Question

Balance each redox reaction occurring in acidic aqueous solution. MISSED THIS? Read Section \(20.2 ;\) Watch \(\mathrm{KCV} 20.2,\) WE 20.2 a. \(\mathrm{K}(s)+\mathrm{Cr}^{3+}(a q) \longrightarrow \mathrm{Cr}(s)+\mathrm{K}^{+}(a q)\) b. \(\mathrm{Al}(s)+\mathrm{Fe}^{2+}(a q) \longrightarrow \mathrm{Al}^{3+}(a q)+\mathrm{Fe}(s)\) c. \(\mathrm{BrO}_{3}^{-}(a q)+\mathrm{N}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{Br}^{-}(a q)+\mathrm{N}_{2}(g)\)

Short answer

a. Balanced equation: 2 K(s) + 2 Cr^{3+}(aq) \rightarrow 2 Cr(s) + 2 K^{+}(aq); b. Balanced equation: 3 Fe^{2+}(aq) + 2 Al(s) \rightarrow 3 Fe(s) + 2 Al^{3+}(aq); c. Balanced equation: 2 BrO3^{-}(aq) + N2H4(g) \rightarrow 2 Br^{-}(aq) + N2(g) + 2H2O(l).

Step-by-step solution

- Separate the redox reactions into two half-reactions

For each redox reaction given, identify and write out the oxidation and reduction half-reactions separately. An oxidation half-reaction involves the loss of electrons, and a reduction half-reaction involves the gain of electrons.

- Balance the atoms other than oxygen and hydrogen

For each half-reaction, balance all the atoms except for oxygen and hydrogen. This is done by adding coefficients in front of the chemical species.

- Balance oxygen atoms by adding water molecules

If there are oxygen atoms in the half-reaction, balance them by adding H2O molecules to the side that requires more oxygen.

- Balance hydrogen atoms by adding hydrogen ions

Balance the hydrogen atoms that were added with the water molecules by adding H+ ions to the opposite side of the half-reaction.

- Balance the charge by adding electrons

Balance the charge of each half-reaction by adding electrons. In an oxidation half-reaction, electrons are added to the right side, and in a reduction half-reaction, electrons are added to the left side.

- Make the number of electrons equal

The number of electrons lost in the oxidation half-reaction must equal the number of electrons gained in the reduction half-reaction. Multiply the half-reactions by appropriate coefficients to achieve this.

- Combine the half-reactions

Add the balanced half-reactions together. Make sure that the electrons cancel out and that the other atoms and charges are balanced.

- Simplify the combined equation if necessary

If there are species that appear on both sides of the equation, cancel them out to simplify the equation.

Key concepts

Oxidation and Reduction Half-Reactions

Understanding oxidation and reduction half-reactions is the backbone of interpreting redox reactions. Oxidation refers to the loss of electrons, often characterized by an increase in oxidation state, while reduction is the gain of electrons, typically indicated by a decrease in oxidation state.

To identify the half-reactions in a given chemical equation, you can look for changes in the oxidation states of the elements. For instance, in the reaction between potassium (K) and chromium (Cr³⁺), the K goes from an oxidation state of 0 to +1, thus it is oxidized, and the half-reaction is written as K(s) → K⁺(aq)+ e^-. Conversely, Cr³⁺ is reduced to Cr(s), which is depicted as Cr³⁺(aq) + 3e^- → Cr(s).

Balancing Charge and Mass in Half-Reactions

In half-reactions, it's crucial to ensure that both charge and mass are balanced. You balance mass by adding coefficients and balance charge by adding electrons. The electrons lost in the oxidation half-reaction must be equal to the electrons gained in the reduction half-reaction to maintain charge balance when the two half-reactions are combined.

Balancing Chemical Equations

To successfully balance a chemical equation, you must ensure that the number of atoms for each element is the same on both sides of the equation, upholding the law of conservation of mass. The process involves adding coefficients in front of chemical species so that atoms and charge are balanced.

In redox reactions, particularly, this exercise can be more complex because you must also make sure that the electrons lost and gained are balanced. This concept is integral, especially when dealing with complex reactions involving multiple oxidation states and compounds. After separately balancing the mass and charges in the half-reactions, you bring them together ensuring that the number of electrons exchanged is equal.

Applying Coefficients

Coefficients are whole numbers that you place in front of compounds or elements in a chemical equation to balance the number of atoms. It’s essential to start with substances that contain elements that are not common or are found in the least amount of compounds within the reaction, gradually moving to those that are more common.

Acidic Aqueous Solution

Chemical reactions that occur in acidic aqueous solutions are common in chemistry, particularly in redox reactions. In such reactions, the presence of an acid often means that there is a surplus of H⁺ ions in the solution. This plays a fundamental role when you come to balance hydrogen atoms in half-reactions.

Balance the hydrogen atoms by adding H⁺ ions to the side of the half-reaction that requires more hydrogen. This also aids in charge balancing since H⁺ carries a positive charge. Furthermore, when balancing oxygen atoms by adding water (H₂O), you’ll often need to balance out the newly introduced hydrogen atoms with more H⁺ ions.

Working with Acids

Because acids introduce H⁺ to reactions, they can influence the direction and products of a chemical reaction. When balancing redox reactions in an acidic solution, you'll need to consider how these H⁺ ions interact with other species in the reaction and ensure that the equation remains balanced in terms of both mass and charge throughout the process.