Problem 6 - Chemistry Matter and Change

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. \(3.58 \times 10^{23} \mathrm{ZnCl}_{2}\)

Step-by-Step Solution

Answer

CO₂: 6.23 moles; ZnCl₂: 0.594 moles.

Step 1: Understanding Representative Particles

Representative particles refer to the smallest unit of a substance that retains the chemical identity of that substance. For molecules like CO₂ and ZnCl₂, they are considered as molecules.

Step 2: Determine the Given Number of Particles

We are given a. for CO₂, we have \(3.75 \times 10^{24}\) molecules and b. for ZnCl₂, we have \(3.58 \times 10^{23}\) molecules.

Step 3: Use Avogadro's Number for Conversion

Avogadro's number, \(6.022 \times 10^{23}\), represents the number of particles in one mole of a substance. This will be used to convert the number of molecules to moles.

Step 4: Convert CO₂ Molecules to Moles

For CO₂, divide the number of molecules by Avogadro's number: \[\text{Moles CO}_2 = \frac{3.75 \times 10^{24} \text{ molecules}}{6.022 \times 10^{23}} = 6.23 \text{ moles}\]

Step 5: Convert ZnCl₂ Molecules to Moles

For ZnCl₂, divide the number of molecules by Avogadro's number: \[\text{Moles ZnCl}_2 = \frac{3.58 \times 10^{23} \text{ molecules}}{6.022 \times 10^{23}} = 0.594 \text{ moles}\]

Key Concepts

Avogadro's Number

Avogadro's number is a fundamental concept in chemistry. It is named after the Italian scientist Amedeo Avogadro. This number is incredibly significant because it connects microscopic atomic scales to macroscopic quantities we use in the laboratory. Avogadro's number is exactly defined as \(6.022 \times 10^{23}\). It tells us how many atoms, molecules, or particles are found in one mole of a substance. So, when we talk about a "mole", we're talking about a quantity that contains this many particles. In our everyday lives, it's like saying a dozen means twelve. Avogadro's number is our chemical "dozen", but much larger!

Representative Particle

A representative particle is the smallest unit that retains the identity of a chemical substance. It can be an atom, a molecule, a formula unit, or an ion. The type of particle depends on the nature of the substance. For example:

• In chemical elements like helium (He), the representative particle is the atom.
• In molecular compounds like carbon dioxide (CO₂), it is the molecule.
• For ionic compounds such as sodium chloride (NaCl), the particle is the formula unit.

Understanding the type of representative particle is crucial because it helps in converting between particles and moles using Avogadro's number. When you know what kind of particle you have, you can more effectively use these particles in chemical reactions and calculations.

Molecular Conversion

Molecular conversion refers to changing the quantity of a substance in terms of representative particles, like molecules, into moles. This conversion is essential because chemical reactions are typically described in terms of moles rather than individual particles. By using Avogadro's number, you can convert the number of particles you have into an equivalent number of moles. Here's how you do it:

• Take the number of particles or molecules you have.
• Divide that number by Avogadro's number \(6.022 \times 10^{23}\).
• This results in how many moles are present.

For example, if you have \(3.75 \times 10^{24}\) CO₂ molecules, you can convert them to moles by dividing by Avogadro's number, resulting in about 6.23 moles.

Chemical Formula

A chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule. It provides essential information at a glance about the substances involved in a chemical reaction. For example, in the formula for carbon dioxide, CO₂, the 'C' stands for one carbon atom, and the 'O₂' indicates there are two oxygen atoms. This tells us that each molecule of carbon dioxide consists of one carbon atom and two oxygen atoms.

• Understanding a chemical formula is essential because it helps determine the representative particle of a compound.
• The formula also helps in calculating the molar mass, which is the mass of one mole of the substance.
• It is crucial for balancing chemical equations and for comprehensive molecular conversions.

Recognizing the structure and symbol of chemical formulas aids in understanding reactions and stoichiometry in chemistry.