Problem 42 - Introductory Chemistry Atoms First

Question

How many \(\mathrm{O}_{2}\) molecules are there in 1 mole of \(\mathrm{O}_{2}\) molecules? How many \(\mathrm{O}\) atoms are there in 1 mole of \(\mathrm{O}_{2}\) molecules?

Step-by-Step Solution

Answer

In 1 mole of O₂ molecules, there are \(6.022 \times 10^{23}\) O₂ molecules and \(1.2044 \times 10^{24}\) O atoms.

Step 1: Recall the definition of a mole and Avogadro's number

A mole is the amount of substance that contains as many particles (such as atoms, molecules, ions, etc.) as there are in 12 grams of pure carbon-12. Avogadro's number (Nₐ) is the number of particles in one mole of a substance and is equal to 6.022 x 10²³ particles per mole.

Step 2: Find the number of O₂ molecules in 1 mole of O₂ molecules

Since there are 6.022 x 10²³ particles in 1 mole of a substance, there are 6.022 x 10²³ O₂ molecules in 1 mole of O₂ molecules.

Step 3: Find the number of O atoms in 1 mole of O₂ molecules

In one O₂ molecule, there are 2 O atoms. Since there are 6.022 x 10²³ O₂ molecules in 1 mole of O₂ molecules, we can multiply this number by the number of O atoms in each O₂ molecule to find the number of O atoms in 1 mole of O₂ molecules: \( (6.022 \times 10^{23}) \times 2 = 1.2044 \times 10^{24} \) O atoms. In conclusion, there are 6.022 x 10²³ O₂ molecules in 1 mole of O₂ molecules, and there are 1.2044 x 10²⁴ O atoms in 1 mole of O₂ molecules.

Key Concepts

Understanding the Mole Concept

The mole is a fundamental concept in chemistry. It provides a bridge between the atomic and macroscopic worlds. A mole represents a specific quantity of particles, be it atoms, molecules, or ions. This specific quantity is determined by Avogadro's number, which is 6.022 x 10²³. This means one mole of any substance contains exactly 6.022 x 10²³ particles.

This concept simplifies calculations in chemistry. Instead of counting individual atoms in reactions, we use moles. This way, large amounts can be expressed more conveniently, allowing chemists to describe chemical reactions, compositional details, and properties effectively.

• The mole provides a way to convert between atoms/molecules and grams.
• It's based on exactly 12 grams of carbon-12.
• This concept applies universally to all chemical entities.

Molecules Calculation Made Simple

Calculating the number of molecules is easy once you have the mole concept down. If you know the amount of substance in moles, multiplying by Avogadro's number gives you the total number of molecules.

In our example, if you have 1 mole of \(\mathrm{O}_{2}\), you simply multiply 1 mole by Avogadro's number:
\[ 1 \text{ mole} \times 6.022 \times 10^{23} \text{ molecules/mole} = 6.022 \times 10^{23} \text{ molecules} \]

• This method works for any molecule or atom.
• Just remember, one mole always equals 6.022 x 10²³ entities.
• Multiply the number of moles you have by Avogadro's number to get the total count.

Delving into Elementary Entities

Elementary entities can be any small unit of matter such as atoms, molecules, or ions. In chemistry, these tiny particles combine in various ways to form substances, and the mole connects these microscopic entities to macroscopic measurements.

For instance, in one molecule of \(\mathrm{O}_{2}\), there are two oxygen atoms. If given 1 mole of \(\mathrm{O}_{2}\) molecules, multiplying Avogadro's number by 2 gives the total number of oxygen atoms:
\[ 6.022 \times 10^{23} \text{ molecules} \times 2 \text{ atoms/molecule} = 1.2044 \times 10^{24} \text{ atoms} \]

• This calculation helps determine the total number of elementary entities in compounds.
• The method applies to any substance where multiple elementary entities form a larger molecule.