How Many Oxygen Atoms Are Present In A 10.0g Sample

How Many Oxygen Atoms Are Present in a 10.0g Sample? A Deep Dive into Stoichiometry

Determining the number of oxygen atoms in a 10.0g sample requires a journey through the fascinating world of chemistry, specifically stoichiometry. This seemingly simple question opens a door to understanding fundamental concepts like molar mass, Avogadro's number, and the relationship between mass, moles, and atoms. This comprehensive guide will not only answer the question but also equip you with the knowledge to tackle similar problems. Let's delve in!

Understanding the Fundamentals: Moles and Avogadro's Number

Before we can calculate the number of oxygen atoms, we need to grasp two crucial concepts:

1. The Mole (mol): The Chemist's Dozen

A mole isn't a furry creature; it's a fundamental unit in chemistry, representing a specific number of particles (atoms, molecules, ions, etc.). This number is Avogadro's number, approximately 6.022 x 10²³. One mole of any substance contains Avogadro's number of particles. Think of it as a chemist's "dozen," but instead of 12, it's a mind-bogglingly large number.

2. Molar Mass: Mass of One Mole

The molar mass of a substance is the mass of one mole of that substance, expressed in grams per mole (g/mol). It's essentially the atomic weight (from the periodic table) expressed in grams. For example, the molar mass of oxygen (O) is approximately 16.00 g/mol, while the molar mass of oxygen gas (O₂) is 32.00 g/mol (16.00 g/mol x 2).

The Importance of Knowing the Substance

The crucial missing piece of information in our initial question is the identity of the 10.0g sample. The number of oxygen atoms will drastically vary depending on whether the sample is pure oxygen (O₂), water (H₂O), carbon dioxide (CO₂), or any other compound containing oxygen. Let's explore a few examples:

Example 1: Calculating Oxygen Atoms in 10.0g of Pure Oxygen Gas (O₂)

1. Calculate the number of moles:

   First, we determine the number of moles of O₂ in 10.0g using the molar mass of O₂ (32.00 g/mol):

   Moles of O₂ = (mass of O₂) / (molar mass of O₂) = 10.0 g / 32.00 g/mol ≈ 0.3125 mol

2. Calculate the number of O₂ molecules:

   Now, we use Avogadro's number to find the number of O₂ molecules:

   Number of O₂ molecules = (moles of O₂) x (Avogadro's number) ≈ 0.3125 mol x 6.022 x 10²³ molecules/mol ≈ 1.88 x 10²³ molecules

3. Calculate the number of oxygen atoms:

   Each O₂ molecule contains two oxygen atoms. Therefore:

   Number of oxygen atoms = (number of O₂ molecules) x 2 ≈ 1.88 x 10²³ molecules x 2 atoms/molecule ≈ 3.76 x 10²³ atoms

Therefore, there are approximately 3.76 x 10²³ oxygen atoms in a 10.0g sample of pure oxygen gas.

Example 2: Calculating Oxygen Atoms in 10.0g of Water (H₂O)

1. Calculate the number of moles:

   The molar mass of water (H₂O) is approximately 18.02 g/mol (2 x 1.01 g/mol for Hydrogen + 16.00 g/mol for Oxygen).

   Moles of H₂O = 10.0 g / 18.02 g/mol ≈ 0.555 mol

2. Calculate the number of H₂O molecules:

   Number of H₂O molecules = 0.555 mol x 6.022 x 10²³ molecules/mol ≈ 3.34 x 10²³ molecules

3. Calculate the number of oxygen atoms:

   Each H₂O molecule contains one oxygen atom. Therefore:

   Number of oxygen atoms = 3.34 x 10²³ molecules ≈ 3.34 x 10²³ atoms

In a 10.0g sample of water, there are approximately 3.34 x 10²³ oxygen atoms.

Example 3: A More Complex Compound – 10.0g of Glucose (C₆H₁₂O₆)

Glucose presents a more complex calculation because it contains multiple oxygen atoms per molecule.

1. Calculate the number of moles:

   The molar mass of glucose (C₆H₁₂O₆) is approximately 180.18 g/mol (6 x 12.01 g/mol for Carbon + 12 x 1.01 g/mol for Hydrogen + 6 x 16.00 g/mol for Oxygen).

   Moles of glucose = 10.0 g / 180.18 g/mol ≈ 0.0555 mol

2. Calculate the number of glucose molecules:

   Number of glucose molecules = 0.0555 mol x 6.022 x 10²³ molecules/mol ≈ 3.34 x 10²² molecules

3. Calculate the number of oxygen atoms:

   Each glucose molecule (C₆H₁₂O₆) contains six oxygen atoms. Therefore:

   Number of oxygen atoms = 3.34 x 10²² molecules x 6 atoms/molecule ≈ 2.00 x 10²³ atoms

A 10.0g sample of glucose contains approximately 2.00 x 10²³ oxygen atoms.

The Significance of Precision and Significant Figures

Note that throughout these calculations, we've maintained an appropriate level of precision using significant figures. The given mass (10.0g) has three significant figures, so our final answers reflect this level of precision. Using more significant figures in the molar masses doesn't necessarily improve accuracy if the initial measurement is limited.

Expanding Your Stoichiometric Skills

The examples above demonstrate the core principles of stoichiometry. To further enhance your understanding, consider these extensions:

• Dealing with Impure Samples: If the 10.0g sample is not pure, you'll need to account for the percentage purity. This involves first calculating the mass of the relevant compound within the sample before proceeding with the mole calculations.

• Hydrated Compounds: Many compounds exist as hydrates, containing water molecules within their crystal structure. You'll need to account for the water molecules when calculating the molar mass and the number of oxygen atoms.

• Empirical and Molecular Formulas: These concepts help determine the simplest whole-number ratio of atoms in a compound (empirical) and the actual number of atoms in a molecule (molecular). This is crucial when dealing with unknown compounds.

• Limiting Reactants: In reactions involving multiple reactants, identifying the limiting reactant is essential to accurately predict the amount of product formed.

Conclusion: Mastering the Art of Stoichiometry

Calculating the number of oxygen atoms in a 10.0g sample highlights the power and elegance of stoichiometry. While seemingly straightforward, the process involves a chain of calculations and requires a thorough understanding of fundamental chemical concepts. Mastering these principles opens doors to a deeper appreciation of chemical reactions and quantitative analysis, essential skills for anyone pursuing a career in chemistry or a related field. Remember, always clearly identify the substance in question to achieve an accurate calculation. By understanding moles, molar mass, Avogadro's number, and paying close attention to significant figures, you can confidently tackle a wide range of stoichiometric problems.