Problem 115 - Chemistry The Science in Context

Question

The mineral magnetite \(\left(\mathrm{Fe}_{3} \mathrm{O}_{4}\right)\) is magnetic, whereas iron(II) oxide is not. a. Write and balance the chemical equation for the formation of magnetite from iron(II) oxide and oxygen. b. Given that \(318 \mathrm{kJ}\) of heat is released for each mole of \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) formed, what is the enthalpy change of the balanced reaction of formation of \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) from iron(II) oxide and oxygen?

Step-by-Step Solution

Answer

Question: Write a balanced chemical equation for the formation of magnetite (Fe3O4) from iron(II) oxide (FeO) and oxygen (O2) and determine the enthalpy change for the formation of Fe3O4 when 318 kJ of heat is released per mole of Fe3O4 formed. Answer: The balanced chemical equation is 6FeO + O2 -> 2Fe3O4. The enthalpy change for the formation of Fe3O4 from iron(II) oxide and oxygen is -636 kJ.

Step 1: Identify the reactants and products

The reactants given in the exercise are iron(II) oxide (FeO) and oxygen (O2). The product is magnetite (Fe3O4).

Step 2: Write the unbalanced equation

Write down the reactants and products involved in the reaction: FeO + O2 -> Fe3O4

Step 3: Balance the chemical equation

We will balance the equation by adjusting the coefficients of the reactant and product substances. In this case, adjust the coefficients of FeO and O2 to balance the number of atoms on both sides of the equation: 6FeO + O2 -> 2Fe3O4 b. Determine the enthalpy change for the formation of Fe3O4 from iron(II) oxide and oxygen

Step 1: Identify the heat released per mole of Fe3O4 formed

The exercise states that 318 kJ of heat is released for each mole of Fe3O4 formed.

Step 2: Determine the moles of Fe3O4 formed in the balanced equation

In the balanced chemical equation: 6FeO + O2 -> 2Fe3O4 We can see that 2 moles of Fe3O4 are formed.

Step 3: Calculate the enthalpy change of the balanced reaction

Since 318 kJ is released for each mole of Fe3O4 formed, we can calculate the enthalpy change for the formation of 2 moles of Fe3O4 using this relationship: Enthalpy change = heat released per mole × moles of Fe3O4 formed Enthalpy change = 318 kJ/mol × 2 mol Enthalpy change = 636 kJ The enthalpy change for the formation of Fe3O4 from iron(II) oxide and oxygen is -636 kJ (because heat is released in an exothermic reaction, the sign is negative).

Key Concepts

Magnetite Formation

Magnetite, a form of iron oxide with the chemical formula \( \mathrm{Fe}_3 \mathrm{O}_4 \), emerges through a fascinating transformation process involving iron(II) oxide and oxygen. This phenomenon is not only chemically compelling but also evokes interest due to magnetite's unique magnetic properties, unlike its precursor, iron(II) oxide. In order to understand the genesis of magnetite, it is essential to begin with the correct representation of the chemical reaction. The balanced chemical equation serves as the recipe for forming this mineral.

The starting point is to note the reactants, which in this case are iron(II) oxide (FeO) and diatomic oxygen (O2), and the product which is magnetite (Fe3O4). The balancing act, which involves ensuring that the number of each type of atom is equal on both sides of the reaction, is akin to solving a puzzle. After carefully placing the right coefficients, the final equation is \(6\mathrm{FeO} + \mathrm{O}_2 \rightarrow 2\mathrm{Fe}_3 \mathrm{O}_4\). This not only conveys the stoichiometry of the reaction but also hints at how the iron atoms from iron(II) oxide rearrange with oxygen to yield the magnetically attractive magnetite.

Enthalpy Change Calculation

Enthalpy change, symbolized as \(\Delta H\), is a measure of the heat absorbed or released during a chemical reaction at constant pressure. It is a central concept in thermodynamics and is crucial for understanding whether a process is energetically favorable or not. In exothermic reactions, like the formation of magnetite, energy is released into the surroundings, indicated by a negative enthalpy change.

Coupling this concept with the balanced chemical equation for the formation of magnetite, calculating the total enthalpy change becomes straightforward. Given that \(318\,\mathrm{kJ}\) of heat is released for each mole of magnetite formed, and observing from the balanced equation that 2 moles of magnetite are produced, the calculation involves a simple multiplication: \(\Delta H = -318\,\mathrm{kJ/mol} \times 2\,\mathrm{mol} = -636\,\mathrm{kJ}\). Here, the negative sign signifies that the reaction releases heat, affirming its exothermic nature.

Chemical Reaction Stoichiometry

Balancing Equations and Stoichiometry

Chemical reaction stoichiometry focuses on the quantitative relationship between reactants and products in a chemical reaction. It's a bit like following a culinary recipe, where precise amounts of ingredients are needed to produce the desired dish. When balancing a chemical equation, one must ensure that the same number of atoms of each element is present on both sides of the equation. This reflects the law of conservation of mass, stating that mass is neither created nor destroyed in a chemical reaction.

Looking at the stoichiometry of the magnetite formation equation, the adjustment of coefficients to balance the number of iron and oxygen atoms is the core challenge. This balancing determines how much reactant is needed to produce a certain amount of product. Understanding this concept allows scientists and engineers to predict the amounts of substances consumed and produced in a reaction, design chemical processes, and even assess the feasibility of large-scale industrial syntheses.