Problem 4 - Chemistry and Chemical Reactivity

Question

The balanced equation for the reduction of iron ore to the metal using CO is $$\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{CO}(\mathrm{g}) \rightarrow 2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}_{2}(\mathrm{g})$$ (a) What is the maximum mass of iron, in grams, that can be obtained from \(454 \mathrm{g}(1.00 \mathrm{lb})\) of iron(III) Oxide? (b) What mass of \(\mathrm{CO}\) is required to react with \(454 \mathrm{g}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3} ?\)

Step-by-Step Solution

Answer

You can obtain 317.25 g of Fe and need 238.82 g of CO.

Step 1: Calculate Molar Mass of Fe2O3

First, calculate the molar mass of iron(III) oxide (\( \mathrm{Fe}_2\mathrm{O}_3 \)). This compound consists of 2 iron atoms and 3 oxygen atoms. The molar mass is calculated as: \[ 2 \times 55.85 (\text{Fe}) + 3 \times 16.00 (\text{O}) = 159.7 \, \text{g/mol} \]

Step 2: Determine Moles of Fe2O3

Next, convert the mass of \( \mathrm{Fe}_2\mathrm{O}_3 \) to moles. With 454 g of \( \mathrm{Fe}_2\mathrm{O}_3 \), the moles are calculated using the formula: \[ \frac{454 \, \text{g}}{159.7 \, \text{g/mol}} \approx 2.842 \, \text{mol of } \mathrm{Fe}_2\mathrm{O}_3\]

Step 3: Use Stoichiometry to Determine Moles of Fe Produced

According to the balanced equation, 1 mole of \( \mathrm{Fe}_2\mathrm{O}_3 \) produces 2 moles of Fe. Calculate moles of Fe: \[ 2.842 \, \text{mol of } \mathrm{Fe}_2\mathrm{O}_3 \times 2 \, \text{mol Fe} / 1 \, \text{mol } \mathrm{Fe}_2\mathrm{O}_3 = 5.684 \, \text{mol Fe}\]

Step 4: Calculate Mass of Iron Produced

Calculate the mass of iron produced from the moles of Fe. The molar mass of Fe is 55.85 g/mol: \[ 5.684 \, \text{mol Fe} \times 55.85 \, \text{g/mol} = 317.25 \, \text{g of Fe} \]

Step 5: Calculate Moles of CO Required

Returning to the stoichiometry of the equation, 1 mole of \( \mathrm{Fe}_2\mathrm{O}_3 \) requires 3 moles of CO. Calculate moles of CO: \[ 2.842 \, \text{mol of } \mathrm{Fe}_2\mathrm{O}_3 \times 3 \, \text{mol CO} / 1 \, \text{mol } \mathrm{Fe}_2\mathrm{O}_3 = 8.526 \, \text{mol CO}\]

Step 6: Calculate Mass of CO Required

The molar mass of CO is 28.01 g/mol. Calculate the mass of CO needed: \[ 8.526 \, \text{mol CO} \times 28.01 \, \text{g/mol} = 238.82 \, \text{g of CO} \]

Key Concepts

Balanced Chemical Equations

A balanced chemical equation ensures that you have the same number of each type of atom on both sides of the equation. This is essential to obey the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction.
In this exercise, the balanced chemical equation is:

• {\[\text{Fe}_2\text{O}_3\text{(s)} + 3\text{CO(g)} \rightarrow 2\text{Fe(s)} + 3\text{CO}_2\text{(g)}\]}

Each side of the equation contains:- 2 iron (Fe) atoms- 6 oxygen (O) atoms - 3 carbon (C) atoms
By balancing this equation, we can precisely calculate how much of each reactant is needed and what amount of product is formed.Understanding balanced equations is crucial for predicting the outcomes of chemical reactions in terms of both reagents and products.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is an important concept in stoichiometry because it allows us to convert between mass and moles.
In this scenario, we first need the molar mass of iron(III) oxide (\( \text{Fe}_2\text{O}_3 \)). It's determined by adding the atomic masses of all atoms within the compound, calculated as:

• 2 Fe atoms: \( 2 \times 55.85 \text{ g/mol} = 111.7 \text{ g/mol} \)
• 3 O atoms: \( 3 \times 16.00 \text{ g/mol} = 48.00 \text{ g/mol} \)

Adding them gives \( 159.7 \text{ g/mol} \) for \( \text{Fe}_2\text{O}_3 \).
Knowing this allows us to convert from mass to moles and vice versa, which is key in calculating how much of a substance is involved in a chemical reaction.

Iron Production

Iron production involves the chemical reduction of iron ore to pure iron metal. This process is not just a simple reaction; it involves transforming ore into a usable form of iron through chemical reactions.
The balanced equation for iron production from iron(III) oxide is crucial:

• 1 mole of \( \text{Fe}_2\text{O}_3 \) yields 2 moles of iron.

For this exercise, starting with 454 g of \( \text{Fe}_2\text{O}_3 \), we calculated its moles, and using stoichiometry, we concluded that it produces 5.684 moles of iron.
By multiplying these moles by the molar mass of iron (55.85 g/mol), we found that this equates to 317.25 g of iron produced.Iron production is a prime example of how stoichiometry applies to real-world processes like metal refining.

Chemical Reactions

Chemical reactions involve the transformation of substances via the rearrangement of their molecular or ionic structure.
This exercise revolves around a specific reaction where iron(III) oxide reacts with carbon monoxide to produce iron and carbon dioxide.
In a chemical reaction:

• Reactants (like \( \text{Fe}_2\text{O}_3 \) and CO) are converted into products (such as Fe and \( \text{CO}_2 \)).
• This conversion is expressed through a balanced chemical equation.

Understanding the underlying chemical changes helps predict how much reactant is needed to form a desired amount of product.
By calculating how many moles of the reactants and products are involved, it's possible to determine the masses of substances required and produced in the reaction.