Problem 91 - Chemistry Matter and Change

Question

Determine the number of representative particles in each substance \begin{equation}\begin{array}{ll}{\text { a. } 4.45 \text { mol of } \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}} & {\text { c. } 2.24 \mathrm{mol} \text { of } \mathrm{H}_{2}} \\ {\text { b. } 0.250 \mathrm{mol}} {\text { of } \mathrm{KNO}_{3}} & {\text { d. } 9.56 \mathrm{mol} \text { of } \mathrm{Zn}}\end{array}\end{equation}

Step-by-Step Solution

Answer

a: \(2.68 \times 10^{24}\) molecules, b: \(1.51 \times 10^{23}\) formula units, c: \(1.35 \times 10^{24}\) molecules, d: \(5.76 \times 10^{24}\) atoms.

Step 1: Understanding Representative Particles

The term 'representative particles' refers to the smallest unit that maintains the chemical identity of a substance. This can be atoms, molecules, or formula units depending on the substance. For compounds like \( \text{C}_6\text{H}_{12}\text{O}_6 \) and \( \text{H}_2 \), these are molecules, while for elements like \( \text{Zn} \), they are atoms, and for ionic compounds like \( \text{KNO}_3 \), they are formula units.

Step 2: Using Avogadro's Number

For each mole of a substance, there are \( 6.022 \times 10^{23} \) representative particles (Avogadro's number). To find the number of representative particles, multiply the number of moles by Avogadro's number.

Step 3: Calculate for \( \text{C}_6 \text{H}_{12} \text{O}_6 \)

The number of molecules in \( 4.45 \) moles of \( \text{C}_6\text{H}_{12}\text{O}_6 \) is calculated as: \[ 4.45 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} = 2.68 \times 10^{24} \text{ molecules}. \]

Step 4: Calculate for \( \text{KNO}_3 \)

The number of formula units in \( 0.250 \) moles of \( \text{KNO}_3 \) is: \[ 0.250 \text{ moles} \times 6.022 \times 10^{23} \text{ formula units/mole} = 1.51 \times 10^{23} \text{ formula units}. \]

Step 5: Calculate for \( \text{H}_2 \)

The number of molecules in \( 2.24 \) moles of \( \text{H}_2 \) is: \[ 2.24 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} = 1.35 \times 10^{24} \text{ molecules}. \]

Step 6: Calculate for \( \text{Zn} \)

The number of atoms in \( 9.56 \) moles of \( \text{Zn} \) is: \[ 9.56 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} = 5.76 \times 10^{24} \text{ atoms}. \]

Key Concepts

Representative Particles

In chemistry, when we talk about representative particles, we refer to the basic units that make up a substance. These particles could be atoms, molecules, or formula units, depending on the type of material. For example:

• Atoms are the representative particles for elements like zinc (Zn).
• Molecules are for molecular compounds, such as glucose (C_6H_{12}O_6) and hydrogen gas (H_2).
• Formula units are used for ionic compounds, like potassium nitrate (KNO_3).

Understanding which type of particle a substance comprises helps in determining the substance's characteristics and behavior in reactions.

Moles

A mole is a way to count particles, similar to how a dozen refers to twelve items. In chemistry, a mole corresponds to Avogadro's number, which is exactly 6.022 imes 10^{23} particles. This standardized number allows chemists to discuss and quantify substances in a meaningful way.
The concept of a mole is pivotal because chemical reactions often occur at the molecular level, and we need a large, consistent unit to connect microscopic interactions to macroscopic measurements, such as grams and liters.

Chemical Identity

The chemical identity of a substance tells us what the substance is composed of and how it behaves. It's largely determined by its representative particles:

• The term 'identity' denotes the arrangement and type of atoms in a molecule or compound.
• It contributes to properties such as reactivity, boiling point, and solubility.

For example, each molecule of glucose (C_6H_{12}O_6) maintains specific atoms and structure, making it unique. Similarly, an element like zinc has atoms that represent its chemical identity.

Calculations with Moles

Calculating with moles often involves using Avogadro's number to convert between moles and the number of particles. Here's how it works:
For any substance, knowing the number of moles allows us to calculate how many individual particles we have by multiplying the moles by Avogadro's number, 6.022 imes 10^{23} particles per mole.

• For instance, if you have 4.45 moles of C_6H_{12}O_6, multiplying this by Avogadro's number gives you 2.68 imes 10^{24} molecules.
• Similarly, calculating for 0.250 moles of KNO_3 provides 1.51 imes 10^{23} formula units.

Calculations like these are essential for working with chemical quantities, planning reactions, and understanding substance composition.