Question

The multistep smelting of ferric oxide to form elemental iron occurs at high temperatures in a blast furnace. In the first step, ferric oxide reacts with carbon monoxide to form \(\mathrm{Fe}_{3} \mathrm{O}_{4}\). This substance reacts with more carbon monoxide to form iron(II) oxide, which reacts with still more carbon monoxide to form molten iron. Carbon dioxide is also produced in each step. (a) Write an overall balanced equation for the iron- smelting process. (b) How many grams of carbon monoxide are required to form 45.0 metric tons of iron from ferric oxide?

Short answer

33.89 metric tons of CO are required.

Step-by-step solution

Write the individual balanced equations for each reaction

The chemical reactions involved are: 1. \(\text{Fe}_{2}\text{O}_{3} + 3\text{CO} \rightarrow \text{Fe}_{3}\text{O}_{4} + \text{CO}_{2}\)2. \(\text{Fe}_{3}\text{O}_{4} + 4\text{CO} \rightarrow 3\text{FeO} + 4\text{CO}_{2}\)3. \(\text{FeO} + \text{CO} \rightarrow \text{Fe} + \text{CO}_{2}\)

Combine the equations to form the overall balanced equation

Summing the three equations, ensuring that all intermediates cancel out:\( \text{Fe}_{2}\text{O}_{3} + 3\text{CO} + \text{Fe}_{3}\text{O}_{4} + 4\text{CO} + 3\text{FeO} + \text{CO} \rightarrow \text{Fe}_{3}\text{O}_{4} + \text{CO}_{2} + 3\text{FeO} + 4\text{CO}_{2} + 3\text{Fe} + \text{CO}_{2} \)Simplifying, we get:\( \text{Fe}_{2}\text{O}_{3} + 3\text{CO} + 4\text{CO} + \text{CO} \rightarrow 3\text{Fe} + 5\text{CO}_{2} \)Therefore, the overall balanced equation is:\( \text{Fe}_{2}\text{O}_{3} + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_{2} \)

Calculate moles of iron

Let's find the number of moles of iron (\(\text{Fe}\)) formed from 45.0 metric tons of iron. 1 metric ton = 1,000,000 grams.Mass of iron = 45.0 metric tons = 45,000,000 grams.Using the molar mass of iron (\(\text{Fe}\)) = 55.845 g/mol:\( \text{Moles of Fe} = \frac{45,000,000 \text{ grams}}{55.845 \text{ g/mol}} = 805,771.42 \text{ mol} \)

Calculate moles of carbon monoxide required

From the stoichiometry of the overall balanced equation \(\text{Fe}_{2}\text{O}_{3} + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_{2}\), 2 moles of Fe require 3 moles of CO.Thus, 805,771.42 moles of Fe will need:\( \text{Moles of CO} = \frac{3}{2} \times 805,771.42 = 1,208,657.14 \text{ moles} \)

Convert moles of carbon monoxide to grams

Using the molar mass of carbon monoxide (\(\text{CO}\)) = 28.01 g/mol:\( \text{Mass of CO} = 1,208,657.14 \times 28.01 = 33,887,361.49 \text{ grams} \)Converting grams to metric tons (1 metric ton = 1,000,000 grams):\( \text{Mass of CO} = \frac{33,887,361.49}{1,000,000} = 33.89 \text{ metric tons} \)

Key concepts

headline of the respective core concept

The process of iron smelting involves several chemical reactions that convert ferric oxide into elemental iron. The multistep reactions occur at high temperatures in a blast furnace. Each step in the iron smelting process has an individual chemical equation, which must be balanced to ensure the law of conservation of mass is obeyed. Balancing chemical reactions is crucial to understanding how reactants transform into products. It helps predict the quantities of substances involved.

headline of the respective core concept

In chemical reactions, starting materials (reactants) undergo a transformation to produce new materials (products). In iron smelting, ferric oxide (Fe2O3) reacts with carbon monoxide (CO), leading to the formation of various iron oxides before finally producing molten iron (Fe).
Reactions tell us how atoms rearrange themselves. Understanding the steps in chemical reactions shows us how to break down complex processes into simpler ones, which is vital for calculations.
Consider these reactions in the iron smelting process:

• Fe2O3 + 3CO --> Fe3O4 + CO2
• Fe3O4 + 4CO --> 3FeO + 4CO2
• FeO + CO --> Fe + CO2

headline of the respective core concept

Stoichiometry involves using balanced chemical equations to determine the amounts of reactants and products involved in a chemical reaction. It relies on the principle of the conservation of mass. This means the total mass of reactants is equal to the total mass of products.
Let's see how this works with the reaction: Fe2O3 + 3CO --> 2Fe + 3CO2. Here, each mole ratio helps convert between amounts of different substances in the reaction.
For example, to find out how much CO is needed to produce 45 metric tons of iron (Fe), we start by calculating the number of moles of Fe, and then use stoichiometry to figure out the moles of CO required. Finally, we convert the moles of CO to grams.

headline of the respective core concept

Balanced equations are essential for understanding chemical reactions correctly. They ensure that the number of each type of atom on the reactants side is equal to the number on the products side, reflecting the conservation of mass law.
While balancing equations, we might need to adjust coefficients but we never change the actual formulas of the reactants or products.
In the iron-smelting process, first we write individual balanced equations for each step. Then, we combine the equations, making sure all intermediates cancel out. This gives us the overall balanced equation.Fe2O3 + 3CO --> 2Fe + 3CO2 This equation tells us the exact amounts of reactants needed to produce a specific amount of product.