Question

Challenge Identify the representative particle for each formula, and convert the given number of representative particles to moles a. \(3.75 \times 10^{24} \mathrm{CO}_{2} \quad\) b. \(3.58 \times 10^{23} \mathrm{ZnCl}_{2}\)

Short answer

The representative particles for the given chemical substances are a. carbon dioxide molecule (\(\mathrm{CO}_{2}\)) and b. formula unit of zinc chloride (\(\mathrm{ZnCl}_{2}\)). After converting the given number of representative particles to moles using Avogadro's number, we find a. \(6.22 \, \text{moles}\) of carbon dioxide (\(\mathrm{CO}_{2}\)) and b. \(0.60 \, \text{moles}\) of zinc chloride (\(\mathrm{ZnCl}_{2}\)).

Step-by-step solution

Identify the representative particles

For each chemical formula, we need to determine the representative particle, which could be a molecule, an ion, etc.: a. For \(\mathrm{CO}_{2}\), the representative particle is the molecule carbon dioxide. b. For \(\mathrm{ZnCl}_{2}\), the representative particle is the formula unit of zinc chloride.

Use Avogadro's number to convert the number of particles to moles

We are given the number of representative particles, and we'll use Avogadro's number to find the moles for each: a. \(3.75 \times 10^{24} \, \mathrm{CO}_{2}\) particles Number of moles = \(\dfrac{3.75 \times 10^{24} \, \mathrm{CO}_{2} \, \text{particles}}{6.022 \times 10^{23} \, \mathrm{particles/mol}}\) b. \(3.58 \times 10^{23} \, \mathrm{ZnCl}_{2}\) particles Number of moles = \(\dfrac{3.58 \times 10^{23} \, \mathrm{ZnCl}_{2} \, \text{particles}}{6.022 \times 10^{23} \, \mathrm{particles/mol}}\)

Calculate the number of moles

Now we can calculate and find the number of moles for both chemical substances: a. \(3.75 \times 10^{24} \, \mathrm{CO}_{2} \, \text{particles}\) Number of moles = \(\dfrac{3.75 \times 10^{24}}{6.022 \times 10^{23}} ≈ 6.22 \, \text{moles}\) b. \(3.58 \times 10^{23} \, \mathrm{ZnCl}_{2} \, \text{particles}\) Number of moles = \(\dfrac{3.58 \times 10^{23}}{6.022 \times 10^{23}} ≈ 0.60 \, \text{moles}\) Thus, we have calculated the number of moles for each chemical substance: a. 6.22 moles of carbon dioxide (\(\mathrm{CO}_{2}\)) and b. 0.60 moles of zinc chloride (\(\mathrm{ZnCl}_{2}\)).

Key concepts

Avogadro's number

Avogadro's number, often denoted by the symbol 6.022×10²³, is a fundamental constant in chemistry. It represents the quantity of representative particles, such as atoms, molecules, or ions, contained in one mole of a substance. This value is pivotal in converting between the number of particles and the amount in moles—a measure of the amount of substance. The sheer size of Avogadro's number illustrates the minuscule scale that atoms and molecules occupy. When dealing with chemical reactions, using moles allows chemists to consider a manageable number rather than trying to count individual atoms or molecules.

Let's look at a practical application of Avogadro's number, as seen in the provided exercise. For example, when converting the given number of carbon dioxide molecules to moles, we divide the number of CO₂ molecules by Avogadro's number. This calculation yields the amount of the substance in moles, a much more practical unit for laboratory and theoretical work. Handling chemical equations and stoichiometric calculations requires a clear understanding of this concept to ensure accuracy in both theoretical and practical chemistry.

Representative particles

The concept of representative particles involves identifying the smallest unit that characterizes a substance's composition. These particles, depending on the nature of the substance, can be atoms, molecules, ions, or formula units. For example, in the exercise, CO₂ is identified as a molecule composed of one carbon atom and two oxygen atoms bonded together, while ZnCl₂ is a formula unit representing the ionic compound made of zinc and chlorine.

Understanding the type of representative particle is crucial when performing mole conversions. This knowledge allows us to correlate the number of these particles with measurable quantities like moles, using Avogadro's number as the bridge. Tackling these conversions requires a blend of conceptual understanding and mathematical skill. When approaching homework or lab experiments involving moles, always start by identifying the representative particle, as it will guide the rest of your calculations.

Molecular formulas

Molecular formulas express the number and type of atoms that make up a single molecule of a compound. They serve as a blueprint, providing essential information on the components of the substance. In chemistry, these formulas are indispensable for understanding the quantitative and qualitative aspects of the material.

In our exercise, CO₂ and ZnCl₂ are the molecular formulas for carbon dioxide and zinc chloride, respectively. The molecular formula for carbon dioxide indicates that each molecule is composed of one carbon atom and two oxygen atoms. For zinc chloride, ZnCl₂ signifies that each formula unit (appropriate for ionic compounds) consists of one zinc ion and two chloride ions. These formulas are more than just symbols; they convey the stoichiometry of the compounds, which directly correlates to the proportion of elements during chemical reactions. Grasping molecular formulas and their link to mole conversions helps to streamline problem-solving and is instrumental in understanding the nuances of chemical composition.