A compound X contains 63.3 percent manganese (Mn) and 36.7 percent O by mass. When \(X\) is heated, oxygen gas is evolved and a new compound Y containing 72.0 percent \(\mathrm{Mn}\) and 28.0 percent \(\mathrm{O}\) is formed. (a) Determine the empirical formulas of X and Y. (b) Write a balanced equation for the conversion of \(\mathrm{X}\) to \(\mathrm{Y}\)

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is founded on the law of conservation of mass, which states that matter cannot be created or destroyed in an isolated system. When applying stoichiometry to determine the empirical formula of a compound, the first step involves converting mass percentages into moles, which are the fundamental unit for measuring quantity in chemistry.

For example, to find the empirical formula of compound X in our exercise, we start by assuming a 100 g sample to make the math straightforward, as the mass percentages then directly translate to grams. After converting the masses of manganese and oxygen into moles, we find their simplest whole-number ratio by dividing by the smallest number of moles obtained. Here, the ratio of 1.15 mol Mn to 2.29 mol O simplifies to approximately 1:2, leading to the empirical formula MnO₂.

Understanding stoichiometry is crucial because it allows chemists to predict the quantities of substances consumed and produced in a given reaction, which is essential for scaling up reactions for industrial applications and for experiments in the lab.

Chemical composition refers to the identity and relative number of the elements that make up a chemical compound. The composition is usually represented using empirical formulas, which show the simplest whole-number ratio of the atoms within a substance. Deducing the chemical composition is a step-by-step process that involves first determining the percentage of each element in the compound and then translating these percentages into the mole ratio of the elements.

In the case of compound Y, we again take a 100 g sample for ease of calculation. The sample consists of 72.0% manganese and 28.0% oxygen by mass. Converting these percentages to moles, we find that the ratio of moles of manganese to moles of oxygen is 1.31 to 1.75. Simplifying this ratio to the smallest whole numbers gives us 3:4, indicating that the empirical formula for compound Y is Mn₃O₄.

Knowing the chemical composition is fundamental, as it not only determines the properties of the compound but also provides information necessary for preparing compounds through chemical reactions, analyzing reaction yields, and understanding the molecular structure.

Balancing chemical equations is essential for describing the changes that occur during a chemical reaction. An equation must be balanced to reflect the conservation of mass, ensuring that the number of atoms of each element is the same on both sides of the equation. To balance an equation, coefficients are placed before the formulas of reactants and products to adjust the number of moles of each substance accordingly.

In our exercise, the conversion of compound X (MnO₂) to compound Y (Mn₃O₄) requires a balanced chemical equation. Initially, the proposed conversion is MnO₂ -> Mn₃O₄ + O₂, which is unbalanced. Through balancing, we add coefficients to make sure there are equal amounts of Mn and O on both sides, resulting in the equation 2 MnO₂ -> Mn₃O₄ + O₂.

Mastering the skill of balancing equations is invaluable in chemistry as it is required for correct stoichiometric calculations, determination of reaction stoichiometry, and ensuring that chemical reactions represented on paper or in laboratory experiments proceed according to the expected ratios of reactants and products.