Question

Which of the following pairs of compounds have the same empirical formula? a. acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2},\) and benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\) b. ethane, \(\mathrm{C}_{2} \mathrm{H}_{6},\) and butane, \(\mathrm{C}_{4} \mathrm{H}_{10}\) c. nitrogen dioxide, \(\mathrm{NO}_{2}\), and dinitrogen tetroxide, \(\mathrm{N}_{2} \mathrm{O}_{4}\) d. diphenyl ether, \(\mathrm{C}_{12} \mathrm{H}_{10} \mathrm{O},\) and phenol, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\)

Short answer

The pair of compounds that have the same empirical formula is (c) nitrogen dioxide, \(\mathrm{NO}_{2}\), and dinitrogen tetroxide, \(\mathrm{N}_{2} \mathrm{O}_{4}\).

Step-by-step solution

Find the Empirical Formula for Each Compound

First, we will find the empirical formula for each of the compounds in the given pairs. a. Acetylene: \(\mathrm{C}_{2} \mathrm{H}_{2}\). There are no common divisors for 2 and 2, so the empirical formula remains \(\mathrm{C}_{2} \mathrm{H}_{2}\). Benzene: \(\mathrm{C}_{6} \mathrm{H}_{6}\). Dividing both subscripts by 6, we have the empirical formula \(\mathrm{CH}\). b. Ethane: \(\mathrm{C}_{2} \mathrm{H}_{6}\). Dividing both subscripts by 2, we have the empirical formula \(\mathrm{CH}_{3}\). Butane: \(\mathrm{C}_{4} \mathrm{H}_{10}\). Dividing both subscripts by 2, we have the empirical formula \(\mathrm{C}_{2} \mathrm{H}_{5}\). c. Nitrogen dioxide: \(\mathrm{NO}_{2}\). There are no common divisors for 1 and 2, so the empirical formula remains \(\mathrm{NO}_{2}\). Dinitrogen tetroxide: \(\mathrm{N}_{2} \mathrm{O}_{4}\). Dividing both subscripts by 2, we have the empirical formula \(\mathrm{NO}_{2}\). d. Diphenyl ether: \(\mathrm{C}_{12} \mathrm{H}_{10} \mathrm{O}\). There are no common divisors for 12, 10, and 1, so the empirical formula remains \(\mathrm{C}_{12} \mathrm{H}_{10} \mathrm{O}\). Phenol: \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\) (the molecular formula can also be written as \(\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}\)). There are no common divisors for 6, 6, and 1, so the empirical formula remains \(\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}\).

Compare the Empirical Formulas from Step 1

Now we will compare the empirical formulas we found in step 1 for each pair of compounds. a. Acetylene: \(\mathrm{C}_{2} \mathrm{H}_{2}\) and benzene: \(\mathrm{CH}\). Different empirical formulas, so they do not have the same empirical formula. b. Ethane: \(\mathrm{CH}_{3}\) and butane: \(\mathrm{C}_{2} \mathrm{H}_{5}\). Different empirical formulas, so they do not have the same empirical formula. c. Nitrogen dioxide: \(\mathrm{NO}_{2}\) and dinitrogen tetroxide: \(\mathrm{NO}_{2}\). The same empirical formulas, so they have the same empirical formula. d. Diphenyl ether: \(\mathrm{C}_{12} \mathrm{H}_{10} \mathrm{O}\) and phenol: \(\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}\). Different empirical formulas, so they do not have the same empirical formula. Therefore, only pair (c) nitrogen dioxide and dinitrogen tetroxide have the same empirical formula.

Key concepts

Understanding Chemical Composition

When we talk about chemical composition, we're referring to the types and amounts of elements in a compound.

The simplest ratio of these elements is known as the empirical formula, which gives the lowest whole number ratio of elements in a compound.

For example, acetylene has a molecular formula of \( C_2H_2 \), but since there are no common factors to reduce the subscripts further, its empirical formula is the same as its molecular formula. This contrasts with benzene, which has a molecular formula of \( C_6H_6 \) but an empirical formula of \( CH \), reflecting the 1:1 ratio after dividing each subscript by 6.

Understanding the chemical composition is vital in recognizing how similar or different two compounds are. Even if compounds share the same elements, differing ratios imply distinct properties and behaviors.

Comparing Molecular and Empirical Formulas

Molecules can have identical or different molecular formulas and empirical formulas.

When comparing molecular formulas, we look at the exact number of each atom in a molecule; these can vary greatly among compounds. The molecular formula is crucial in understanding the molecular structure and properties of a compound.

Empirical vs. Molecular Formula

On the other hand, the empirical formula tells us the simplest whole-number ratio of atoms. It doesn’t necessarily provide information about the molecule’s actual size or structure, only the proportional relation of elements present.

For instance, nitrogen dioxide (\( NO_2 \) is its own empirical formula), and dinitrogen tetroxide (\( N2O4 \) that simplifies to the empirical formula \( NO_2 \) when we divide by 2) illustrate how compounds can differ molecularly but be identical empirically, with significant implications in their physical and chemical properties.

Stoichiometry: The Heart of Chemical Reactions

At its core, stoichiometry is the study of the quantitative relationships or ratios between substances as they participate in chemical reactions.

It is grounded in the law of conservation of mass where the total mass of reactants equals the total mass of products in a chemical reaction. Understanding ratios of substances allows chemists to predict the amounts of products that will form in a reaction or the amount of reactants needed to create a desired amount of product.

Stoichiometric Calculations

For stoichiometric calculations, the empirical formula can serve as a foundation for calculating the relative weights of reactant and product molecules.

Using the empirical formula aids in simplifying complex reactions into more manageable equations that correspond to the actual amounts of substances involved. This knowledge is indispensable in both the laboratory and industrial applications where precise measurements are crucial for successful chemical synthesis.