Question

The relative number of atoms of elements, ' \(\boldsymbol{X}\) and \({ }^{\prime} Y^{\prime}\) in a compound is \(0.25\) and \(0.5\). The empirical formula of compound is (a) \(X Y\) (b) \(X_{2} Y\) (c) \(\mathrm{XY}_{2}\) (d) \(X_{2} Y_{2}\)

Short answer

The empirical formula of the compound is XY2.

Step-by-step solution

Ratio Determination

To determine the empirical formula, first find the simplest whole number ratio of atoms in the compound. Given the relative numbers 0.25 for X and 0.5 for Y, divide by the smallest number to find the whole number ratio for each element. For element X: 0.25/0.25 = 1. For element Y: 0.5/0.25 = 2.

Write Empirical Formula

With the whole number ratios, the empirical formula can be written with each element followed by its subscript that represents the ratio from Step 1. For element X, the ratio is 1 (no subscript necessary). For element Y, the ratio is 2, represented as Y2.

Select The Correct Answer

Based on the empirical formula derived, which is XY2, the correct answer matches option (c).

Key concepts

Mole Concept

The mole concept is a fundamental principle in chemistry that allows chemists to count atoms, molecules, and ions in a way that's comparable to counting everyday objects. A mole is defined as the amount of substance that contains as many entities (atoms, ions, molecules, etc.) as there are atoms in 12 grams of pure carbon-12. This number is known as Avogadro's number, which is approximately equal to \(6.022 \times 10^{23}\).

When dealing with chemical reactions, understanding how moles relate to mass and number of particles is crucial. The mass of one mole of a substance in grams is equal to its relative atomic or molecular mass in atomic mass units (amu). This connection is the bridge between the microscopic world of atoms and the macroscopic world we can measure and observe in the laboratory.

For instance, to determine the empirical formula of a compound from its component elements, as shown in the exercise, we need to find the ratio of moles of each element. The mole concept enables us to convert the given relative numbers into mole ratios, leading us to the simplest whole number ratio as required for determining the empirical formula.

Chemical Composition

Chemical composition refers to the identity and relative number of the elements that make up any particular compound. This composition can be expressed in terms of the percentage by mass of each element within the compound, or more commonly for the purposes of chemical formulae, by the mole ratio of the elements.

Understanding the chemical composition of a compound is vital for various applications in chemistry, including predicting the properties of the compound, determining its molecular structure, and in the study of chemical reactions. When chemists analyze a compound, they can use techniques like mass spectrometry or spectroscopy to determine its composition and subsequently its empirical or molecular formula.

In the exercise provided, the relative number of atoms of elements X and Y is a direct clue to their chemical composition in the compound. In a practical sense, if we knew what elements X and Y were, and their respective atomic masses, we could further determine the percentage composition and use that information for more complex calculations or to predict the behavior of the compound under different conditions.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is based on the law of conservation of mass and the concept of the mole. Stoichiometric calculations use the balanced chemical equation of a reaction to relate the amount of reactants to that of the products.

In practice, stoichiometry can help us calculate how much reactant is needed to produce a desired quantity of product, or how much product will be created from certain amounts of reactants. It's also imperative for determining the limiting reagent in a reaction and the reaction yield.

Connecting stoichiometry to the exercise, once the empirical formula is determined, stoichiometry could then be applied to calculate how many moles of each element are required to form a given amount of the compound, or vice versa. If we were to take those calculations further, we could, for instance, predict how much energy would be released or absorbed during the formation or decomposition of the compound, among other practical results.