Chapter 7: Problem 39

Balance each of the following equations according to the half-reaction method: (a) \(\operatorname{Sn}^{2+}(a q)+\mathrm{Cu}^{2+}(a q) \rightarrow \mathrm{Sn}^{4+}(a q)+\mathrm{Cu}^{+}(a q)\) (b) \(\mathrm{H}_{2} \mathrm{S}(g)+\mathrm{Hg}_{2}^{2+}(a q) \longrightarrow \mathrm{H} g(l)+\mathrm{S}(s)\) (in acid) (c) \(\mathrm{CN}^{-}(a q)+\mathrm{ClO}_{2}(a q) \longrightarrow \mathrm{CNO}^{-}(a q)+\mathrm{Cl}^{-}(a q)\) (in acid) (d) \(\mathrm{Fe}^{2+}(a q)+\mathrm{Ce}^{4+}(a q) \rightarrow \mathrm{Fe}^{3+}(a q)+\mathrm{Ce}^{3+}(a q)\) (e) \(\operatorname{HBrO}(a q) \rightarrow \operatorname{Br}^{-}(a q)+\mathrm{O}_{2}(g)\) (in acid)

Short Answer

Expert verified

The equations, once balanced using the half-reaction method would be: (a) Sn^{2+} + 2Cu^{2+} \rightarrow Sn^{4+} + 2Cu^{+}; (b) For H2S + Hg22+ \rightarrow Hg + S, adjust the equation with H+ and electrons; (c) For CN- + ClO2 \rightarrow CNO- + Cl-, balance the atoms and charges with H+ and electrons; (d) For Fe^{2+} + Ce^{4+} \rightarrow Fe^{3+} + Ce^{3+}, make sure the loss and gain of electrons are equal; (e) HBrO \rightarrow Br^- + O2 can be balanced with water molecules and H+ ions. All balanced equations should contain equal numbers of each type of element, and both sides should have the same overall charge.

Step by step solution

Title - Identify the Oxidation and Reduction Half-Reactions

Separate the given reactions into their oxidation and reduction components. An oxidation half-reaction involves a loss of electrons, while a reduction half-reaction involves a gain of electrons.

Title - Balance Atoms Other Than Oxygen and Hydrogen

Balance all elements except for oxygen and hydrogen in each half-reaction.

Title - Balance Oxygen Atoms

If there are oxygen atoms in the half-reaction, balance them by adding water molecules (H2O) to the side lacking oxygen.

Title - Balance Hydrogen Atoms

After balancing oxygen, balance the hydrogen atoms by adding hydrogen ions (H+) to the side that requires more hydrogen atoms.

Title - Balance Charge with Electrons

Balance the charge of each half-reaction by adding electrons (e-) to the appropriate side.

Title - Multiply Half-Reactions to Equalize Electron Transfer

If necessary, multiply the half-reactions by appropriate factors so that the number of electrons gained in the reduction half equals the number of electrons lost in the oxidation half.

Title - Combine Half-Reactions

Add the half-reactions together, canceling out electrons and any other species that appear on both sides of the equation.

Title - Verify Mass and Charge Balance

Check that both mass and charge are balanced in the final equation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Balancing Redox Reactions

To master the art of chemistry, balancing redox reactions is a fundamental skill. A redox reaction involves the transfer of electrons between two substances, leading to changes in their oxidation states. To balance these complex reactions, we use the half-reaction method, which breaks down the process into manageable steps. Let’s simplify this task by understanding that each redox reaction consists of two key parts: the oxidation half-reaction, where a substance loses electrons, and the reduction half-reaction, where another substance gains electrons.

Step-by-Step Balancing

First, you need to identify what is being oxidized and what is being reduced. Write these down as separate half-reactions. Once you have your half-reactions, it's a matter of balancing each element, adding water to balance oxygen atoms, and using hydrogen ions to balance hydrogen atoms in acidic solutions. Lastly, add electrons to one side of each half-reaction to balance the charges.

Remember, the electrons lost in the oxidation half-reaction must equal the electrons gained in the reduction half-reaction. Once both half-reactions are balanced, they can be combined, making sure to cancel out any species that appear on both sides. Finish by ensuring that atoms and charges are balanced in the final equation. By following these steps methodically, you can simplify the balancing of complex redox reactions and achieve chemical equilibrium.

Oxidation Half-Reaction

The oxidation half-reaction is a process where an atom, ion, or molecule loses electrons and increases its oxidation state. Think of it as the chemical 'giving away' electrons. This loss of electrons corresponds to the oxidation part of our redox reaction.

Identifying Oxidation

To determine the oxidation half-reaction, look for species that have a higher oxidation number after the reaction than before. For instance, if an iron ion goes from Fe^{2+} to Fe^{3+}, it has lost an electron and become oxidized. In the context of balancing, it is crucial to account for each electron lost in order to match them with the reduction half-reaction later on.

During the balancing phase, you'll add electrons to the product side of the oxidation half-reaction to ensure that both mass and charge are preserved. Seeing electrons explicitly in the equation serves as your reminder that during oxidation, electrons are indeed being lost. With a clear understanding of oxidation half-reactions, students can more intuitively balance and comprehend the bigger picture of what's occurring in a redox process.

Reduction Half-Reaction

Opposite to oxidation, the reduction half-reaction is where the magic of 'gaining' electrons takes place. Here, the species decreases its oxidation state by acquiring electrons, becoming more negative or less positive as a result.

Identifying Reduction

In identifying the species undergoing reduction, look for a decrease in the oxidation number between reactants and products. For example, a copper ion Cu^{2+} gaining an electron to become Cu^+ is undergoing reduction. In balancing these reactions, you add electrons to the reactant side to balance the increase in the negative charge that occurs with the gain of electrons.

It's critical to understand that reduction is the other half of the redox equation and cannot occur without oxidation - they are two sides of the same coin. By thoroughly understanding and balancing reduction half-reactions, you're setting a strong foundation for recognizing the complete transfer of electrons within the reaction. This knowledge allows not only for better-balanced equations but also a deeper appreciation of the interplay between oxidation and reduction in chemical processes.

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Short Answer

Step by step solution

Title - Identify the Oxidation and Reduction Half-Reactions

Title - Balance Atoms Other Than Oxygen and Hydrogen

Title - Balance Oxygen Atoms

Title - Balance Hydrogen Atoms

Title - Balance Charge with Electrons

Title - Multiply Half-Reactions to Equalize Electron Transfer

Title - Combine Half-Reactions

Title - Verify Mass and Charge Balance

Key Concepts

Balancing Redox Reactions

Step-by-Step Balancing

Oxidation Half-Reaction

Identifying Oxidation

Reduction Half-Reaction

Identifying Reduction

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