Problem 91 - Chemistry Matter and Change

Question

Determine the number of representative particles in each substance. a. 4.45 \(\mathrm{mol}\) of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) b. 0.250 \(\mathrm{mol}\) of \(\mathrm{KNO}_{3}\) c. 2.24 \(\mathrm{mol}\) of \(\mathrm{H}_{2}\) d. 9.56 \(\mathrm{mol}\) of \(\mathrm{Zn}\)

Step-by-Step Solution

Answer

The number of representative particles in each substance are: a. \(2.68 \times 10^{24}\) molecules of C6H12O6 b. \(1.51 \times 10^{23}\) molecules of KNO3 c. \(1.34 \times 10^{24}\) molecules of H2 d. \(5.75 \times 10^{24}\) atoms of Zn

Step 1: Use Avogadro's number

Multiply the given number of moles by Avogadro's Number, to find the number of representative particles (molecules) in the substance. \[ Number\ of\ molecules = Moles \times Avogadro's\ number \]

Step 2: Calculate the number of molecules in 4.45 mol of C6H12O6

Using the formula from Step 1, plug in the values. \[ Number\ of\ molecules = 4.45 \times 6.022 \times 10^{23} \] Calculate the number of molecules. \[ Number\ of\ molecules \approx 2.68 \times 10^{24} \] b. 0.250 mol of KNO3

Step 3: Calculate the number of molecules in 0.250 mol of KNO3

Using the formula from Step 1, plug in the values. \[ Number\ of\ molecules = 0.250 \times 6.022 \times 10^{23} \] Calculate the number of molecules. \[ Number\ of\ molecules \approx 1.51 \times 10^{23} \] c. 2.24 mol of H2

Step 4: Calculate the number of molecules in 2.24 mol of H2

Using the formula from Step 1, plug in the values. \[ Number\ of\ molecules = 2.24 \times 6.022 \times 10^{23} \] Calculate the number of molecules. \[ Number\ of\ molecules \approx 1.34 \times 10^{24} \] d. 9.56 mol of Zn

Step 5: Calculate the number of atoms in 9.56 mol of Zn

Since Zn is an element and not a molecule, we will calculate the number of atoms. Using the formula from Step 1, plug in the values. \[ Number\ of\ atoms = 9.56 \times 6.022 \times 10^{23} \] Calculate the number of atoms. \[ Number\ of\ atoms \approx 5.75 \times 10^{24} \]

Key Concepts

representative particles

In chemistry, representative particles refer to the smallest unit of a substance that retains its properties. Such particles can be atoms, molecules, ions, or even formula units, depending on the type of substance in question. For instance, in a sample of Glucose (\(\text{C}_6\text{H}_{12}\text{O}_6\)) or water (\(\text{H}_2\text{O}\)), the representative particles are molecules.
In contrast, for an element like Zinc (Zn), the representative particle is an atom.

• Atoms: smallest unit of an element.
• Molecules: smallest unit of compounds with covalently bonded atoms.
• Formula Units: used for ionic compounds.
• Ions: charged particles for substances in ionic form.

Understanding representative particles is crucial in stoichiometry and chemical reactions as it helps predict how substances interact on a molecular level.Remember, regardless of whether the particle is an atom, molecule, or an ion, Avogadro's Number allows us to count these particles effectively by using moles.

moles

The concept of moles in chemistry is like a bridge between the atomic scale and the macroscopic world we deal with daily. A mole is a quantity used to express a certain number of atoms, ions, or molecules, usually equal to Avogadro’s Number, which is approximately \(6.022 \times 10^{23}\).

• A mole of atoms: \(6.022 \times 10^{23}\) atoms.
• A mole of molecules: \(6.022 \times 10^{23}\) molecules.
• A mole of ions: \(6.022 \times 10^{23}\) ions.

This large number is due to the fact that at the atomic/executive level, particles are incredibly small. Therefore, using moles simplifies weighing and measuring reactions, since chemistry calculations and equations are based on moles rather than directly on atoms or molecules.

chemistry calculations

Chemistry calculations often revolve around conversions between moles and representative particles. This conversion employs Avogadro's Number, allowing chemists to translate between microscopic scales (atoms or molecules) and measurable quantities in labs.
To carry out these calculations:

• Start by identifying the given quantity (usually in moles or grams).
• If working from grams to moles, use the molar mass of the substance.
• To find atoms, molecules, or particles, multiply moles by Avogadro’s Number.

For example, to compute the number of molecules in 4.45 \(\text{mol}\) of Glucose (\(\text{C}_6\text{H}_{12}\text{O}_6\)), use:\[Number\ of\ molecules = 4.45 \times 6.022 \times 10^{23}\]The result gives the total molecules in that sample. Understanding these calculations enables precise measurements and is crucial for the formulation of chemical reactions and the interpretation of experimental results.

molecular formula

A molecular formula resembles a chemical recipe, detailing the types and numbers of atoms in a single molecule of a substance. It provides an essential clue about the composition and structure of the molecule in question. Using this formula, chemists understand:

• How many and which types of atoms are in a molecule.
• The ratio of these atoms in the compound.
• How such molecules might interact with others.

For instance:- In \(\text{C}_6\text{H}_{12}\text{O}_6\) (Glucose), this formula signifies that each molecule comes with 6 Carbon, 12 Hydrogen, and 6 Oxygen atoms.- For \(\text{H}_2\), it highlights that each molecule contains two hydrogen atoms bonded together.
Understanding a molecular formula is vital for determining how much of each element participates in reactions, and it’s a key step in achieving a balanced chemical equation. This knowledge aids in determining the compound's molar mass and predictive stoichiometric calculations.