m u l a w e i g h t \times n & = & e m p i r i c a l f o r m u l a w e i g h t \times 2 \\ n & = & 2 \end{array}$
Now the molecular formula is given by
$m o l e c u l a r f o r m u l a = n \times e m p i r i c a l f o r m u l a m o l e c u l a r f o r m u l a = 2 \times (X Y_{2}) m o l e c u l a r f o r m u l a = X_{2} Y_{4}$
Therefore, the molecular formula is $X_{2} Y_{4}$

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