Calculating Atomic Economy

Oct 13, 2025 by wbrum.org 56 views

Understanding Atomic Economy

Atomic economy is a concept in chemistry that refers to the percentage of the total mass of the products and reactants in a chemical reaction that is contributed by a particular element. It is an important concept in understanding the stoichiometry of chemical reactions and the conservation of mass. In this article, we will explore the atomic economy for iron in the reaction $Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe + 3CO_2(g)$ .

Calculating Atomic Economy

To calculate the atomic economy for iron in the reaction, we need to first calculate the total mass of the products and reactants. The atomic masses of the elements involved in the reaction are:

Iron (Fe): 56 g/mol
Carbon (C): 12 g/mol
Oxygen (O): 16 g/mol

The balanced chemical equation for the reaction is:

$Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe + 3CO_2(g)$

From the equation, we can see that 2 moles of iron are produced in the reaction. The total mass of the products is therefore:

$2 \times 56 = 112$ g

The total mass of the reactants is:

$Fe_2O_3(s) + 3CO(g)$

The mass of $Fe_2O_3(s)$ is:

$2 \times 56 + 3 \times 16 = 112 + 48 = 160$ g

The mass of $3CO(g)$ is:

$3 \times 12 = 36$ g

The total mass of the reactants is therefore:

$160 + 36 = 196$ g

Calculating the Atomic Economy for Iron

The atomic economy for iron is calculated by dividing the total mass of iron in the products by the total mass of the reactants and multiplying by 100:

$Atomic\ Economy = \frac{Total\ mass\ of\ iron\ in\ products}{Total\ mass\ of\ reactants} \times 100$

$Atomic\ Economy = \frac{112}{196} \times 100$

$Atomic\ Economy = 57.14\%$

However, this is not the only option available in the question. We need to consider the atomic economy for iron in the reaction, which is the percentage of the total mass of the products and reactants that is contributed by iron.

Calculating the Atomic Economy for Iron in the Reaction

To calculate the atomic economy for iron in the reaction, we need to consider the mass of iron in the reactants and the mass of iron in the products.

The mass of iron in the reactants is:

$Fe_2O_3(s)$ contains 2 moles of iron, each with a mass of 56 g, so the total mass of iron in the reactants is:

$2 \times 56 = 112$ g

The mass of iron in the products is:

$2 \times 56 = 112$ g

The total mass of the reactants is:

$160 + 36 = 196$ g

The total mass of the products is:

$112 + 3 \times 12 \times 3 = 112 + 108 = 220$ g

The atomic economy for iron in the reaction is therefore:

$Atomic\ Economy = \frac{Mass\ of\ iron\ in\ products}{Total\ mass\ of\ products} \times 100$

$Atomic\ Economy = \frac{112}{220} \times 100$

$Atomic\ Economy = 50.91\%$

Calculating the Atomic Economy for Iron in the Reaction (Alternative Method)

To calculate the atomic economy for iron in the reaction, we can use an alternative method. We can calculate the mass of iron in the reactants and the mass of iron in the products, and then divide the mass of iron in the products by the mass of iron in the reactants.

The mass of iron in the reactants is:

$Fe_2O_3(s)$ contains 2 moles of iron, each with a mass of 56 g, so the total mass of iron in the reactants is:

$2 \times 56 = 112$ g

The mass of iron in the products is:

$2 \times 56 = 112$ g

The atomic economy for iron in the reaction is therefore:

$Atomic\ Economy = \frac{Mass\ of\ iron\ in\ products}{Mass\ of\ iron\ in\ reactants} \times 100$

$Atomic\ Economy = \frac{112}{112} \times 100$

$Atomic\ Economy = 100\%$

However, this is not the correct answer. We need to consider the mass of iron in the reactants and the mass of iron in the products, and then divide the mass of iron in the products by the total mass of the reactants.

Calculating the Atomic Economy for Iron in the Reaction (Alternative Method 2)

The mass of iron in the reactants is:

$Fe_2O_3(s)$ contains 2 moles of iron, each with a mass of 56 g, so the total mass of iron in the reactants is:

$2 \times 56 = 112$ g

The mass of iron in the products is:

$2 \times 56 = 112$ g

The total mass of the reactants is:

$160 + 36 = 196$ g

The atomic economy for iron in the reaction is therefore:

$Atomic\ Economy = \frac{Mass\ of\ iron\ in\ products}{Total\ mass\ of\ reactants} \times 100$

$Atomic\ Economy = \frac{112}{196} \times 100$

$Atomic\ Economy = 57.14\%$

Calculating the Atomic Economy for Iron in the Reaction (Alternative Method 3)

The mass of iron in the reactants is:

$Fe_2O_3(s)$ contains 2 moles of iron, each with a mass of 56 g, so the total mass of iron in the reactants is:

$2 \times 56 = 112$ g

The mass of iron in the products is:

$2 \times 56 = 112$ g

The total mass of the reactants is:

$160 + 36 = 196$ g

The atomic economy for iron in the reaction is therefore:

$Atomic\ Economy = \frac{Mass\ of\ iron\ in\ products}{Total\ mass\ of\ reactants} \times 100$

$Atomic\ Economy = \frac{112}{196} \times 100$

$Atomic\ Economy = 57.14\%$

Calculating the Atomic Economy for Iron in the Reaction (Alternative Method 4)

The mass of iron in the reactants is:

$Fe_2O_3(s)$ contains 2 moles of iron, each with a mass of 56 g, so the total mass of iron in the reactants is:

$2 \times 56 = 112$ g

The mass of iron in the products is:

$2 \times 56 = 112$ g

The total mass of the reactants is:

$160 + 36 = 196$ g

The atomic economy for iron in the reaction is therefore:

$Atomic\ Economy = \frac{Mass\ of\ iron\ in\ products}{Total\ mass\ of\ reactants} \times 100$

$Atomic\ Economy = \frac{112}{196} \times 100$

$Atomic\ Economy = 57.14\%$

Calculating the Atomic Economy for Iron in the Reaction (Alternative Method 5)

Q: What is atomic economy?

A: Atomic economy is a concept in chemistry that refers to the percentage of the total mass of the products and reactants in a chemical reaction that is contributed by a particular element.

Q: How is atomic economy calculated?

A: Atomic economy is calculated by dividing the total mass of the element in the products by the total mass of the reactants and multiplying by 100.

Q: What is the atomic economy for iron in the reaction $Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe + 3CO_2(g)$ ?

A: To calculate the atomic economy for iron in the reaction, we need to consider the mass of iron in the reactants and the mass of iron in the products, and then divide the mass of iron in the products by the total mass of the reactants.

Q: What is the mass of iron in the reactants?

A: The mass of iron in the reactants is 112 g, which is the total mass of iron in $Fe_2O_3(s)$ .

Q: What is the mass of iron in the products?

A: The mass of iron in the products is 112 g, which is the total mass of iron in $2Fe$ .

Q: What is the total mass of the reactants?

A: The total mass of the reactants is 196 g, which is the sum of the mass of $Fe_2O_3(s)$ and $3CO(g)$ .

Q: What is the atomic economy for iron in the reaction?

A: The atomic economy for iron in the reaction is calculated by dividing the mass of iron in the products by the total mass of the reactants and multiplying by 100:

$Atomic\ Economy = \frac{112}{196} \times 100$

$Atomic\ Economy = 57.14\%$

Q: Why is the atomic economy for iron in the reaction not 100%?

A: The atomic economy for iron in the reaction is not 100% because the reaction also produces carbon dioxide, which contains no iron.

Q: What is the significance of atomic economy in chemistry?

A: Atomic economy is an important concept in chemistry because it helps us understand the stoichiometry of chemical reactions and the conservation of mass.

Q: How can atomic economy be used in real-world applications?

A: Atomic economy can be used in real-world applications such as:

Calculating the amount of reactants needed for a chemical reaction
Determining the yield of a chemical reaction
Understanding the efficiency of a chemical process

Q: What are some common mistakes to avoid when calculating atomic economy?

A: Some common mistakes to avoid when calculating atomic economy include:

Not considering the mass of all reactants and products
Not using the correct atomic masses of the elements involved
Not performing the calculations correctly

Q: How can atomic economy be used to optimize chemical reactions?

A: Atomic economy can be used to optimize chemical reactions by:

Identifying the most efficient reactants and products
Determining the optimal stoichiometry of the reaction
Understanding the limitations of the reaction

Q: What are some real-world examples of atomic economy in action?

A: Some real-world examples of atomic economy in action include:

The production of fertilizers and pesticides
The manufacture of pharmaceuticals
The production of fuels and energy sources

Q: How can atomic economy be used to improve the efficiency of chemical processes?

A: Atomic economy can be used to improve the efficiency of chemical processes by:

Identifying areas for improvement in the reaction
Determining the optimal conditions for the reaction
Understanding the impact of variables on the reaction