Problem 13 - Chemistry Matter and Change

Question

Calculate the number of representative particles of each substance. \begin{equation}\begin{array}{ll}{\text { a. } 11.5 \mathrm{mol} \mathrm{Ag}} & {\text { c. } 0.150 \mathrm{mol} \mathrm{NaCl}} \\ {\text { b. } 18.0 \mathrm{mol} \mathrm{H}_{2} \mathrm{O}} & {\text { d. } 1.35 \times 10^{-2} \mathrm{mol} \mathrm{CCH}_{4}}\end{array}\end{equation}

Step-by-Step Solution

Answer

a. \(6.9253 \times 10^{24}\) atoms Ag; b. \(1.08396 \times 10^{25}\) molecules H₂O; c. \(9.033 \times 10^{22}\) formula units NaCl; d. \(8.1297 \times 10^{21}\) molecules CCH₄.

Step 1: Understand the concept

In chemistry, the term 'representative particles' can refer to atoms, molecules, or ions, depending on the substance. For molecules, such as water (H₂O), the representative particles are the molecules themselves, while for ionic compounds like sodium chloride (NaCl), the particles are formula units.

Step 2: Recall Avogadro's Number

The number of representative particles in one mole of any substance is given by Avogadro's number, which is approximately \(6.022 \times 10^{23}\). This constant is crucial for converting moles to particles.

Step 3: Calculate for Silver, \(\text{Ag}\)

For silver, which is an atomic element, the representative particles are atoms. Use Avogadro's number to convert moles to atoms: \[11.5 \text{ mol Ag} \times 6.022 \times 10^{23} \text{ atoms/mol} = 6.9253 \times 10^{24} \text{ atoms Ag}\]

Step 4: Calculate for Water, \(\text{H}_2\text{O}\)

For water, the representative particles are molecules. Convert moles to molecules:\[18.0 \text{ mol H}_2\text{O} \times 6.022 \times 10^{23} \text{ molecules/mol} = 1.08396 \times 10^{25} \text{ molecules H}_2\text{O}\]

Step 5: Calculate for Sodium Chloride, \(\text{NaCl}\)

For sodium chloride, the representative particles are formula units. Convert moles to formula units:\[0.150 \text{ mol NaCl} \times 6.022 \times 10^{23} \text{ formula units/mol} = 9.033 \times 10^{22} \text{ formula units NaCl}\]

Step 6: Calculate for Acetylene, \(\text{CCH}_4\)

For acetylene, the representative particles are molecules. Convert moles to molecules:\[1.35 \times 10^{-2} \text{ mol CCH}_4 \times 6.022 \times 10^{23} \text{ molecules/mol} = 8.1297 \times 10^{21} \text{ molecules CCH}_4\]

Key Concepts

Moles to Particles Conversion

When it comes to chemistry, converting moles to particles is a fundamental concept that helps us understand the quantity of substances we work with. Moles provide a bridge between the atomic scale and the macroscopic scale we can observe. Imagine having a really big collection of something, like LEGO bricks. It's cumbersome to count each one, so we use a larger unit of measurement. In chemistry, this unit is called the mole.

The key player in this conversion process is Avogadro's Number, which is approximately \(6.022 \times 10^{23}\). This large number tells us how many representative particles exist in one mole of a substance, whether it's atoms, molecules, or ions. To convert from moles to particles:

• Multiply the number of moles by Avogadro's Number.
• This gives you the total number of particles.

For instance, if you have 1 mole of a substance, it contains \(6.022 \times 10^{23}\) particles. Similarly, converting back from particles to moles involves dividing the number of particles by Avogadro's Number.

Representative Particles

In chemistry, the term 'representative particles' is used to indicate the smallest unit of a substance that retains the chemical properties of that substance. Depending on the substance, these particles could be atoms, molecules, or formula units.

• Atoms: For elements like silver (Ag), the representative particle is the atom.
• Molecules: For molecular compounds such as water (\(\text{H}_2\text{O}\)), the representative particles are the molecules themselves.
• Formula Units: For ionic compounds like sodium chloride (\(\text{NaCl}\)), the smallest repeating unit is called a formula unit.

Understanding these terms is crucial for solving problems involving particle conversions. Recognizing the type of particles involved allows you to correctly use Avogadro’s number in your calculations. Whether you're dealing with atoms, molecules, or formula units, the process of calculating the total number of these particles is fundamentally the same.

Chemistry Calculations

Chemistry involves various calculations that help us predict and understand the behavior of substances at the molecular level. Calculating the number of representative particles in a substance is one of the many calculative aspects you will encounter. Here's a simple breakdown of how you manage these calculations:

1. **Identify the Substance:** Determine whether you are dealing with an element, compound, or a mixture. Knowing this will help you identify the appropriate representative particle.

2. **Use Avogadro’s Number:** As discussed, this number is essential for converting between moles and particles. It acts as a conversion factor allowing you to switch from the macroscopic view of chemistry to the atomic scale.

3. **Perform the Calculations:** Depending on your initial quantity, you will either multiply or divide by Avogadro’s number to find the number of representative particles or the number of moles. Use this when determining quantities in experiments or predicting outcomes in chemical reactions.

• Multiplying when converting from moles to particles.
• Dividing when converting from particles to moles.

By mastering these calculations, you lay a solid foundation for deeper topics in chemistry such as stoichiometry, reaction yields, and concentration measurements.