Question

The relative number of atoms of elements X and Y in a compound is 0.25 and 0.5. The empirical formula of compound is:
A ) \[{\text{XY}}\]
B ) \[{{\text{X}}_2}{\text{Y}}\]
C ) \[{\text{X}}{{\text{Y}}_2}\]
D ) \[{{\text{X}}_2}{{\text{Y}}_2}\]

Answer 1

Hint: Calculate the ratio of the relative number of atoms of element X to the relative number of atoms of element Y. For this divide 0.25 with 0.5. 0.25 is the relative number of atoms of element X and 0.5 is the relative number of atoms of element Y.

Complete step by step answer:
Let the empirical formula of the compound be \[{{\text{X}}_a}{{\text{Y}}_b}\].
In the empirical formula, a and b represents the relative number of atoms of X and Y respectively. Write the ratio of the relative number of atoms of element X to the relative number of atoms of element Y.

\[\dfrac{{{\text{The relative number of atoms of element X}}}}{{{\text{The relative number of atoms of element Y}}}} = \dfrac{a}{b}\]

The relative number of atoms of elements X and Y in a compound is 0.25 and 0.5.
The ratio of the relative number of atoms of element X to the relative number of atoms of element Y will be
\[\dfrac{{{\text{The relative number of atoms of element X}}}}{{{\text{The relative number of atoms of element Y}}}} = \dfrac{a}{b} \\
= \dfrac{{0.25}}{{0.5}} \\
= \dfrac{1}{2} \\\]
Rearrange the above ratio.
\[{\text{The relative number of atoms of element Y}} = 2 \times {\text{The relative number of atoms of element X}}\]
This is the relative number of atoms of element X to the relative number of atoms of element Y. You can conclude that the number of atoms of element Y is twice the number of atoms of element X.
Hence, the empirical formula of compound is \[{\text{X}}{{\text{Y}}_2}\].

Hence, option C ) \[{\text{X}}{{\text{Y}}_2}\] is the correct option.

Note: Empirical formula gives the ratio of atoms of different elements present in a compound. This ratio is the simplest positive integer ratio. Empirical formula can be obtained from the molecular formula by dividing with an integer. For example, the molecular formula of ethane is \[{{\text{C}}_2}{{\text{H}}_6}\] but its empirical formula is \[{\text{C}}{{\text{H}}_3}\].