Question

Balance these redox reactions that occur in aqueous solution. Use whatever water-derived species is necessary; there may be more than one correct balanced equation. a) \(\mathrm{ClO}^{-}+\mathrm{Ti}^{2+} \rightarrow \mathrm{Ti}^{4+}+\mathrm{Cl}^{-}\) b) \(\mathrm{BrO}_{3}^{-}+\mathrm{Ag} \rightarrow \mathrm{Ag}^{+}+\mathrm{BrO}_{2}\)

Short answer

a) \(\mathrm{ClO}^{-} + \mathrm{Ti}^{2+} + 2\mathrm{H^+} \rightarrow \mathrm{Ti}^{4+} + \mathrm{Cl}^{-} + \mathrm{H_2O}\); b) \(\mathrm{BrO}_{3}^{-} + \mathrm{H_2O} + 2\mathrm{Ag} \rightarrow 2\mathrm{Ag}^{+} + \mathrm{BrO}_{2} + 2\mathrm{H^+}\).

Step-by-step solution

Separate the Reactions

For each reaction, identify the oxidation and reduction half-reactions.For a) \(\mathrm{ClO}^{-} \rightarrow \mathrm{Cl}^{-}\) (Reduction) and \(\mathrm{Ti}^{2+} \rightarrow \mathrm{Ti}^{4+}\) (Oxidation).For b) \(\mathrm{BrO}_{3}^{-} \rightarrow \mathrm{BrO}_{2}\) (Reduction) and \(\mathrm{Ag} \rightarrow \mathrm{Ag}^{+}\) (Oxidation).

Balance the Atoms Other than O and H

Focus on elements undergoing changes in oxidation state. For a) Cl is already balanced and Ti is balanced. For b) Br is already balanced and Ag is balanced.

Balance Oxygen Atoms Using \(\mathrm{H_2O}\)

Add \(\mathrm{H_2O}\) molecules to balance the oxygen atoms.For a) Add 1 \(\mathrm{H_2O}\) to the right side of the reduction half-reaction: \(\mathrm{ClO}^{-} \rightarrow \mathrm{Cl}^{-} + \mathrm{H_2O}\).For b) Add 1 \(\mathrm{H_2O}\) to the left side of the reduction half-reaction: \(\mathrm{BrO}_{3}^{-} + \mathrm{H_2O} \rightarrow \mathrm{BrO}_{2}\).

Balance Hydrogen Atoms Using \(\mathrm{H^+}\)

Add \(\mathrm{H^+}\) ions to balance the hydrogen atoms.For a) Add 2 \(\mathrm{H^+}\) to the left side: \(\mathrm{ClO}^{-} + 2\mathrm{H^+} \rightarrow \mathrm{Cl}^{-} + \mathrm{H_2O}\).For b) Add 2 \(\mathrm{H^+}\) to the right side: \(\mathrm{BrO}_{3}^{-} + \mathrm{H_2O} \rightarrow \mathrm{BrO}_{2} + 2\mathrm{H^+}\).

Balance the Charges with Electrons

Add electrons to balance the charges in each half-reaction.For a) Reduction: \(\mathrm{ClO}^{-} + 2\mathrm{H^+} + 2\mathrm{e}^{-} \rightarrow \mathrm{Cl}^{-} + \mathrm{H_2O}\) and Oxidation: \(\mathrm{Ti}^{2+} \rightarrow \mathrm{Ti}^{4+} + 2\mathrm{e}^{-}\).For b) Reduction: \(\mathrm{BrO}_{3}^{-} + \mathrm{H_2O} + 2\mathrm{e}^{-} \rightarrow \mathrm{BrO}_{2} + 2\mathrm{H^+}\) and Oxidation: \(\mathrm{Ag} \rightarrow \mathrm{Ag}^{+} + \mathrm{e}^{-}\).

Combine the Half-Reactions

For each reaction, make sure the electrons lost equal the electrons gained, then combine the half-reactions.For a): The electrons are already balanced. Combine to get \(\mathrm{ClO}^{-} + \mathrm{Ti}^{2+} + 2\mathrm{H^+} \rightarrow \mathrm{Ti}^{4+} + \mathrm{Cl}^{-} + \mathrm{H_2O}\).For b): Multiply the oxidation half by 2. Combine to get \(\mathrm{BrO}_{3}^{-} + \mathrm{H_2O} + 2\mathrm{Ag} \rightarrow 2\mathrm{Ag}^{+} + \mathrm{BrO}_{2} + 2\mathrm{H^+}\).

Key concepts

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry that ensures the same number of atoms occurs on both sides of the equation. This preserves the law of conservation of mass. When balancing redox reactions, it is crucial to account for the transfer of electrons. It helps in identifying whether the given species are being oxidized or reduced.

• The first step in balancing an equation is to separate it into oxidation and reduction half-reactions. This allows for a focused balancing of each process.
• Next, balance all atoms in each half-reaction except for oxygen and hydrogen. This generally involves adjusting coefficients before each reactant and product in the reaction.
• Once the core elements are balanced, deal with the oxygen atoms by adding water molecules (H₂O) as needed. Finally, adjust for hydrogen atoms by adding protons (H⁺).

By systematically following these steps, we ensure that the chemical reactions are properly balanced, thereby representing the actual chemical process accurately.

Half-Reaction Method

The half-reaction method is an essential technique used in balancing redox reactions. This method breaks down the original redox equation into two separate half-reactions: one for oxidation and one for reduction.

• The oxidation half-reaction involves the increase in oxidation state of the molecule, meaning it loses electrons.
• The reduction half-reaction, in contrast, involves a decrease in oxidation state, signifying a gain of electrons.

Each half-reaction is balanced for mass and charge separately. Once both half-reactions are balanced, they are recombined to form the overall balanced equation. The key to this method is ensuring that the number of electrons lost in the oxidation process equals the number of electrons gained in the reduction process. This ensures the conservation of charge and mass.

Oxidation and Reduction

Oxidation and reduction are two interconnected chemical processes that involve the transfer of electrons. They occur simultaneously in a redox reaction.
OXIDATION:

• This process involves the loss of electrons from a molecule or atom. When a species is oxidized, its oxidation state increases.
• In the equation from the exercise, Ti²⁺ being oxidized to Ti⁴⁺ is an example of oxidation, as electrons are lost from the titanium ion.

REDUCTION:

• Conversely, reduction involves the gain of electrons, leading to a decrease in the oxidation state of the species.
• For example, the transformation of ClO^- to Cl^- illustrates reduction, as the chlorite ion gains electrons.

These processes are essential for understanding electrochemical reactions, where the exchange of electrons drives the chemical changes.

Aqueous Solution Chemistry

Aqueous solution chemistry is the study of reactions that occur in water. Water is a versatile solvent and plays a pivotal role in facilitating chemical reactions. Many of these reactions involve dissolving ionic compounds, leading to their dissociation into ions.

• In the context of redox reactions, water molecules (H₂O) are often used to help balance oxygen atoms. The inclusion of H⁺ ions further assists in balancing hydrogen atoms.
• Reactions in aqueous solutions are characterized by the movement of ions, making it possible to visualize redox reactions in terms of the flow of electrons.
• This environment also allows for precise manipulation through the addition of acids or bases to influence the reaction pathways and achieve balanced chemical equations.

Understanding reactions in aqueous solutions is crucial, as they form the basis for many biological and environmental processes and are central to industrial chemical applications.