How many grams of Fe2O3 are produced when 48 grams of O2 react?

This article explains step-by-step how to solve a chemical reaction problem involving the production of magnetite (Fe2O3) from the reaction of iron (Fe) with oxygen (O2). The process involves understanding the balanced chemical equation, mole calculations, and the final conversion from mass of oxygen to mass of magnetite. We will also explore the steps to balance the equation for the reaction, understand the reaction ratio, and calculate the grams of Fe2O3 generated.

Introduction to the Chemical Reaction and Relevant Information

When elemental iron (Fe) reacts with oxygen (O2) under the right conditions, it results in the formation of magnetite, represented by the chemical compound Fe2O3. The balanced chemical equation for this reaction is as follows:

4Fe 3O2 → 2Fe2O3

Understanding the Balanced Equation

The equation shows that for every 3 moles of oxygen (O2) that react, 2 moles of magnetite (Fe2O3) are produced. This relationship between the reactants and products can be used to solve the problem at hand.

Calculations Required to Solve the Problem

To determine the mass of Fe2O3 produced when 48 grams of O2 react, we follow these steps:

Step 1: Calculate the Moles of O2 Reacted

First, we need to convert the mass of O2 into moles using its molar mass.

Molar mass of O2 32.0 g/mol Moles of O2 48 g / 32.0 g/mol 1.5 mol

Step 2: Calculate the Moles of Fe2O3 Produced

Next, we use the stoichiometry of the balanced equation to find the moles of Fe2O3 produced.

From the balanced equation, 3 moles of O2 produce 2 moles of Fe2O3. Moles of Fe2O3 1.5 mol × (2/3) 1 mol

Step 3: Calculate the Mass of Fe2O3 Produced

Finally, we convert the moles of Fe2O3 into grams using its molar mass.

Molar mass of Fe2O3 159.6 g/mol Mass of Fe2O3 1 mol × 159.6 g/mol 160 g

Alternative Method Through Dimensional Analysis

Another way to solve this problem is through the method of dimensional analysis, which simplifies the calculations by directly converting the given mass to the desired mass through appropriate unit conversions.

48 g O2 × (1 mol O2) / (32.0 g O2) × (2 mol Fe2O3) / (3 mol O2) × (159.6 g Fe2O3) / (1 mol Fe2O3) 160 g Fe2O3

Further Exploration of the Reaction

Understanding the balanced equation and the stoichiometric coefficients is crucial in solving problems related to chemical reactions. The balanced equation highlights the specific mole ratios and helps in accurately predicting the amount of product formed from a given amount of reactants. These calculations are essential for various applications, including environmental science, materials science, and industrial processes.

By utilizing the principles of stoichiometry and dimensional analysis, you can solve a wide range of chemical reaction problems. These techniques are particularly useful in industrial settings, where precise control over reactions is necessary for efficient and safe operations.