Question

For each of the following unbalanced oxidation-reduction chemical equations, balance the equation by inspection, and identify which species is the reducing agent. a. \(\mathrm{Fe}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) b. \(\mathrm{Al}(s)+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{AlCl}_{3}(s)\) c. \(\mathrm{Mg}(s)+\mathrm{P}_{4}(s) \rightarrow \mathrm{Mg}_{3} \mathrm{P}_{2}(s)\)

Short answer

Short Answer: a. Balanced equation: \(4\mathrm{Fe}(s) + 3\mathrm{O}_{2}(g) \rightarrow 2\mathrm{Fe}_{2}\mathrm{O}_{3}(s)\); Reducing agent: Fe(s) b. Balanced equation: \(2\mathrm{Al}(s) + 3\mathrm{Cl}_{2}(g) \rightarrow 2\mathrm{AlCl}_{3}(s)\); Reducing agent: Al(s) c. Balanced equation: \(3\mathrm{Mg}(s) + \mathrm{P}_{4}(s) \rightarrow \mathrm{Mg}_{3}\mathrm{P}_{2}(s)\); Reducing agent: Mg(s)

Step-by-step solution

Determine the oxidation states

We start by assigning oxidation states to the atoms in each species: Fe(s): 0 since it's in its elemental form. O₂(g): 0 since it's in its elemental form. Fe₂O₃(s): The oxidation state of Fe will be +3 (as it's the common oxidation state of Fe in its compounds), and that of O will be -2.

Identify the change in oxidation states

Now, we can see that Fe changes from an oxidation state of 0 to +3 (an increase) and O changes from 0 to -2 (a decrease). Since Fe loses electrons (oxidation), it is the reducing agent.

Balance the equation by adjusting the coefficients

Multiply the reactants and products appropriately to balance the total charge and the number of each atoms: \(4 \times \mathrm{Fe}(s) + 3 \times \mathrm{O}_{2}(g) \rightarrow 2 \times \mathrm{Fe}_{2}\mathrm{O}_{3}(s)\) The balanced equation is: \(4\mathrm{Fe}(s) + 3\mathrm{O}_{2}(g) \rightarrow 2\mathrm{Fe}_{2}\mathrm{O}_{3}(s)\) Reducing agent: Fe(s) #b. Redox reaction: Al(s) + Cl₂(g) → AlCl₃(s)#

Determine the oxidation states

Assign oxidation states to the atoms: Al(s): 0 Cl₂(g): 0 AlCl₃(s): Al has an oxidation state of +3 and Cl has an oxidation state of -1.

Identify the change in oxidation states

Al changes from 0 to +3 and Cl changes from 0 to -1. Therefore, the reducing agent is Al since it loses electrons (oxidation).

Balance the equation by adjusting the coefficients

Multiply the reactants and products appropriately to balance the total charge and the number of each atoms: \(2 \times \mathrm{Al}(s) + 3 \times \mathrm{Cl}_{2}(g) \rightarrow 2 \times \mathrm{AlCl}_{3}(s)\) The balanced equation is: \(2\mathrm{Al}(s) + 3\mathrm{Cl}_{2}(g) \rightarrow 2\mathrm{AlCl}_{3}(s)\) Reducing agent: Al(s) #c. Redox reaction: Mg(s) + P₄(s) → Mg₃P₂(s)#

Determine the oxidation states

Assign oxidation states to the atoms: Mg(s): 0 P₄(s): 0 Mg₃P₂(s): Mg has an oxidation state of +2 and P has an oxidation state of -3.

Identify the change in oxidation states

Mg changes from an oxidation state of 0 to +2 and P changes from 0 to -3. This means that Mg is the reducing agent since it loses electrons (oxidation).

Balance the equation by adjusting the coefficients

Multiply the reactants and products appropriately to balance the total charge and the number of each atoms: \(3 \times \mathrm{Mg}(s) + \mathrm{P}_{4}(s) \rightarrow \mathrm{Mg}_{3}\mathrm{P}_{2}(s)\) The balanced equation is: \(3\mathrm{Mg}(s) + \mathrm{P}_{4}(s) \rightarrow \mathrm{Mg}_{3}\mathrm{P}_{2}(s)\) Reducing agent: Mg(s)

Key concepts

Balancing Chemical Equations

Balancing chemical equations is fundamental in chemistry because it ensures that matter is conserved during a reaction. In a chemical equation, atoms cannot be created or destroyed, so the number of each type of atom on the reactant side must equal the number on the product side. This portrays the law of conservation of mass.
To balance a chemical equation, adjust the coefficients (the numbers in front of molecules) to make the number of each type of atom on both sides equal. For example, while balancing the reaction of iron (\( ext{Fe}(s) \)) and oxygen (\( ext{O}_2(g) \)) to form iron (III) oxide (\( ext{Fe}_2 ext{O}_3(s) \)):

• First, notice each iron atom in \( ext{Fe}_2 ext{O}_3 \) has an oxidation state of +3, while oxygen has -2. Thus, balance Fe by multiplying by 4, and \( ext{O}_2 \) by 3 to satisfy both sides.
• This gives the balanced equation: \( 4 ext{Fe}(s) + 3 ext{O}_2(g) \rightarrow 2 ext{Fe}_2 ext{O}_3(s) \).

Remember, balancing equations often requires some trial and error for best results. Keep practicing for perfection.

Oxidation States

Oxidation states, or oxidation numbers, are used to keep track of electron transfers in chemical reactions, especially in oxidation-reduction (redox) reactions. An oxidation state represents the total number of electrons an atom can lose, gain, or share when forming chemical bonds.
Identifying oxidation states involves understanding some rules:

• Pure elements, like \( ext{Fe}(s) \) or \( ext{O}_2(g) \), have an oxidation state of 0.
• For a compound, the sum of the oxidation states should tally to zero. For instance, in \( ext{Fe}_2 ext{O}_3 \), iron has a +3 oxidation state, whereas oxygen is -2 per atom. For stability, the sum equals zero.
• In ions, the sum of oxidation states equals the ion charge; e.g., in \( ext{Fe}^{3+} \), iron has an oxidation state of +3.

Understanding these concepts will help determine which substances are oxidized and which are reduced in a reaction.

Reducing Agents

In redox reactions, the reducing agent is a substance that donates electrons to another, effectively reducing it, and in turn, becoming oxidized itself. The key is that reducing agents lose electrons while allowing another species (the oxidizing agent) to gain them.
For example, consider the reaction of aluminum \( ext{Al}(s) \) with chlorine \( ext{Cl}_2(g) \) to form aluminum chloride:

• As \( ext{Al} \) transitions from an oxidation state of 0 to +3, it loses electrons, making it the reducing agent.
• Meanwhile, \( ext{Cl}_2 \), moving from 0 to -1, gains electrons. Hence, \( ext{Al} \) provides the electrons for \( ext{Cl}_2 \) to become reduced.

The role of reducing agents is crucial as they facilitate the electron transfer process necessary for various chemical transformations. Identifying the reducing agent helps in fully understanding the electron flow and energy changes in a reaction.