Question

The simplest formula of a compound containing 50% of an element X (atomic mass = 10) and 50% of the element Y (atomic mass = 20) is:
A. \[XY\]
B. \[{X_2}Y\]
C. \[{X_2}{Y_2}\]
D. \[{X_2}{Y_3}\]

Answer 1

Hint: To answer this question, we must first recall the concept of empirical formula. It is the simplest whole number ratio of the number of atoms present in the molecule.

Complete step by step answer:
The elemental constituents of a compound define its chemical identity, and chemical formulas are the most appropriate way of representing this elemental makeup. When a compound’s formula is not known to us, measuring the mass of each of its constituent elements is obviously the first step in the process of determining the formula experimentally. The results of these measurements allow the calculation of the compound’s percentage composition which can be defined as the percentage by mass of each element in the compound.
Let us assume the total mass to be 100g
Hence, according to the question we have 50gm of X whose atomic mass is 10
Thus, number of moles of X = \[\dfrac{{50}}{{10}} = 5\]
And, we have 50gm of Y whose atomic mass is 20
Thus, number of moles of Y = \[\dfrac{{50}}{{20}} = 2.5\]
Hence, the molar ratio in whole numbers is \[\dfrac{X}{Y} = \dfrac{5}{{2.5}} = \dfrac{2}{1}\]
We can now calculate the empirical formula as: \[{X_2}Y\]

Hence, the correct answer is \[{X_2}Y\]

Note: We should remember that with regard to deriving empirical formulas; we must consider examples in which a compound’s percent composition is available rather than the absolute masses of the compound’s constituent elements. This will make our calculations much easier.