Question

Balance each of the following oxidation-reduction reactions by using the oxidation states method. a. \(\mathrm{Cl}_{2}(g)+\mathrm{Al}(s) \rightarrow \mathrm{Al}^{3+}(a q)+\mathrm{Cl}^{-}(a q)\) b. \(\mathrm{O}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Pb}(s) \rightarrow \mathrm{Pb}(\mathrm{OH})_{2}(s)\) c. \(\mathrm{H}^{+}(a q)+\mathrm{MnO}_{4}^{-}(a q)+\mathrm{Fe}^{2+}(a q) \rightarrow\) \(\mathrm{Mn}^{2+}(a q)+\mathrm{Fe}^{3+}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\)

Short answer

a. Balanced reaction: \(2Cl_2 + 3Al \rightarrow 2Al^{3+} + 6Cl^-\) b. Balanced reaction: \(2H_2O + O_2 + 2Pb \rightarrow 2Pb(OH)_2\) c. Balanced reaction: \(8H^+ + MnO_4^- + 5Fe^{2+} \rightarrow Mn^{2+} + 5Fe^{3+} + 4H_2O\)

Step-by-step solution

a. Reaction to be balanced: Cl₂(g) + Al(s) → Al³⁺(aq) + Cl⁻(aq)

First, identify the oxidation states of each species in the reaction: Cl₂, - Cl has an oxidation state of ₀ Al, - Al has an oxidation state of ₀ Al³⁺ - Al has an oxidation state of +3 Cl⁻ - Cl has an oxidation state of -1 The change in oxidation states: - Cl is gaining an electron (reduced): ₀ to -1 (1 electron gained) - Al is losing 3 electrons (oxidized): ₀ to +3 (3 electrons lost) Now we balance the number of atoms and the charges on both sides: ₂Cl₂ + 3Al → 2Al³⁺ + 6Cl⁻ Now the equation is balanced.

b. Reaction to be balanced: O₂(g) + H₂O(l) + Pb(s) → Pb(OH)₂(s)

First, identify the oxidation states of each species in the reaction: O₂, - O has an oxidation state of ₀ H₂O, - O has an oxidation state of -2, H has an oxidation state of +1 Pb, - Pb has an oxidation state of ₀ Pb(OH)₂, - Pb has an oxidation state of +2, O has an oxidation state of -2, H has an oxidation state of +1 The change in oxidation states: - O is gaining 2 electrons (reduced): ₀ to -2 (2 electrons gained) - Pb is losing 2 electrons (oxidized): ₀ to +2 (2 electrons lost) Now we balance the number of atoms and the charges on both sides: 2H₂O + O₂ + 2Pb → 2Pb(OH)₂ Now the equation is balanced.

c. Reaction to be balanced: H⁺(aq) + MnO₄⁻(aq) + Fe²⁺(aq) → Mn²⁺(aq) + Fe³⁺(aq) + H₂O(l)

First, identify the oxidation states of each species in the reaction: H⁺, - H has an oxidation state of +1 MnO₄⁻, - Mn has an oxidation state of +7, O has an oxidation state of -2 Fe²⁺, - Fe has an oxidation state of +2 On the product side: Mn²⁺, - Mn has an oxidation state of +2 Fe³⁺, - Fe has an oxidation state of +3 H₂O, - O has an oxidation state of -2, H has an oxidation state of +1 The change in oxidation states: - Mn is gaining 5 electrons (reduced): +7 to +2 (5 electrons gained) - Fe is losing 1 electron (oxidized): +2 to +3 (1 electron lost) We need to multiply the Mn reduction by 1 and the Fe oxidation by 5 to balance the number of electrons lost and gained. Now we balance the number of atoms and the charges on both sides: 8H⁺ + MnO₄⁻ + 5Fe²⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O Now the equation is balanced.

Key concepts

Oxidation States

Oxidation states, also known as oxidation numbers, are used to keep track of electron transfer in chemical reactions. They provide a way to determine how many electrons are gained or lost in a reaction.
For example, elemental substances like O₂ or Cl₂ have an oxidation state of zero because the atoms are in their natural states without any loss or gain of electrons.

• In the reaction where Cl₂ is changed into Cl⁻, the oxidation state goes from 0 to -1. This indicates that Cl gained electrons and was reduced.
• In contrast, when Al changes from its elemental state to Al³⁺, the change in oxidation state from 0 to +3 shows that electrons were lost, and Al was oxidized.

Understanding oxidation states is fundamental because it helps identify which reactants are oxidized and which are reduced. This forms the basis of redox reactions.

Balancing Chemical Equations

Balancing chemical equations is vital in ensuring that the number of atoms for each element is equal on both sides of the equation. This reflects the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction.
To balance an equation:

• Begin by writing down the number of atoms for each element involved.
• Adjust the coefficients (the numbers in front of molecules or compounds) to balance the atoms on both sides.
• Make sure the total charge is also balanced.

Remember, only coefficients can change when balancing equations, not the chemical formulas of the reactants or products. This keeps the substances involved unchanged chemically, just corrected in proportion.

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, involve the transfer of electrons between two species. These reactions result in changes in oxidation states of the elements involved.
In a redox reaction:

• Reduction refers to the gain of electrons by a molecule, atom, or ion.
• Oxidation involves the loss of electrons.

For example, in the reaction between Cl₂ and Al, chlorine atoms are reduced (gaining electrons), while aluminum atoms are oxidized (losing electrons). Understanding this concept is crucial as it explains both the electron transfer process and its impact on the oxidation state of each participating element.

Electron Transfer

Electron transfer is the underlying process in redox reactions. It involves the movement of electrons from one element to another. This transfer is what causes one element to be oxidized and another to be reduced.
For instance, in the equation involving Al and Cl₂, Al loses electrons (is oxidized) and Cl₂ gains electrons (is reduced). Specifically, each Al atom gives up three electrons, while each Cl₂ molecule gains two electrons from the environment (or from multiple Al atoms, in practice) reflecting their changes in oxidation states.

• This gain or loss of electrons significantly affects the chemical stability and reactivity of elements, making electron transfer a central point in redox chemistry.
• Visualizing redox reactions as exchanges of electrons helps simplify the understanding of these processes.

Chemical Reactions Balancing Methods

Balancing chemical reactions, especially redox reactions, can be done using different methods. The most common method is the oxidation states method, but there are others like the half-reaction method.
The oxidation states method requires you to:

• Identify the oxidation state changes before and after the reaction.
• Use these changes to determine the number of electrons transferred.
• Adjust coefficients to ensure that the same number of electrons are lost and gained.

Alternatively, the half-reaction method involves dividing the redox reaction into two half-reactions, one for oxidation and one for reduction. Each half-reaction is balanced separately, and then they are combined, ensuring that electrons are balanced between the half-reactions. These balancing methods help ensure that both matter and charge are balanced in redox processes.