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Question: The relative number of atoms of elements X and Y in a compound is 0.25 and 0.5. The empirical formul...

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 ) XY{\text{XY}}
B ) X2Y{{\text{X}}_2}{\text{Y}}
C ) XY2{\text{X}}{{\text{Y}}_2}
D ) X2Y2{{\text{X}}_2}{{\text{Y}}_2}

Explanation

Solution

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 XaYb{{\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.

The relative number of atoms of element XThe relative number of atoms of element Y=ab\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{{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 $${\text{C}}{{\text{H}}_3}$$.