Question

Determine the empirical formula for the compound represented by each molecular formula. $$ \mathrm{a} \cdot \mathrm{N}_{2} \mathrm{O}_{4} \quad \text { b. } \mathrm{C}_{5} \mathrm{H}_{12} \quad \text { c. } \mathrm{C}_{4} \mathrm{H}_{10} $$

Short answer

The empirical formulas are a. NO2, b. C5H12, and c. C4H10.

Step-by-step solution

Understanding the Empirical Formula

The empirical formula of a compound represents the simplest whole-number ratio of the elements within the compound. To find the empirical formula, you need to divide the subscripts in the molecular formula by their greatest common divisor.

Simplifying N2O4

For the compound N2O4, note that both nitrogen (N) and oxygen (O) have even subscripts. Dividing them by their greatest common divisor, which is 2, we obtain the empirical formula NO2.

Simplifying C5H12

For the compound C5H12, there is no common divisor for 5 and 12 since 5 is a prime number. Therefore, the empirical formula is the same as the molecular formula, C5H12.

Simplifying C4H10

For the compound C4H10, there is no common divisor for 4 and 10. The smallest whole number ratio of carbon to hydrogen is 4:10, which simplifies to 2:5. However, since we cannot have fractional subscripts in the empirical formula, it remains as C4H10.

Key concepts

Molecular Formula

The molecular formula of a substance tells us the exact number of atoms of each element in one molecule of the compound. For instance, when looking at a molecular formula like \( C_5H_{12} \), this tells us that a single molecule contains 5 carbon atoms and 12 hydrogen atoms.

However, understanding the molecular formula goes beyond counting atoms. It is vital for discerning the molecular structure and the potential chemical properties of the substance. While the molecular formula provides a clear picture of the components within a compound, it does not necessarily offer insight into its structure; for that, chemists look to structural formulas or three-dimensional models.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships of reactants and products in a chemical reaction. It is grounded in the law of conservation of mass, which states that matter is neither created nor destroyed during a chemical reaction.

Thus, stoichiometry allows scientists to predict how much of each substance is necessary for a reaction to occur and how much of each substance will be produced in the reaction. Understanding the relationship between the empirical formula and the molecular formula is a key part of stoichiometry. For instance, knowing the empirical formula, which represents the simplest whole-number ratio of atoms in a compound, can help in making calculations regarding the amount of reactants needed. In the steps provided, dividing subscripts by the greatest common divisor is an example of applying stoichiometric principles to derive an empirical formula from a molecular formula.

Chemical Composition

Chemical composition refers to the identity and proportion of the elements that make up a chemical compound. Every compound has a specific chemical composition characterized by its empirical and molecular formulas. For instance, \( N_2O_4 \) and \( NO_2 \) differ in their composition; \( N_2O_4 \) contains twice as many atoms of each element as \( NO_2 \), though they share the same empirical formula.

Understanding a substance's chemical composition is essential for a variety of practical applications, such as creating medicine, designing materials, and understanding environmental impacts. The determination of a compound's chemical composition is often the first step in analyzing a substance and predicting how it will interact with other chemicals.