Problem 93 - Chemistry Matter and Change

Question

Determine the number of moles in each substance. \begin{equation}\begin{array}{l}{\text { a. } 3.25 \times 10^{20} \text { atoms of lead }} \\ {\text { b. } 4.96 \times 10^{24} \text { molecules of glucose }} \\ {\text { c. } 1.56 \times 10^{23} \text { formula units of sodium hydroxide }} \\ {\text { d. } 1.25 \times 10^{25} \text { copper (II) ions }}\end{array}\end{equation}

Step-by-Step Solution

Answer

a. \(5.40 \times 10^{-4}\) moles of lead; b. 8.23 moles of glucose; c. 0.259 moles of NaOH; d. 20.75 moles of Cu^{2+}.

Step 1: Understanding Avogadro's Number

Avogadro's number, which is \(6.022 \times 10^{23}\), represents the number of atoms, molecules, or formula units in one mole of a substance. It is a fundamental constant used to convert between atoms/molecules and moles.

Step 2: Calculating Moles for Lead

Given: \(3.25 \times 10^{20}\) atoms of lead. Number of moles is calculated using: \[\text{moles} = \frac{\text{atoms}}{6.022 \times 10^{23}}\] Plug the values: \[\text{moles of lead} = \frac{3.25 \times 10^{20}}{6.022 \times 10^{23}} \approx 5.40 \times 10^{-4}\]

Step 3: Calculating Moles for Glucose

Given: \(4.96 \times 10^{24}\) molecules of glucose. Use the formula: \[\text{moles} = \frac{\text{molecules}}{6.022 \times 10^{23}}\] Plug the values: \[\text{moles of glucose} = \frac{4.96 \times 10^{24}}{6.022 \times 10^{23}} \approx 8.23\]

Step 4: Calculating Moles for Sodium Hydroxide

Given: \(1.56 \times 10^{23}\) formula units of sodium hydroxide. Use the formula: \[\text{moles} = \frac{\text{formula units}}{6.022 \times 10^{23}}\] Plug the values: \[\text{moles of NaOH} = \frac{1.56 \times 10^{23}}{6.022 \times 10^{23}} \approx 0.259\]

Step 5: Calculating Moles for Copper (II) Ions

Given: \(1.25 \times 10^{25}\) copper (II) ions. Use the formula: \[\text{moles} = \frac{\text{ions}}{6.022 \times 10^{23}}\] Plug the values: \[\text{moles of Cu^{2+}} = \frac{1.25 \times 10^{25}}{6.022 \times 10^{23}} \approx 20.75\]

Key Concepts

Moles Calculation

Moles are a fundamental unit in chemistry that allows scientists to count particles like atoms, molecules, and ions in a convenient way. One mole of any substance contains exactly Avogadro's number of particles, which is crucial for doing calculations involving very large or very small amounts. To convert the number of atoms, molecules, or formula units to moles, you use the relationship:

• Moles = \(\text{Number of Particles} / 6.022 \times 10^{23}\)

This equation can be customized for any calculation involving atoms, molecules, or formula units, making it an indispensable tool in chemistry. The goal is to use this equation to find out how many moles are present when given a specific number of particles.
Identifying what kind of particles you are dealing with (atoms, molecules, etc.) and using Avogadro's number correctly is key to getting accurate calculations.

Atoms to Moles Conversion

When you want to convert atoms into moles, it is essential to understand that any element has atoms that are countable using Avogadro's number. For example, if you know there are \(3.25 \times 10^{20}\) atoms of lead, you would use the formula:

• Moles of lead = \(\frac{3.25 \times 10^{20} \text{ atoms}}{6.022 \times 10^{23}}\)

This calculation helps you determine how many moles are equivalent to the given number of atoms. Since the number is so small compared to Avogadro's number, the result is a fraction, showing that you have less than one mole. Always remember to check your units to ensure they are consistent, as this can help prevent errors during calculations.

Molecules to Moles Conversion

Much like atoms, molecules can also be converted to moles using Avogadro's number. For molecules like glucose, if given \(4.96 \times 10^{24}\) molecules, the conversion is as follows:

• Moles of glucose = \(\frac{4.96 \times 10^{24} \text{ molecules}}{6.022 \times 10^{23}}\)

This division yields the number of moles of glucose. In this case, the number is quite large and exceeds one mole, indicating a substantial amount of molecules. This conversion is vital in biochemistry, where understanding and interpreting the amount of biomolecules in moles can help elucidate reaction mechanisms and stoichiometry.

Formula Units to Moles Conversion

Lastly, converting formula units into moles is a similar process applied to ionic compounds. If you're working with sodium hydroxide, with \(1.56 \times 10^{23}\) formula units, use the formula:

• Moles of sodium hydroxide = \(\frac{1.56 \times 10^{23} \text{ formula units}}{6.022 \times 10^{23}}\)

Formula units express the lowest ratio of ions in an ionic compound, just as molecules represent covalent substances. Performing the conversion helps understand the substance's scale in a reaction, aiding in successful experiment setups. It is crucial to differentiate between formula units, molecules, and atoms based on the type of substance you are dealing with to achieve accurate results.