Which Of The Following Contains The Most Moles Of Atoms

Determining which substance contains the most moles of atoms requires a clear understanding of moles, atoms, and how to calculate the number of moles present in a given amount of substance. This involves considering the chemical formula of each substance and using Avogadro's number as a bridge between the macroscopic world of grams and the microscopic world of atoms. Let's delve into the process with a comprehensive approach.

Understanding the Basics

Before diving into comparisons, it's crucial to grasp the fundamental concepts:

• Mole: The mole is the SI unit for the amount of a substance. One mole contains exactly 6.02214076 × 10^23 elementary entities (atoms, molecules, ions, etc.). This number is known as Avogadro's number (Nₐ).
• Avogadro's Number (Nₐ): A fundamental constant in chemistry that represents the number of entities (usually atoms or molecules) in one mole. Its value is approximately 6.022 × 10^23.
• Molar Mass: The mass of one mole of a substance, expressed in grams per mole (g/mol). It is numerically equal to the substance's atomic or molecular weight.
• Chemical Formula: A symbolic representation of a molecule that indicates the types of atoms and their ratios in the compound (e.g., H₂O, NaCl).

The General Approach

To determine which substance contains the most moles of atoms, follow these steps:

1. Determine the Number of Moles of Each Substance: Divide the given mass of the substance by its molar mass.
2. Determine the Number of Atoms per Molecule or Formula Unit: Examine the chemical formula of the substance to find out how many atoms of each element are present in one molecule or formula unit.
3. Calculate the Total Moles of Atoms: Multiply the number of moles of the substance by the number of atoms per molecule or formula unit.
4. Compare the Results: The substance with the highest total moles of atoms is the answer.

Example Scenario and Detailed Calculations

Let's consider a scenario where we need to determine which of the following samples contains the most moles of atoms:

1. 4.0 g of Helium (He)
2. 4.0 g of Water (H₂O)
3. 4.0 g of Methane (CH₄)

Here's a step-by-step breakdown of how to solve this problem:

Step 1: Calculate Moles of Each Substance

• Helium (He):

  • Molar mass of He = 4.00 g/mol
  • Moles of He = Mass / Molar mass = 4.0 g / 4.00 g/mol = 1.0 mole

• Water (H₂O):

  • Molar mass of H₂O = (2 × 1.01 g/mol) + 16.00 g/mol = 18.02 g/mol
  • Moles of H₂O = Mass / Molar mass = 4.0 g / 18.02 g/mol ≈ 0.222 mole

• Methane (CH₄):

  • Molar mass of CH₄ = 12.01 g/mol + (4 × 1.01 g/mol) = 16.05 g/mol
  • Moles of CH₄ = Mass / Molar mass = 4.0 g / 16.05 g/mol ≈ 0.249 mole

Step 2: Determine Number of Atoms per Molecule/Formula Unit

• Helium (He): Each He atom is a single atom. So, there is 1 atom per He "molecule."

• Water (H₂O): Each water molecule consists of 2 hydrogen atoms and 1 oxygen atom. So, there are 3 atoms per H₂O molecule.

• Methane (CH₄): Each methane molecule consists of 1 carbon atom and 4 hydrogen atoms. So, there are 5 atoms per CH₄ molecule.

Step 3: Calculate Total Moles of Atoms

• Helium (He):

  • Moles of atoms = Moles of He × Atoms per molecule = 1.0 mole × 1 atom/molecule = 1.0 mole of atoms

• Water (H₂O):

  • Moles of atoms = Moles of H₂O × Atoms per molecule = 0.222 mole × 3 atoms/molecule ≈ 0.666 mole of atoms

• Methane (CH₄):

  • Moles of atoms = Moles of CH₄ × Atoms per molecule = 0.249 mole × 5 atoms/molecule ≈ 1.245 moles of atoms

Step 4: Compare Results

Comparing the total moles of atoms:

• Helium: 1.0 mole of atoms
• Water: 0.666 mole of atoms
• Methane: 1.245 moles of atoms

Conclusion: 4.0 g of methane (CH₄) contains the most moles of atoms.

Additional Examples and Considerations

To further illustrate, let's consider a few more examples with different substances and masses.

Example 1: Comparing Different Compounds

Which of the following contains the most moles of atoms?

1. 10.0 g of Sodium Chloride (NaCl)
2. 10.0 g of Glucose (C₆H₁₂O₆)
3. 10.0 g of Diamond (C)

• Sodium Chloride (NaCl):

  • Molar mass of NaCl = 22.99 g/mol (Na) + 35.45 g/mol (Cl) = 58.44 g/mol
  • Moles of NaCl = 10.0 g / 58.44 g/mol ≈ 0.171 mole
  • Atoms per formula unit = 1 Na + 1 Cl = 2 atoms
  • Moles of atoms = 0.171 mole × 2 atoms ≈ 0.342 mole of atoms

• Glucose (C₆H₁₂O₆):

  • Molar mass of C₆H₁₂O₆ = (6 × 12.01) + (12 × 1.01) + (6 × 16.00) = 180.18 g/mol
  • Moles of Glucose = 10.0 g / 180.18 g/mol ≈ 0.0555 mole
  • Atoms per molecule = 6 C + 12 H + 6 O = 24 atoms
  • Moles of atoms = 0.0555 mole × 24 atoms ≈ 1.332 moles of atoms

• Diamond (C):

  • Molar mass of C = 12.01 g/mol
  • Moles of C = 10.0 g / 12.01 g/mol ≈ 0.833 mole
  • Atoms per "molecule" = 1 atom
  • Moles of atoms = 0.833 mole × 1 atom ≈ 0.833 mole of atoms

Conclusion: 10.0 g of Glucose (C₆H₁₂O₆) contains the most moles of atoms.

Example 2: Comparing Elements and Compounds

Which of the following contains the most moles of atoms?

1. 5.0 g of Iron (Fe)
2. 5.0 g of Ammonia (NH₃)

• Iron (Fe):

  • Molar mass of Fe = 55.85 g/mol
  • Moles of Fe = 5.0 g / 55.85 g/mol ≈ 0.0895 mole
  • Atoms per "molecule" = 1 atom
  • Moles of atoms = 0.0895 mole × 1 atom ≈ 0.0895 mole of atoms

• Ammonia (NH₃):

  • Molar mass of NH₃ = 14.01 g/mol (N) + (3 × 1.01 g/mol) (H) = 17.04 g/mol
  • Moles of NH₃ = 5.0 g / 17.04 g/mol ≈ 0.293 mole
  • Atoms per molecule = 1 N + 3 H = 4 atoms
  • Moles of atoms = 0.293 mole × 4 atoms ≈ 1.172 moles of atoms

Conclusion: 5.0 g of Ammonia (NH₃) contains the most moles of atoms.

Common Pitfalls and How to Avoid Them

• Incorrect Molar Mass: Double-check the molar masses using a reliable periodic table or online resource. Errors in molar mass will propagate through the entire calculation.
• Miscounting Atoms: Carefully count the number of atoms in each molecule or formula unit. For complex molecules, it's helpful to write out the formula and count systematically.
• Forgetting to Multiply by the Number of Atoms: This is a common mistake. Remember that you are calculating the moles of atoms, not just the moles of the substance.
• Unit Confusion: Always use consistent units (grams for mass, grams/mole for molar mass) to avoid errors.

Theoretical Considerations

The number of moles of atoms is directly proportional to the mass of the substance divided by its molar mass and multiplied by the number of atoms per molecule. This relationship can be expressed as:

Moles of atoms = (Mass / Molar mass) × (Atoms per molecule)

This formula highlights the key factors that influence the number of moles of atoms:

• Mass: A larger mass generally leads to more moles of atoms, assuming other factors are constant.
• Molar Mass: A smaller molar mass generally leads to more moles of atoms for the same mass of substance.
• Atoms per Molecule: Compounds with more atoms per molecule will have a higher number of moles of atoms.

Practical Applications

Understanding how to calculate and compare moles of atoms has several practical applications in chemistry:

• Stoichiometry: Essential for calculating the amounts of reactants and products in chemical reactions.
• Materials Science: Important for determining the composition and properties of materials.
• Environmental Science: Used in analyzing pollutants and their impact on the environment.
• Biochemistry: Applied in studying the composition and reactions of biological molecules.

Tips for Success

• Practice: Work through plenty of examples to become comfortable with the calculations.
• Organization: Keep your work organized and clearly label each step.
• Attention to Detail: Pay close attention to units and significant figures.
• Use Resources: Utilize online calculators, periodic tables, and other resources to verify your answers.

Conclusion

Determining which substance contains the most moles of atoms involves a careful and systematic approach. By calculating the moles of each substance, counting the number of atoms per molecule, and multiplying these values, you can accurately compare the number of moles of atoms in different samples. Remember to double-check your work and pay attention to detail to avoid common pitfalls. Understanding this concept is fundamental to success in chemistry and related fields.