Problem 197 - Chemistry Matter and Change

Question

Which of these molecular formulas are also empirical formulas: ethyl ether \(\left(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}\right),\) aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right),\) butyl dichloride \(\left(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2}\right),\) glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right) ?\)

Step-by-Step Solution

Answer

Ethyl ether and aspirin are also empirical formulas.

Step 1: Define Empirical Formula

An empirical formula is the simplest whole-number ratio of atoms in a compound. For example, the empirical formula for \( ext{H}_2 ext{O}_2 \) is \( ext{HO} \). Our goal is to see if each given molecular formula is already in this simplest form.

Step 2: Analyzing Ethyl Ether

The molecular formula for ethyl ether is \( ext{C}_4 ext{H}_{10} ext{O} \). Let's find the greatest common divisor (GCD) of the subscripts: 4, 10, and 1. The GCD is 1. This means \( ext{C}_4 ext{H}_{10} ext{O} \) cannot be simplified further, and it is an empirical formula.

Step 3: Analyzing Aspirin

The molecular formula for aspirin is \( ext{C}_9 ext{H}_8 ext{O}_4 \). We find the GCD of the subscripts: 9, 8, and 4. The GCD is 1. Thus, \( ext{C}_9 ext{H}_8 ext{O}_4 \) is an empirical formula.

Step 4: Analyzing Butyl Dichloride

The molecular formula for butyl dichloride is \( ext{C}_4 ext{H}_8 ext{O}_2 \). We determine the GCD of the subscripts: 4, 8, and 2, which is 2. Dividing each subscript by 2, we get \( ext{C}_2 ext{H}_4 ext{O} \). \( ext{C}_4 ext{H}_8 ext{O}_2 \) is not an empirical formula as it can be simplified.

Step 5: Analyzing Glucose

The molecular formula for glucose is \( ext{C}_6 ext{H}_{12} ext{O}_6 \). The GCD of the subscripts 6, 12, and 6 is 6. Dividing each subscript by 6, we obtain \( ext{C}_1 ext{H}_2 ext{O} \). Therefore, \( ext{C}_6 ext{H}_{12} ext{O}_6 \) is not an empirical formula.

Key Concepts

Understanding Molecular Formulas

A molecular formula represents the actual number of atoms of each element in a molecule of a compound. They provide a clear picture of how many atoms are present and help us understand the composition of the compound at the molecular level. For example, in the molecular formula for glucose, \( \text{C}_6 \text{H}_{12} \text{O}_6 \), there are 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms in each molecule.

Molecular formulas are crucial because they give insight into the molecular structure and properties of substances. They show:

• How elements combine to form compounds.
• The stoichiometry of reactions involving the compound.
• The molecular mass, which is essential for stoichiometric calculations in chemistry.

Understanding molecular formulas helps chemists to work out how different molecules interact and react with each other. Hence, they form the building block of understanding chemical reactions and properties.

Exploring Chemical Compounds

Chemical compounds are substances formed when two or more elements bond together. The types of compounds can vary widely, including ionic, covalent, and metallic compounds, each characterized by different types of bonds and properties.

A chemical compound like aspirin, with the molecular formula \( \text{C}_9 \text{H}_8 \text{O}_4 \), demonstrates how multiple elements, in specific numbers, come together to form a single molecule with unique properties. These compounds are described by their molecular formulas as well as their names, providing a dual means of reference.

• Ionic Compounds: Formed from metals and non-metals, where electrons are transferred.
• Covalent Compounds: Formed from non-metals, where electrons are shared.
• Metallic Compounds: Formed between metal atoms.

Each chemical compound has distinct properties. These properties - like melting point, boiling point, solubility, and reactivity - are influenced by the type of atoms in the compound and their arrangement. Working with chemical compounds is a fundamental aspect of chemistry and is essential for create new materials and understanding natural processes.

Simplification of Formulas

The simplification of chemical formulas involves converting a molecular formula to its empirical form. This process is about expressing the simplest whole-number ratio of the elements in a compound.

Take for example glucose with the molecular formula \( \text{C}_6 \text{H}_{12} \text{O}_6 \). By finding the greatest common divisor (GCD) of the subscripts, which is 6, and dividing each by this number, we simplify it to the empirical formula \( \text{CH}_2 \text{O} \). This indicates the simplest ratio of carbon, hydrogen, and oxygen atoms in glucose.

• The empirical formula reveals the ratio of elements, whereas the molecular formula reveals the exact number of atoms.
• Simplifying formulas helps in identifying compounds by their basic components and understanding how they might react.

Simplification is an essential skill in chemistry as it provides a clear and concise way to represent compounds, especially when comparing different substances or analyzing their composition. Understanding how to derive this form can greatly assist in experimental work and theoretical calculations in chemistry.