Question

Balance each of the following half-reactions, which take place in acidic solution. a. \(\mathrm{NO}_{3}^{-}(a q) \rightarrow \mathrm{NO}(g)\) b. \(\mathrm{NO}_{3}^{-}(a q) \rightarrow \mathrm{NO}_{2}(g)\) c. \(\mathrm{H}_{2} \mathrm{SO}_{4}(l) \rightarrow \mathrm{SO}_{2}(g)\) d. \(\mathrm{H}_{2} \mathrm{O}_{2}(a q) \rightarrow \mathrm{H}_{2} \mathrm{O}(l)\)

Short answer

The balanced half-reactions in acidic solutions are: a. \(NO_3^-(aq) + 4H^+(aq) + 3e^- \rightarrow NO(g) + 2H_2O(l)\) b. \(NO_3^-(aq) + 2H^+(aq) + e^- \rightarrow NO_2(g) + H_2O(l)\) c. \(H_2SO_4(l) + 2e^- \rightarrow SO_2(g) + H_2O(l)\) d. \(H_2O_2(aq) + 2e^- \rightarrow 2H_2O(l)\)

Step-by-step solution

a. Balancing \(NO_3^-(aq) \rightarrow NO(g)\)

: 1. Balancing atoms other than oxygen and hydrogen: Nitrogen atoms are already balanced. 2. Balancing oxygen atoms using H2O molecules: \[NO_3^-(aq) \rightarrow NO(g) + 2H_2O(l)\] 3. Balancing hydrogen atoms using H+ ions: \[NO_3^-(aq) + 4H^+(aq) \rightarrow NO(g) + 2H_2O(l)\] 4. Balancing charges with electrons: \[NO_3^-(aq) + 4H^+(aq) + 3e^- \rightarrow NO(g) + 2H_2O(l)\] The balanced half-reaction in an acidic solution is: \[NO_3^-(aq) + 4H^+(aq) + 3e^- \rightarrow NO(g) + 2H_2O(l)\]

b. Balancing \(NO_3^-(aq) \rightarrow NO_2(g)\)

: 1. Balancing atoms other than oxygen and hydrogen: Nitrogen atoms are already balanced. 2. Balancing oxygen atoms using H2O molecules: \[NO_3^-(aq) \rightarrow NO_2(g) + H_2O(l)\] 3. Balancing hydrogen atoms using H+ ions: \[NO_3^-(aq) + 2H^+(aq) \rightarrow NO_2(g) + H_2O(l)\] 4. Balancing charges with electrons: \[NO_3^-(aq) + 2H^+(aq) + e^- \rightarrow NO_2(g) + H_2O(l)\] The balanced half-reaction in an acidic solution is: \[NO_3^-(aq) + 2H^+(aq) + e^- \rightarrow NO_2(g) + H_2O(l)\]

c. Balancing \(H_2SO_4(l) \rightarrow SO_2(g)\)

: 1. Balancing atoms other than oxygen and hydrogen: Sulfur atoms are already balanced. 2. Balancing oxygen atoms using H2O molecules: \[H_2SO_4(l) \rightarrow SO_2(g) + H_2O(l)\] 3. Balancing hydrogen atoms using H+ ions: No need to add H+ ions, as already balanced. 4. Balancing charges with electrons: \[H_2SO_4(l) + 2e^- \rightarrow SO_2(g) + H_2O(l)\] The balanced half-reaction in an acidic solution is: \[H_2SO_4(l) + 2e^- \rightarrow SO_2(g) + H_2O(l)\]

d. Balancing \(H_2O_2(aq) \rightarrow H_2O(l)\)

: 1. Balance atoms other than oxygen and hydrogen: There are no other atoms to balance. 2. Balancing oxygen atoms using H2O molecules: Oxygen atoms are already balanced. 3. Balancing hydrogen atoms using H+ ions: Hydrogen atoms are already balanced. 4. Balancing charges with electrons: \[H_2O_2(aq) + 2e^- \rightarrow 2H_2O(l)\] The balanced half-reaction in an acidic solution is: \[H_2O_2(aq) + 2e^- \rightarrow 2H_2O(l)\]

Key concepts

Acidic Solution Reactions

Reactions occurring in acidic solutions are common lab and environmental processes, where an acid provides H+ ions in the solution. In these reactions, the presence of excess hydrogen ions (H+) from the acid must be taken into account when balancing redox equations. This characteristic of acidic solution reactions affects the method used for balancing, as seen in the provided exercise. For instance, to balance the oxygen atoms, water (H2O) is often added on one side of the reaction, and then H+ ions are subsequently added on the other side of the equation to balance the hydrogen atoms. The importance of considering the acidic environment can't be understated, as it directly influences how chemical species will interact and which products will form.

Half-Reaction Method

The half-reaction method is an efficient process for balancing redox reactions, which are split into two separate equations showing the oxidation and reduction that occur. The key steps involve balancing atoms and charges in each half-reaction independently before combining them back. As demonstrated in the exercise solutions:

• Atoms of elements other than oxygen and hydrogen are balanced first.
• Oxygen atoms are balanced by adding water molecules.
• Hydrogen atoms are balanced by adding H+ ions in acidic solutions.
• Finally, the charges are balanced by adding electrons (e-).

When using the half-reaction method, always remember to balance the number of electrons in the oxidation and reduction half-reactions. This ensures that the overall charge is the same on each side of the equation when you combine the two half-reactions back together.

Oxidation State Adjustment

Oxidation states are assigned to atoms to keep track of electron transfers in redox reactions. They are integral to balancing redox reactions because they help identify which species are oxidized and which are reduced. During the process:

• Substances that gain electrons have their oxidation state decrease, indicating reduction.
• Substances that lose electrons have their oxidation state increase, meaning they are oxidized.

The change in oxidation state is balanced out by adding electrons to the appropriate side of the half-reaction. As seen in the provided solutions, electrons are added to the left side of the reduction reactions, and for oxidation, electrons would be added to the right. Adjusting oxidation states is fundamental and acts as the cornerstone for balancing using the half-reaction method.

Stoichiometry in Chemistry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. In the context of redox reactions, stoichiometry is used to ensure that mass and charge are conserved by balancing the number of atoms of each element and the total charge on both sides of the equation. The step-by-step solutions provided exemplify the careful calculation required to maintain the proportion of atoms and charges, highlighting the meticulous nature of stoichiometric balancing. This is not only crucial for academic exercises but also plays a critical role in practical chemistry where reactants must be measured and reactions controlled for desired outcomes.