Problem 72 - Chemistry and Chemical Reactivity

Question

What is the difference between an empirical formula and a molecular formula? Use the compound ethane, \(\mathrm{C}_{2} \mathrm{H}_{6},\) to illustrate your answer.

Step-by-Step Solution

Answer

The empirical formula is \(\mathrm{CH}_{3},\) and the molecular formula is \(\mathrm{C}_{2}\mathrm{H}_{6}.\) The empirical formula is the simplest ratio, while the molecular formula is the actual count of atoms.

Step 1: Identify the Empirical Formula

Begin by understanding what an empirical formula is: it is the simplest whole-number ratio of atoms of each element in a compound. For ethane, \( \text{the molecular formula is } \mathrm{C}_{2} \mathrm{H}_{6}.\)To find the empirical formula, reduce the subscripts to the smallest whole numbers possible by dividing both by their greatest common divisor, which is 2: \(\mathrm{C}_{2}\mathrm{H}_{6} \div 2 = \mathrm{CH}_{3}.\) Therefore, the empirical formula of ethane is \(\mathrm{CH}_{3}.\)

Step 2: Understand the Molecular Formula

The molecular formula represents the actual number of each type of atom in a molecule of the compound. For ethane, this is exactly what is given by the molecular formula \(\mathrm{C}_{2}\mathrm{H}_{6},\) indicating there are 2 carbon atoms and 6 hydrogen atoms in each ethane molecule. This formula is not reduced further.

Step 3: Compare the Two Formulas

To understand the difference, compare the empirical formula and the molecular formula of ethane. The empirical formula (\(\mathrm{CH}_{3}\)) is the simplest integer ratio of the elements, whereas the molecular formula (\(\mathrm{C}_{2}\mathrm{H}_{6}\)) shows the exact count of each type of atom in the molecule. In this case, the molecular formula is a whole-number multiple of the empirical formula.

Key Concepts

Molecular Formula

A molecular formula is like a detailed map of a compound, showing us exactly how many atoms of each element are bonded together in a single molecule. By illustrating the precise number of atoms, it gives us an accurate view of its structure. For example, the molecular formula of ethane is \( \mathrm{C}_{2}\mathrm{H}_{6} \). This tells us that each molecule of ethane contains two carbon atoms and six hydrogen atoms. These numbers give a full picture of the ethane molecule.

Understanding molecular formulas helps in calculating molecular weights, identifying compounds, and predicting molecules' reactivity. They are like blueprints for chemists, giving vital information about molecules' compositions.

Ethane

Ethane is a simple hydrocarbon, an organic compound consisting only of carbon and hydrogen. Specifically, it is a member of the alkane family, characterized by single bonds between carbon atoms. Ethane has a molecular formula of \( \mathrm{C}_{2}\mathrm{H}_{6} \), indicating it contains two carbon atoms and six hydrogen atoms per molecule.

This compound is a colorless, odorless gas at room temperature and is a significant component of natural gas. It's often used in the production of ethylene, an important chemical in the plastics industry.

• Ethane represents a basic building block for more complex organic molecules.
• It helps illustrate fundamental chemistry concepts like empirical and molecular formulas.

Its simplicity makes ethane a great example for learning about chemistry.

Simplest Whole-Number Ratio

The simplest whole-number ratio is what we describe when determining an empirical formula. This ratio simplifies the elements in a compound to their smallest integer proportions.

Taking ethane as an example, its molecular formula is \( \mathrm{C}_{2}\mathrm{H}_{6} \). To find its empirical formula, we divide the number of each type of atom by their greatest common divisor. In ethane's case, this is 2, resulting in the empirical formula \( \mathrm{CH}_{3} \). This simplifies the carbon and hydrogen atoms from a ratio of 2:6 to 1:3.

• Empirical formulas are useful for comparing compounds with similar elements.
• They are key for analyzing substance proportions in chemistry.

The simplest whole-number ratio offers insights into compounds' foundational structures.

Chemical Formulas

Chemical formulas are vital tools in chemistry that express the composition of molecules. They can be empirical, molecular, or structural, each serving its own purpose in explaining chemical compositions.

An empirical formula provides the simplest integer ratio of elements, like \( \mathrm{CH}_{3} \) for ethane.
The molecular formula provides the precise count of atoms in a molecule, like \( \mathrm{C}_{2}\mathrm{H}_{6} \). Each type of formula gives chemists different attributes of a compound to study.

• Empirical formulas help in understanding the basic framework of compounds.
• Molecular formulas give detailed insights into molecular structure.

Recognizing the different types of chemical formulas is essential for any student studying chemistry as they present a clearer picture of how substances are constructed and react.