Question

Write balanced chemical equations for the reduction of \(\mathrm{FeO}\) and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) by \(\mathrm{H}_{2}\) and by \(\mathrm{CO}\).

Short answer

The four balanced chemical equations for the reduction of FeO and Fe₂O₃ by H₂ and CO are: 1) Reduction of FeO by H₂: \(FeO + 2H_{2} \rightarrow Fe + 2H_{2}O\) 2) Reduction of Fe₂O₃ by H₂: \(Fe_{2}O_{3} + 3H_{2} \rightarrow 2Fe + 3H_{2}O\) 3) Reduction of FeO by CO: \(FeO + CO \rightarrow Fe + CO_{2}\) 4) Reduction of Fe₂O₃ by CO: \(Fe_{2}O_{3} + 3CO \rightarrow 2Fe + 3CO_{2}\)

Step-by-step solution

Reduction of FeO by H₂

Say we start with the given reactants: FeO and H₂. The reduction reaction would produce Fe and H₂O. Now we write the unbalanced equation: FeO + H₂ → Fe + H₂O Now we balance the equation by ensuring there are equal numbers of atoms of each element on both sides of the equation. In this case, to balance the number of oxygen atoms, we just need to add a 2 in front of H₂ and H₂O. The balanced equation for the reduction of FeO by H₂ is: FeO + 2H₂ → Fe + 2H₂O

Reduction of Fe₂O₃ by H₂

We start with the given reactants: Fe₂O₃ and H₂. The reduction reaction would produce Fe and H₂O. Now we write the unbalanced equation: Fe₂O₃ + H₂ → Fe + H₂O Now we balance the equation by ensuring there are equal numbers of atoms for each element on both sides of the equation. In this case, to balance the number of iron atoms, we just need to multiply Fe by 2, and to balance the number of oxygen atoms, we need to multiply H₂O by 3. Also, to balance the number of hydrogen atoms, we need to multiply H₂ by 3 as well. The balanced equation for the reduction of Fe₂O₃ by H₂ is: Fe₂O₃ + 3H₂ → 2Fe + 3H₂O

Reduction of FeO by CO

We start with the given reactants: FeO and CO. The reduction reaction would produce Fe and CO₂. Now we write the unbalanced equation: FeO + CO → Fe + CO₂ In this case, the equation is already balanced, and we don't need to change any coefficients. The balanced equation for the reduction of FeO by CO is: FeO + CO → Fe + CO₂

Reduction of Fe₂O₃ by CO

We start with the given reactants: Fe₂O₃ and CO. The reduction reaction would produce Fe and CO₂. Now we write the unbalanced equation: Fe₂O₃ + CO → Fe + CO₂ Now we balance the equation by ensuring there are equal numbers of atoms for each element on both sides of the equation. In this case, to balance the number of oxygen atoms, we just need to multiply CO and CO₂ by 3. Also, we need to multiply Fe by 2 to balance the number of iron atoms. The balanced equation for the reduction of Fe₂O₃ by CO is: Fe₂O₃ + 3CO → 2Fe + 3CO₂

Key concepts

Chemical Reaction Balancing

Understanding how to balance chemical equations is a fundamental skill in chemistry. A balanced chemical equation has an equal number of each type of atom on both sides of the reaction arrow, abiding by the law of conservation of mass. Let's take the provided reduction of FeO by H₂ as an example. The unbalanced equation is: FeO + H₂ → Fe + H₂OBalancing such equations involves adjusting the coefficients – the numbers placed before the chemical formulas – to ensure the same number of atoms of each element on both sides. Start by listing the number of atoms of each element in the reactants and products. For instance, initially, there is one Fe atom and one O atom on the left, and one Fe atom and two H and one O atoms on the right. To balance the oxygen atoms, we can place a coefficient of two in front of H₂ and H₂O, thus also balancing the hydrogen atoms. The result is a balanced equation: FeO + 2H₂ → Fe + 2H₂OBalancing equations requires practice and patience. When dealing with more complex equations, you might need to balance one element at a time and iterate until all elements are balanced.

Reduction Reactions

Reduction reactions are a type of chemical reaction where an element gains electrons, resulting in a decrease in its oxidation state. When discussing the reduction of iron oxides FeO and Fe₂O₃ by H₂ and CO, it is the iron oxide that is being reduced, meaning the Fe atoms are gaining electrons and reducing their oxidation state from +2 or +3 in the oxides to 0 in elemental Fe. In the context of the exercise, hydrogen (H₂) and carbon monoxide (CO) act as reducing agents. They donate electrons to Fe in the iron oxides. During the process, the reducing agents themselves get oxidized; for example, hydrogen is oxidized to water (H₂O) and carbon monoxide to carbon dioxide (CO₂). Understanding the electron transfer concept can significantly aid in comprehending reduction reactions and their balanced equations.

Stoichiometry

Stoichiometry refers to the calculation of reactants and products in chemical reactions. It is based on the balanced chemical equations. The coefficients in a balanced equation are crucial—they represent the molar ratio of the reactants and products, known as stoichiometric coefficients. These ratios can be used to determine how much of each reactant you need to produce a desired amount of product, or how much product can be made from given amounts of reactants. For instance, in the balanced reduction reaction of Fe₂O₃ by hydrogen, the stoichiometry of the balanced equation Fe₂O₃ + 3H₂ → 2Fe + 3H₂O tells us that 1 mole of Fe₂O₃ reacts with 3 moles of H₂ to yield 2 moles of Fe and 3 moles of H₂O. Using stoichiometry, quantitative predictions about the results of a reaction can be made, making it an invaluable part of chemical calculations.