Problem 92 - Chemistry Matter and Change

Question

How many molecules are contained in each compound? \begin{equation}\begin{array}{l}{\text { a. } 1.35 \text { mol of carbon disulfide }\left(\mathrm{CS}_{2}\right)} \\ {\text { b. } 0.254 \text { mol of diarsenic trioxide }\left(\mathrm{As}_{2} \mathrm{O}_{3}\right)} \\ {\text { c. } 1.25 \text { mol of water }} \\ {\text { d. } 150.0 \text { mol of } \mathrm{HCl}}\end{array}\end{equation}

Step-by-Step Solution

Answer

a. 8.13 x 10^{23}, b. 1.53 x 10^{23}, c. 7.53 x 10^{23}, d. 9.033 x 10^{25} molecules.

Step 1: Understanding the Relationship Between Moles and Molecules

To determine the number of molecules in a given amount of moles, we need to use Avogadro’s number, which is \(6.022 \times 10^{23}\) molecules per mole. This number tells us how many individual entities (atoms, ions, molecules) are contained in one mole of a substance.

Step 2: Calculating Molecules for CS2

We have 1.35 moles of carbon disulfide (\( \text{CS}_2 \)). Using Avogadro's number, we multiply: \[ \text{Number of molecules} = 1.35 \times 6.022 \times 10^{23} = 8.13 \times 10^{23} \] molecules of \( \text{CS}_2 \).

Step 3: Calculating Molecules for As2O3

For diarsenic trioxide (\( \text{As}_2 \text{O}_3 \)), we have 0.254 moles. Multiply this by Avogadro's number:\[ \text{Number of molecules} = 0.254 \times 6.022 \times 10^{23} = 1.53 \times 10^{23} \] molecules of \( \text{As}_2 \text{O}_3 \).

Step 4: Calculating Molecules for Water

We are given 1.25 moles of water. We again use Avogadro's number:\[ \text{Number of molecules} = 1.25 \times 6.022 \times 10^{23} = 7.53 \times 10^{23} \] molecules of water.

Step 5: Calculating Molecules for HCl

For 150.0 moles of HCl, the same process applies:\[ \text{Number of molecules} = 150.0 \times 6.022 \times 10^{23} = 9.033 \times 10^{25} \] molecules of HCl.

Key Concepts

Understanding the Mole Concept

The mole is a fundamental concept in chemistry that refers to a specific quantity of particles, such as atoms, ions, or molecules. A mole of any substance contains Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\). This large number allows chemists to describe and calculate the amount of substance at the atomic or molecular level in a manner that aligns with macroscopic measurements. The mole concept is essential because it establishes a bridge between the atomic scale and tangible amounts of material that one can work with in a laboratory.

• A mole is similar to a dozen, but instead of 12, it uses \(6.022 \times 10^{23}\).
• Understanding moles aids in determining how reactions occur and how chemical equations are balanced.

By using the mole, chemists can convert between mass, number of entities (like atoms or molecules), and volume in a straightforward manner, when gases are involved. Overall, the concept of the mole simplifies calculations that involve large quantities of small particles.

Molecular Calculation Made Simple

Molecular calculation is a crucial component in chemistry that allows us to determine the number of molecules in a given sample. To perform these calculations correctly, Avogadro's number serves as the bridge between the macroscopic quantities we measure and the microscopic entities they consist of.To find the number of molecules in a sample, you will start with the number of moles provided for a compound:

• Multiply the number of moles by Avogadro's number \(6.022 \times 10^{23}\).
• The result is the total number of molecules in that sample.

For instance, if you have 1 mole of water, multiplying 1 by \(6.022 \times 10^{23}\) will give you \(6.022 \times 10^{23}\) water molecules. This approach is universal for all compounds regardless of their complexity.Using this methodology, students can comprehend and solve exercises involving the mole concept more efficiently, gaining a more concrete understanding of chemical quantifications.

Exploring Chemical Compounds

Chemical compounds are substances formed from two or more elements that are chemically bonded together in fixed ratios. Each compound has a unique chemical formula that indicates the types and numbers of atoms it contains. For example, water is a compound composed of two hydrogen atoms and one oxygen atom, thus represented as \(H_2O\).In the context of mole-based calculations, compounds show how individual atoms combine and the total number of a compound's molecules can be determined.

• Understanding chemical formulas allows chemists to predict how different substances will react.
• Each formula unit in a compound stands for a specific number of atoms, extending to large groups when scaled by moles.

For practical purposes, knowing the chemical compounds involved allows us to understand the inherent relationships between reactants and products in reactions. In exercises like calculating molecules, recognizing the compound's formula is key to understanding its composition and behavior during reactions.Comprehension of chemical compounds is foundational in applying chemistry to real-world problems, ultimately allowing for effective use in synthesis, analysis, and broader chemical engineering processes.