Problem 29 - Chemistry for Allied Health

Question

How many molecules of water are present in each of the following samples? a. 1 mole b. 2 moles c. \(2.5\) moles d. \(0.5\) moles e. \(0.35\) moles

Step-by-Step Solution

Answer

a. \(6.022 \times 10^{23}\), b. \(1.2044 \times 10^{24}\), c. \(1.5055 \times 10^{24}\), d. \(3.011 \times 10^{23}\), e. \(2.1077 \times 10^{23}\) molecules.

Step 1: First Understand the Concept

Avogadro's number is a key number in chemistry and it tells us how many atoms, ions, or molecules are in one mole of a substance. Avogadro's number is approximately \(6.022 \times 10^{23}\). Thus, one mole of any substance, including water, contains \(6.022 \times 10^{23}\) molecules.

Step 2: Calculate for 1 Mole

For 1 mole of water, the number of molecules is calculated by multiplying the moles by Avogadro's number. So, the number of molecules is: \[1 \text{ mole} \times 6.022 \times 10^{23} = 6.022 \times 10^{23} \text{ molecules}\]

Step 3: Calculate for 2 Moles

For 2 moles of water, multiply the number of moles by Avogadro's number to find the number of molecules: \[2 \text{ moles} \times 6.022 \times 10^{23} = 1.2044 \times 10^{24} \text{ molecules}\]

Step 4: Calculate for 2.5 Moles

For 2.5 moles, similarly, you multiply the moles by Avogadro's number: \[2.5 \text{ moles} \times 6.022 \times 10^{23} = 1.5055 \times 10^{24} \text{ molecules}\]

Step 5: Calculate for 0.5 Moles

For 0.5 moles, you perform the multiplication with Avogadro's number: \[0.5 \text{ moles} \times 6.022 \times 10^{23} = 3.011 \times 10^{23} \text{ molecules} \]

Step 6: Calculate for 0.35 Moles

For 0.35 moles, again multiply by Avogadro's number to find the number of molecules: \[0.35 \text{ moles} \times 6.022 \times 10^{23} = 2.1077 \times 10^{23} \text{ molecules}\]

Key Concepts

Understanding the Mole Concept

In chemistry, the mole concept is fundamental for dealing with chemical quantities. It provides a bridge between the atomic world and the real-world quantities that we can measure. The mole is a unit that measures the amount of substance. One mole of any substance contains exactly Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\). This large number makes it practical to count particles like atoms or molecules that are extremely small. For example, one mole of water molecules contains \(6.022 \times 10^{23}\) water molecules. This concept allows chemists to easily convert between the mass of a substance and the number of molecules, atoms, or ions it contains, which is crucial in chemical reactions and processes. The mole simplifies calculations that would otherwise be tedious with such enormous numbers of particles.

Molecular Calculations Using Avogadro's Number

Molecular calculations in chemistry often involve converting between moles and the number of molecules using Avogadro's number. This type of calculation helps us understand chemical formulas and reactions on a molecular level. To determine the number of molecules in a given number of moles, multiply the number of moles by Avogadro's number:

• For 1 mole, it's \(1 \times 6.022 \times 10^{23} = 6.022 \times 10^{23}\) molecules.
• For 2 moles, \(2 \times 6.022 \times 10^{23} = 1.2044 \times 10^{24}\) molecules.
• For 2.5 moles, \(2.5 \times 6.022 \times 10^{23} = 1.5055 \times 10^{24}\) molecules.
• For 0.5 moles, \(0.5 \times 6.022 \times 10^{23} = 3.011 \times 10^{23}\) molecules.
• For 0.35 moles, \(0.35 \times 6.022 \times 10^{23} = 2.1077 \times 10^{23}\) molecules.

These calculations are essential for understanding not only how much of a substance is present but also how it will interact in chemical reactions. With molecular calculations, chemists can predict the quantities of products and reactants involved in reactions.

Importance of Mole Concept in Chemistry Education

The mole concept is a critical aspect of chemistry education. It introduces students to how chemists use a special counting unit to make sense of substances in both experimental and theoretical studies. Understanding the mole concept is crucial at all levels of chemistry because it forms the basis for stoichiometry, thermodynamics, and kinetics, among others. Teachers emphasize mastering the mole concept for several reasons:

• It provides a quantitative framework for deeper understandings of chemical reactions.
• Converts atomic scale measurements to macroscopic quantities that can be measured and observed.
• Illustrates how chemical equations are balanced and reactions are quantitatively analyzed.

Incorporating this concept effectively in education ensures students can confidently approach problems involving chemical quantities and fosters a better understanding of molecular dynamics. This foundation is essential for tackling more advanced topics in chemistry, making the mole concept a keystone in chemistry curricula across the world.