Question

Balance the following equations. (a) \(\mathrm{Zn}(\mathrm{s})+\mathrm{VO}^{2+}(\mathrm{aq}) \longrightarrow\) $$\mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{V}^{3+}(\mathrm{aq}) \text { (acid solution) }$$ (b) \(\mathrm{Zn}(\mathrm{s})+\mathrm{VO}_{3}^{-}(\mathrm{aq}) \longrightarrow\) $$\mathrm{V}^{2+}(\mathrm{aq})+\mathrm{Zn}^{2+}(\mathrm{aq}) \text { (acid solution) }$$ (c) \(\mathrm{Zn}(\mathrm{s})+\mathrm{ClO}^{-}(\mathrm{aq}) \longrightarrow\) $$\mathrm{Zn}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{Cl}^{-}(\mathrm{aq}) \text { (basic solution) }$$ (d) \(\mathrm{ClO}^{-}(\mathrm{aq})+\left[\mathrm{Cr}(\mathrm{OH})_{4}\right]^{-}(\mathrm{aq}) \longrightarrow\) $$\mathrm{Cl}^{-}(\mathrm{aq})+\mathrm{CrO}_{4}^{2-}(\mathrm{aq}) \text { (basic solution) }$$

Short answer

Equations are balanced by identifying half-reactions, balancing atoms/charges, and combining them.

Step-by-step solution

Identify Half-Reactions

For each of the reactions, identify the oxidation and reduction half-reactions. For (a), \( \mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} \) (oxidation) and \( \mathrm{VO}^{2+} \rightarrow \mathrm{V}^{3+} \) (reduction). For (b), \( \mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} \) (oxidation) and \( \mathrm{VO}_{3}^{-} \rightarrow \mathrm{V}^{2+} \) (reduction). For (c), \( \mathrm{Zn} \rightarrow \mathrm{Zn(OH)}_{2} \) (oxidation) and \( \mathrm{ClO}^{-} \rightarrow \mathrm{Cl}^{-} \) (reduction). For (d), \( \mathrm{ClO}^{-} \rightarrow \mathrm{Cl}^{-} \) (reduction) and \( \mathrm{Cr(OH)}_{4}^{-} \rightarrow \mathrm{CrO}_{4}^{2-} \) (oxidation).

Balance Atoms other than O and H

Ensure that all atoms except oxygen and hydrogen are balanced in each half-reaction. In reactions (a), (b), and (c), Zinc and Chlorine are already balanced. For (d), Chromium atoms are already balanced.

Balance Oxygen Atoms

Add \( \mathrm{H}_2\mathrm{O} \) to balance the oxygen atoms. For (a) and (b), add water to the vanadium compounds as needed. For (c), ensure \( \mathrm{ClO}^{-} \rightarrow \mathrm{Cl}^{-} \) is balanced. For (d), balance \( \mathrm{Cr(OH)}_{4}^{-} \rightarrow \mathrm{CrO}_{4}^{2-} \) with water.

Balance Hydrogen Atoms

For acidic solutions ((a) and (b)), add \( \mathrm{H}^{+} \) to balance hydrogen. In basic solutions ((c) and (d)), add \( \mathrm{OH}^{-} \) as necessary, making sure to cancel out any \( \mathrm{H}^{+} \) added prior.

Balance Charge

Balance the charge of each half-reaction by adding electrons. For (a), add electrons to the more positive side. For (b), ensure the vanadium side is balanced with electrons. For (c) and (d), add electrons to balance the overall charge.

Combine and Simplify

Combine the half-reactions, ensuring that electrons are canceled out. Adjust coefficients as needed to achieve this. Verify that all atoms and charges are balanced in the final equation.

Key concepts

Oxidation-Reduction Reactions

In chemistry, an oxidation-reduction (redox) reaction involves the transfer of electrons between two species. This type of reaction results in changes to the oxidation states of the elements involved.

- **Oxidation** is the process where an element loses electrons, increasing its oxidation state. For example, in the reaction where zinc transforms into zinc ions (\(\mathrm{Zn} \rightarrow \mathrm{Zn}^{2+}\)), it loses two electrons, thus, oxidizing.

- **Reduction** is the gaining of electrons by an element, decreasing its oxidation state. In the case of vanadium \(\mathrm{VO}^{2+} \rightarrow \mathrm{V}^{3+}\), it gains electrons, thereby being reduced.

Understanding redox reactions is crucial in balancing equations as it allows us to keep track of how electrons are transferred, ensuring that the same amount is given and received. Identifying which elements are oxidized and reduced is the starting point in solving these problems.

Acid-Base Reactions

Acid-base reactions are another fundamental concept in chemistry, involving the transfer of protons (\(\mathrm{H}^+\)) between substances. These reactions can proceed in aqueous solutions that are either acidic or basic in nature.

- In **acidic solutions**, excess \(\mathrm{H}^+\) ions encourage the solution to act as a medium for reactions. In the redox reaction given, if the solution is acidic, additional \(\mathrm{H}^+\) is used to balance hydrogen atoms after balancing oxygen with water. \(\mathrm{H}^+\) ensures the transfer of protons to complete the balance.

- **Basic solutions** contain excess \(\mathrm{OH}^-\) ions, causing different balance needs. Here, \(\mathrm{OH}^-\) ions are employed to neutralize any extra \(\mathrm{H}^+\) ions and keep the solution alkaline. \(\mathrm{OH}^-\) compensates for the hydrogen balance created by water molecule addition, often converting existing \(\mathrm{H}^+\) to water.

The understanding of acidic and basic environments affects the steps required to balance redox reactions, as it dictates the chemicals used to achieve a balanced state.

Half-Reaction Method

The half-reaction method is a systematic procedure employed to balance redox equations. This technique breaks down the overall reaction into two simpler half-reactions: oxidation and reduction processes.

- **Step 1: Identification** begins by determining which species are oxidized and reduced. Separate these processes to focus on each independently, as seen in zinc and vanadium reactions.

- **Step 2: Balancing Atoms** other than oxygen and hydrogen is straightforward. Sit back and verify they match on both product and reactant sides.

- **Step 3: Balancing Oxygen** is achieved by adding water molecules. This ensures oxygen atoms are equal on both sides.

- **Step 4: Balancing Hydrogen** adapts to the solution's nature—adding \(\mathrm{H}^+\) in acidic conditions and \(\mathrm{OH}^-\) in basic ones.

- **Step 5: Charge Balancing** is key. Use electrons as balancing tools, adding them to the more positive side in each half-reaction so that each side has the same total charge.

- **Step 6: Combining** ensures a complete and balanced equation by canceling electrons and verifying that all elements and charges are balanced.

The half-reaction method provides a step-by-step framework to accurately balance even the most complex redox reactions, ensuring that the physical laws of conservation of mass and charge are upheld.