Calculating the Theoretical Yield of Iron

Oct 13, 2025 by magicalceylontours.com 93 views

Theoretical Yield of Iron from the Reduction of Iron(III) Oxide

The reduction of iron(III) oxide ( $Fe_2 O_3$ ) to iron ( $Fe$ ) is a crucial process in various industrial applications, including the production of steel and other alloys. In this process, iron(III) oxide reacts with carbon monoxide ( $CO$ ) to produce iron and carbon dioxide ( $CO_2$ ). The balanced chemical equation for this reaction is:

Fe_2 O_3(s) + 3 CO(g) \rightarrow 2 Fe(s) + 3 CO_2(g)

In this article, we will discuss the theoretical yield of iron ( $Fe$ ) from the reduction of iron(III) oxide ( $Fe_2 O_3$ ) when 150 g of $Fe_2 O_3$ is used as the limiting reactant.

Molar Mass of Iron(III) Oxide and Iron

To calculate the theoretical yield of iron, we need to know the molar masses of iron(III) oxide ( $Fe_2 O_3$ ) and iron ( $Fe$ ). The molar masses of these compounds are:

$Fe_2 O_3$ : 159.69 g/mol
$Fe$ : 55.85 g/mol

Calculating the Number of Moles of Iron(III) Oxide

To calculate the number of moles of iron(III) oxide, we can use the formula:

n = \frac{m}{M}

where $n$ is the number of moles, $m$ is the mass of the substance, and $M$ is the molar mass.

For 150 g of $Fe_2 O_3$ , the number of moles is:

n = \frac{150 \text{ g}}{159.69 \text{ g/mol}} = 0.938 \text{ mol}

Calculating the Theoretical Yield of Iron

From the balanced chemical equation, we can see that 1 mole of $Fe_2 O_3$ produces 2 moles of $Fe$ . Therefore, the number of moles of $Fe$ produced is:

n_{Fe} = 2 \times n_{Fe_2 O_3} = 2 \times 0.938 \text{ mol} = 1.876 \text{ mol}

The mass of $Fe$ produced is:

m_{Fe} = n_{Fe} \times M_{Fe} = 1.876 \text{ mol} \times 55.85 \text{ g/mol} = 104.7 \text{ g}

Therefore, the theoretical yield of $Fe$ from the reduction of 150 g of $Fe_2 O_3$ is 104.7 g.

In this article, we calculated the theoretical yield of iron ( $Fe$ ) from the reduction of iron(III) oxide ( $Fe_2 O_3$ ) when 150 g of $Fe_2 O_3$ is used as the limiting reactant. We found that the theoretical yield of $Fe$ is 104.7 g. This calculation is based on the balanced chemical equation for the reaction and the molar masses of the reactants and products.

This calculation assumes that the reaction is carried out under ideal conditions, with no losses or impurities. In practice, the actual yield of $Fe$ may be lower due to various factors such as incomplete reaction, losses during handling, and impurities in the reactants. Future work could involve experimental verification of the theoretical yield and investigation of the factors that affect the actual yield.

[1] "Iron(III) oxide." Wikipedia, Wikimedia Foundation, 10 Mar. 2023, en.wikipedia.org/wiki/Iron(III)_oxide.
[2] "Iron." Wikipedia, Wikimedia Foundation, 10 Mar. 2023, en.wikipedia.org/wiki/Iron.
[3] "Chemical reactions." Wikipedia, Wikimedia Foundation, 10 Mar. 2023, en.wikipedia.org/wiki/Chemical_reactions.

The following table summarizes the calculations performed in this article:

Substance	Mass (g)	Molar Mass (g/mol)	Number of Moles	Mass of Product (g)
$Fe_2 O_3$	150	159.69	0.938	-
$Fe$	-	55.85	1.876	104.7

Note: The minus sign in the table indicates that the mass of the product is not given for the reactant.
Q&A: Theoretical Yield of Iron from the Reduction of Iron(III) Oxide

In our previous article, we discussed the theoretical yield of iron ( $Fe$ ) from the reduction of iron(III) oxide ( $Fe_2 O_3$ ) when 150 g of $Fe_2 O_3$ is used as the limiting reactant. We calculated the theoretical yield of $Fe$ to be 104.7 g. In this article, we will answer some frequently asked questions related to this topic.

Q: What is the limiting reactant in this reaction?

A: The limiting reactant is the reactant that is present in the smallest amount relative to the stoichiometry of the reaction. In this case, 150 g of $Fe_2 O_3$ is the limiting reactant.

Q: How do you determine the limiting reactant?

A: To determine the limiting reactant, you need to know the masses of all the reactants and the stoichiometry of the reaction. You can then calculate the number of moles of each reactant and compare them to the stoichiometry of the reaction. The reactant with the smallest number of moles is the limiting reactant.

Q: What is the role of carbon monoxide ( $CO$ ) in this reaction?

A: Carbon monoxide ( $CO$ ) is a reactant in this reaction. It reacts with iron(III) oxide ( $Fe_2 O_3$ ) to produce iron ( $Fe$ ) and carbon dioxide ( $CO_2$ ).

Q: What is the molar mass of iron(III) oxide ( $Fe_2 O_3$ )?

A: The molar mass of iron(III) oxide ( $Fe_2 O_3$ ) is 159.69 g/mol.

Q: What is the molar mass of iron ( $Fe$ )?

A: The molar mass of iron ( $Fe$ ) is 55.85 g/mol.

Q: How do you calculate the number of moles of a substance?

A: To calculate the number of moles of a substance, you can use the formula:

n = \frac{m}{M}

where $n$ is the number of moles, $m$ is the mass of the substance, and $M$ is the molar mass.

Q: What is the theoretical yield of iron ( $Fe$ ) from the reduction of 150 g of $Fe_2 O_3$ ?

A: The theoretical yield of iron ( $Fe$ ) from the reduction of 150 g of $Fe_2 O_3$ is 104.7 g.

Q: What are some factors that can affect the actual yield of iron ( $Fe$ )?

A: Some factors that can affect the actual yield of iron ( $Fe$ ) include incomplete reaction, losses during handling, and impurities in the reactants.

In this article, we answered some frequently asked questions related to the theoretical yield of iron ( $Fe$ ) from the reduction of iron(III) oxide ( $Fe_2 O_3$ ). We hope that this article has provided a better understanding of this topic and has helped to clarify any confusion.

[1] "Iron(III) oxide." Wikipedia, Wikimedia Foundation, 10 Mar. 2023, en.wikipedia.org/wiki/Iron(III)_oxide.
[2] "Iron." Wikipedia, Wikimedia Foundation, 10 Mar. 2023, en.wikipedia.org/wiki/Iron.
[3] "Chemical reactions." Wikipedia, Wikimedia Foundation, 10 Mar. 2023, en.wikipedia.org/wiki/Chemical_reactions.

The following table summarizes the calculations performed in this article:

Substance	Mass (g)	Molar Mass (g/mol)	Number of Moles	Mass of Product (g)
$Fe_2 O_3$	150	159.69	0.938	-
$Fe$	-	55.85	1.876	104.7

Note: The minus sign in the table indicates that the mass of the product is not given for the reactant.