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 with the same empirical formula is nitrogen dioxide (NO₂) and dinitrogen tetroxide (NO₂).

Step-by-step solution

Find empirical formulas of each compound

Let's start by finding the empirical formulas of each compound in the given pairs. a. acetylene (C₂H₂): The empirical formula is the same as the molecular formula as there's no common factor to simplify the formula further. So its empirical formula is C₂H₂. Benzene (C₆H₆): This molecular formula can be simplified by dividing both subscripts by the common factor 2. Empirical formula: C₃H₃ b. ethane (C₂H₆): The empirical formula is the same as the molecular formula as there's no common factor to simplify the formula further. So its empirical formula is C₂H₆. Butane (C₄H₁₀): This molecular formula can be simplified by dividing both subscripts by the common factor 2. Empirical formula: C₂H₅ c. nitrogen dioxide (NO₂): The empirical formula is the same as the molecular formula as there's no common factor to simplify the formula further. So its empirical formula is NO₂. Dinitrogen tetroxide (N₂O₄): This molecular formula can be simplified by dividing both subscripts by the common factor 2. Empirical formula: NO₂ d. diphenyl ether (C₁₂H₁₀O): The empirical formula is the same as the molecular formula as there's no common factor to simplify the formula further. So its empirical formula is C₁₂H₁₀O. Phenol (C₆H₅OH): The empirical formula is the same as the molecular formula as there's no common factor to simplify the formula further (Note that the hydroxyl group -OH remains as it is). So its empirical formula is C₆H₅OH.

Compare empirical formulas of given pairs

Now, let's compare the empirical formulas of the given pairs of compounds. a. acetylene (C₂H₂) and benzene (C₃H₃) Empirical formulas are different. b. ethane (C₂H₆) and butane (C₂H₅) Empirical formulas are different. c. nitrogen dioxide (NO₂) and dinitrogen tetroxide (NO₂) Empirical formulas are the same: NO₂ d. diphenyl ether (C₁₂H₁₀O) and phenol (C₆H₅OH) Empirical formulas are different. Based on the comparisons, the answer is: c. nitrogen dioxide, NO₂, and dinitrogen tetroxide, N₂O₄, have the same empirical formula.

Key concepts

Molecular Formula

Understanding chemical formulas is essential in chemistry. A molecular formula gives the total number of each type of atom in a molecule of a compound. It's like noting how many apples and oranges you have in a basket. For example, in the molecule of acetylene (\(\text{C}_2\text{H}_2\)), there are 2 carbon atoms and 2 hydrogen atoms present.
Each molecular formula reveals not only the types of atoms but also their exact count per molecule.
Here are some key points to remember about molecular formulas:

• They specify the actual number of atoms of each element in a molecule.
• They represent the complete picture of a molecule's composition.
• They are crucial for understanding the properties and reactivities of molecules.

Learning to decipher molecular formulas helps you compare and understand various chemical compounds.

Compound Comparison

Comparing compounds becomes insightful by looking at their empirical and molecular formulas. This comparison helps us understand a compound's makeup and behavior.
When analyzing compounds, such as nitrogen dioxide (\(\text{NO}_2\)) and dinitrogen tetroxide ((\(\text{N}_2\text{O}_4\)), comparing their formulas reveals interesting details. Though their molecular formulas differ, their empirical formulas match, both being \(\text{NO}_2\).

• Empirical formulas provide a reduced version, showing the simplest ratio.
• Molecular formulas offer a precise count of atoms inside a molecule, showing possibly higher multiples.

Such comparisons allow chemists to identify differences or similarities that might influence the physical and chemical properties of these compounds.

Simplifying Chemical Formulas

Simplifying chemical formulas means finding the empirical formula, which represents the simplest ratio of atoms in a compound. Imagine it as reducing a recipe to its essence.
For benzene (\(\text{C}_6\text{H}_6\)), the reduction ends with \(\text{C}_3\text{H}_3\) after dividing by their greatest common factor.
This simplification provides a stripped-down view of the compound's composition.

• Empirical formulas are especially useful for compounds with large, complex molecular formulas.
• They help in identifying how elements are proportioned in a compound.
• In some cases, the empirical formula is the same as the molecular formula, like in ethane (\(\text{C}_2\text{H}_6\)).

By simplifying, you gain a quick and clearer insight into how elements are arranged in the smallest whole number ratios.

Chemical Compounds

Chemical compounds are substances formed from two or more elements chemically bonded together. They show unique properties differing from the individual elements themselves.
Each compound holds its identity marked by its unique chemical formula, revealing the type and number of atoms.
For instance, when carbon and hydrogen bond differently, they could form various compounds such as acetylene (\(\text{C}_2\text{H}_2\)) or ethane (\(\text{C}_2\text{H}_6\)).

• Compounds are categorized based on their properties, like ionic or covalent compounds.
• The combination of elements leads to diverse compounds crucial for numerous applications.

Understanding chemical compounds involves recognizing these transformations and the resulting new properties, helping you appreciate the wide spectrum of materials formed in chemistry.