Iron Oxide Formation: Grams Of Fe₂O₃ From 448g Of Fe

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Hey guys! Today, we're diving into a classic chemistry problem: figuring out how much ferric oxide (Fe₂O₃) forms when 448 grams of iron (Fe) rusts, or oxidizes. This is a super practical example of stoichiometry, which is just a fancy way of saying we're looking at the quantitative relationships between reactants and products in a chemical reaction. So, grab your calculators, and let's get started!

Understanding the Problem

Okay, so first things first, let’s break down the problem. We know that 448 grams of iron (Fe) is reacting with oxygen (O₂) to form ferric oxide (Fe₂O₃), which we commonly know as rust. The unbalanced chemical equation is given as:

Fe + O₂ → Fe₂O₃

But hold on a second! This equation isn't balanced. And why is balancing important, you ask? Well, the Law of Conservation of Mass tells us that matter can't be created or destroyed in a chemical reaction. This means the number of atoms of each element must be the same on both sides of the equation. So, we need to balance it before we can do any calculations. Balancing chemical equations is fundamental. Without a balanced equation, we can't accurately determine the mole ratios, which are crucial for stoichiometric calculations. It’s like trying to bake a cake without measuring the ingredients – you might end up with a mess!

Balancing the Chemical Equation

Let's balance this equation together. This is a crucial step, guys, so pay close attention!

  1. We have one Fe atom on the left and two on the right. Let’s put a 2 in front of Fe on the left:

    2Fe + O₂ → Fe₂O₃

  2. Now we have two oxygen atoms on the left and three on the right. To balance the oxygen, we need to find the least common multiple of 2 and 3, which is 6. Let’s put a 3 in front of O₂ on the left and a 2 in front of Fe₂O₃ on the right:

    2Fe + 3O₂ → 2Fe₂O₃

  3. Oops! Now we've messed up the iron balance. We have two Fe atoms on the left and four on the right (2 x 2). Let’s change the coefficient in front of Fe on the left to 4:

    4Fe + 3O₂ → 2Fe₂O₃

Alright! Now we have 4 Fe atoms, 6 O atoms on both sides. The equation is finally balanced! This balanced equation is the foundation for our calculations, providing the necessary mole ratios between reactants and products.

Calculating Molar Masses

Next up, we need to find the molar masses of iron (Fe) and ferric oxide (Fe₂O₃). Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). Think of it as the weight of a specific number of atoms or molecules (Avogadro's number, to be exact!).

  • Iron (Fe): Looking at the periodic table, the molar mass of Fe is approximately 55.85 g/mol.
  • Ferric Oxide (Fe₂O₃): To find the molar mass of Fe₂O₃, we need to add up the molar masses of each element, considering the number of atoms:
    • 2 Fe atoms: 2 * 55.85 g/mol = 111.7 g/mol
    • 3 O atoms: 3 * 16.00 g/mol = 48.00 g/mol
    • Total: 111.7 g/mol + 48.00 g/mol = 159.7 g/mol

Converting Grams of Iron to Moles

Now we can convert the given mass of iron (448 g) to moles. Remember, moles are like the chemist's counting unit – they tell us how many particles (atoms, molecules, etc.) we have. To do this, we use the formula:

Moles = Mass / Molar Mass

So, for iron:

Moles of Fe = 448 g / 55.85 g/mol ≈ 8.02 moles

We now know that 448 grams of iron is approximately 8.02 moles. This conversion is vital because the balanced chemical equation relates the moles of reactants and products, not their masses directly. Converting to moles allows us to use the stoichiometric ratios from the balanced equation.

Using the Mole Ratio

Here's where the balanced equation really shines! It tells us the ratio in which the substances react and are produced. From the balanced equation:

4Fe + 3O₂ → 2Fe₂O₃

We see that 4 moles of Fe produce 2 moles of Fe₂O₃. This is our mole ratio! We can write it as a fraction: (2 moles Fe₂O₃) / (4 moles Fe). This ratio allows us to convert from moles of iron to moles of ferric oxide. This is a direct application of stoichiometry – using the quantitative relationship from the balanced equation to predict the amount of product formed from a given amount of reactant.

To find out how many moles of Fe₂O₃ are produced, we multiply the moles of Fe by the mole ratio:

Moles of Fe₂O₃ = 8.02 moles Fe * (2 moles Fe₂O₃ / 4 moles Fe) ≈ 4.01 moles Fe₂O₃

So, approximately 4.01 moles of ferric oxide are formed.

Converting Moles of Ferric Oxide to Grams

We're almost there! Now we need to convert the moles of Fe₂O₃ back to grams. We use the same formula as before, but rearranged:

Mass = Moles * Molar Mass

For ferric oxide:

Mass of Fe₂O₃ = 4.01 moles * 159.7 g/mol ≈ 640.4 g

The Answer!

So, guys, if 448 grams of iron (Fe) oxidizes completely, approximately 640.4 grams of ferric oxide (Fe₂O₃) will be formed. Awesome!

Why This Matters

This problem might seem like just a textbook exercise, but it has real-world applications! Understanding stoichiometry is essential in many fields, including:

  • Industrial Chemistry: Chemical engineers use these calculations to optimize chemical reactions for the production of various materials, from plastics to pharmaceuticals.
  • Environmental Science: Stoichiometry helps in understanding and mitigating pollution, like calculating the amount of pollutants released in a chemical process.
  • Materials Science: It's crucial for designing new materials with specific properties, like rust-resistant alloys.
  • Cooking: Even in the kitchen, recipes are essentially stoichiometric ratios! You need the right proportions of ingredients to get the desired result.

Key Takeaways

Let's recap the key steps we took to solve this problem:

  1. Balanced the chemical equation: 4Fe + 3O₂ → 2Fe₂O₃
  2. Calculated molar masses: Fe (55.85 g/mol), Fe₂O₃ (159.7 g/mol)
  3. Converted grams of Fe to moles: 8.02 moles
  4. Used the mole ratio to find moles of Fe₂O₃: 4.01 moles
  5. Converted moles of Fe₂O₃ to grams: 640.4 g

Remember, guys, practice makes perfect! The more you work through these types of problems, the easier they become. And understanding stoichiometry is a valuable skill that opens doors to many exciting areas of science and engineering.

Practice Problems

Want to test your skills? Try these practice problems:

  1. If 100 grams of aluminum (Al) reacts with oxygen to form aluminum oxide (Al₂O₃), how many grams of aluminum oxide are formed?
  2. How many grams of water (H₂O) are produced when 50 grams of methane (CH₄) combusts completely in oxygen?

Good luck, and happy calculating!