Question

Two elements ${\text{X}}$ (atomic mass$= 75$) and ${\text{Y}}$ (atomic mass$= 16$) combine to give a compound having $75.8\%$ of ${\text{X}}$. The formula of the compound is:
A. ${{\text{X}}_2}{{\text{Y}}_2}$
B. ${{\text{X}}_2}{\text{Y}}$
C. ${{\text{X}}_2}{{\text{Y}}_3}$
D. ${\text{XY}}$

Answer 1

Molecular formulas tell the actual number of atoms of each element in a compound. Empirical formula shows the simplest ratio among atoms in a compound. It is the reduced chemical formula. The amount of elements for a given amount of compound is determined by percentage composition.

Complete step by step answer:
Empirical formula is the simplest formula of a compound which expresses its composition by mass, and which expresses the ratio of the number of different atoms in the molecule.
It is given that the atomic mass of ${\text{X = 75}}$
Atomic mass of ${\text{Y = 16}}$
The composition of ${\text{X = 75}}{{.8\% }}$
Therefore composition of ${\text{Y = 100 - 75}}{{.8\% = 24}}{{.2\% }}$
Let’s assume that we have $100{\text{g}}$ of the sample. Multiply the percent of each element by $100{\text{g}}$ to determine the amount in grams of each element.
But we have to calculate the number of moles of each element. It can be calculated by dividing the composition of each element by the atomic mass.
Number of moles of ${\text{X = }}\dfrac{{75.8}}{{75}} = 1.01$
Number of moles of ${\text{Y = }}\dfrac{{24.2}}{{16}} = 1.51$
When we multiply the number of moles of ${\text{X}}$ and ${\text{Y}}$ with a common number, we get the ratio.
i.e. ratio of ${\text{X}}$to ${\text{Y}}$ $= \dfrac{{1 \times 2}}{{1.5 \times 2}} = \dfrac{2}{3}$
Hence the formula of the compound is ${{\text{X}}_2}{{\text{Y}}_3}$.

Thus, the correct option is C .

Note:
The molecular formula of a compound is related to empirical formula. The molecular formula is always a whole number multiple of the empirical formula. Percentage composition can be determined experimentally or from the formula of a substance.