Problem 8 - Chemistry and Chemical Reactivity

Question

Iron ore is converted to iron metal in a reaction with carbon. $$2 \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \rightarrow 4 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}_{2}(\mathrm{g})$$ If 6.2 mol of \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})\) is used, what amount of \(\mathrm{C}(\mathrm{s})\) is needed, and what amounts of Fe and \(\mathrm{CO}_{2}\) are produced?

Step-by-Step Solution

Answer

9.3 moles of \( \mathrm{C} \), 12.4 moles of \( \mathrm{Fe} \), and 9.3 moles of \( \mathrm{CO}_{2} \) are produced.

Step 1: Understand the Reaction

The chemical reaction given is \( 2\mathrm{Fe}_{2}\mathrm{O}_{3} + 3\mathrm{C} \rightarrow 4\mathrm{Fe} + 3\mathrm{CO}_{2} \). This tells us the ratios in which the reactants combine and the products are formed.

Step 2: Mole Ratio from Balanced Equation

From the balanced equation \( 2\mathrm{Fe}_{2}\mathrm{O}_{3} + 3\mathrm{C} \rightarrow 4\mathrm{Fe} + 3\mathrm{CO}_{2} \), we see that 2 moles of \( \mathrm{Fe}_{2}\mathrm{O}_{3} \) react with 3 moles of \( \mathrm{C} \). Therefore, the mole ratio of \( \mathrm{Fe}_{2}\mathrm{O}_{3} \) to \( \mathrm{C} \) is 2:3.

Step 3: Calculate Moles of Carbon Needed

Given 6.2 moles of \( \mathrm{Fe}_{2}\mathrm{O}_{3} \) is used, use the mole ratio of 2:3 to find the moles of \( \mathrm{C} \) needed. \[\text{Moles of C} = \left( \frac{3}{2} \right) \times 6.2 = 9.3 \, \text{moles}\]

Step 4: Calculate Moles of Iron Produced

Using the balanced equation, 2 moles of \( \mathrm{Fe}_{2}\mathrm{O}_{3} \) produce 4 moles of \( \mathrm{Fe} \). Thus, \[\text{Moles of Fe} = \left( \frac{4}{2} \right) \times 6.2 = 12.4 \, \text{moles}\]

Step 5: Calculate Moles of CO2 Produced

According to the reaction, 2 moles of \( \mathrm{Fe}_{2}\mathrm{O}_{3} \) produce 3 moles of \( \mathrm{CO}_{2} \). Therefore,\[\text{Moles of CO}_{2} = \left( \frac{3}{2} \right) \times 6.2 = 9.3 \, \text{moles}\]

Key Concepts

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, transform into different substances, called products.
This transformation involves the breaking and forming of chemical bonds, leading to a change in the chemical composition.
There are several types of chemical reactions, and they can be categorized by their most common features, such as synthesis, decomposition, single displacement, and double displacement.

• In synthesis reactions, multiple reactants combine to form a single product.
• Decomposition involves a single compound breaking down into two or more simpler substances.
• Single displacement occurs when one element replaces another in a compound.
• Double displacement involves an exchange of components between two compounds.

In the context of iron production, the reaction between iron ore and carbon is a type of reduction reaction. Here, carbon acts as a reducing agent to transform iron oxide into metallic iron.

Mole Ratios

Mole ratios are fundamental in stoichiometry and serve as conversion factors that relate the amounts of reactants to products in a chemical reaction.
These ratios come from the coefficients of a balanced chemical equation, which represent the relative number of moles of each substance involved.
For example, in the equation \( 2\mathrm{Fe}_{2}\mathrm{O}_{3} + 3\mathrm{C} \rightarrow 4\mathrm{Fe} + 3\mathrm{CO}_{2} \), the mole ratio between iron(III) oxide and carbon is 2:3.
This means that for every 2 moles of iron(III) oxide consumed, 3 moles of carbon are required.
Understanding these ratios allows us to predict how much of each reactant is needed or how much product will be formed. This is crucial in calculations, such as determining the amount of carbon needed to fully react with a given amount of iron(III) oxide.

Balancing Chemical Equations

Balancing chemical equations ensures that the same number of each type of atom appears on both sides of the equation, satisfying the law of conservation of mass.
This process involves adjusting the coefficients in front of reactants and products without changing the chemical identity of the substances.
In a balanced equation, the total mass of reactants equals the total mass of products, which is critical for accurate stoichiometric calculations.
For instance, in the reaction \( 2\mathrm{Fe}_{2}\mathrm{O}_{3} + 3\mathrm{C} \rightarrow 4\mathrm{Fe} + 3\mathrm{CO}_{2} \), the equation is balanced, as it contains equal numbers of iron, oxygen, and carbon atoms on both sides.

• To balance an equation, one must count the number of atoms for each element in reactants and products.
• Adjust the coefficients as needed to achieve balance.
• Verify the balance by recounting atoms on both sides.

Iron Production

Iron production involves converting iron ore into metallic iron through a series of chemical reactions.
Iron ore, typically composed of iron oxides like \( \mathrm{Fe}_{2}\mathrm{O}_{3} \), is reduced to iron using a suitable reductant.
One common method is the blast furnace process, where iron ore reacts with carbon at high temperatures in an oxygen-limited environment.
In this reduction reaction, carbon or its monoxide counterpart reduces the iron oxide into molten iron. This molten iron can then be further refined to produce steel or other iron products.
Besides carbon, other reducing agents or methods could be utilized, depending on the desired end product and economic considerations.

Carbon Reduction Reaction

Carbon reduction reactions are processes where carbon acts as a reducing agent to extract metals from their oxides.
In iron production, carbon reduction is critical for converting iron ore (iron oxide) into metallic iron.
The carbon reduction reaction proceeds as iron ore and carbon react at high temperatures, producing metallic iron and carbon dioxide gas: \( 2\mathrm{Fe}_{2}\mathrm{O}_{3} + 3\mathrm{C} \rightarrow 4\mathrm{Fe} + 3\mathrm{CO}_{2} \).
This chemical reaction is fundamental to the traditional blast furnace method of iron extraction, which relies on achieving the necessary heat and chemical environment to facilitate the reduction process.
The selection of carbon as a reducing agent is due to its availability, affordability, and high reduction potential, making it ideal for industrial-scale metal production.