Which of the following are electron-transfer reactions? For those that are, indicate which reactant is the reducing agent and which reactant is the oxidizing agent. (a) \(3 \mathrm{H}_{2} \mathrm{SO}_{3}+2 \mathrm{HNO}_{3} \rightarrow 3 \mathrm{H}_{2} \mathrm{SO}_{4}+2 \mathrm{NO}+\mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{Mg}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Mg}(\mathrm{OH})_{2}+\mathrm{H}_{2}\) (c) \(\mathrm{SO}_{3}{ }^{2-}+2 \mathrm{H}^{+} \rightarrow \mathrm{SO}_{2}+\mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{PbO}+\mathrm{CO} \rightarrow \mathrm{Pb}+\mathrm{CO}_{2}\)

Understanding oxidation numbers is key when analyzing redox reactions, which involve the transfer of electrons between reactants. Oxidation numbers, or oxidation states, are assigned to elements in a chemical compound to determine the distribution of electrons among them. They are hypothetical charges that an atom would have if the compound was composed of ions.

For example, in the compound H₂O, hydrogen has an oxidation number of +1, and oxygen has an oxidation number of -2. In a neutral molecule, the sum of the oxidation numbers equals zero, whereas in an ion, it equals the ion's charge. By comparing the oxidation numbers of each element before and after the reaction, we can identify which elements have been oxidized or reduced—meaning whether they have lost or gained electrons, respectively.

Using oxidation numbers, students can easily track electron flow, which is essential for determining the reducing and oxidizing agents in a reaction. For instance, in the given exercise solutions, we see that sulfur's oxidation number in H₂SO₃ increases from +4 to +6, indicating it has lost electrons and thus has been oxidized.

A reducing agent, or reductant, plays a vital role in redox reactions as it donates electrons to another substance, causing the reduction of the other substance. It effectively reduces the oxidation state of the other reactant while itself becoming oxidized. This means that during the reaction, the reducing agent will have an increase in its oxidation number.

For instance, in reaction (b) from the exercise, Mg starts with an oxidation number of 0 and ends with an oxidation number of +2 after the reaction. The increase in oxidation state indicates that Mg has lost electrons to hydrogen ions in H₂O, which have been reduced. Consequently, magnesium (Mg) is the reducing agent because it causes the reduction of hydrogen while being oxidized. Understanding the function of a reducing agent is critical for analyzing and balancing redox reactions.

In contrast to the reducing agent, the oxidizing agent, or oxidant, gains electrons in a redox reaction. This means it causes the oxidation of another substance and is itself reduced in the process. The oxidizing agent will see a decrease in its oxidation number as it accepts electrons.

Take the first reaction from our exercise, where HNO₃ serves as the oxidizing agent. The oxidation number of nitrogen decreases from +5 in HNO₃ to +2 in NO after the reaction, signaling a gain of electrons, hence the reduction of nitrogen. Oxidizing agents are important in driving redox processes, and they're often used in industrial and laboratory settings to spur oxidations vital to chemical synthesis. Identifying the oxidizing agent can help students understand the direction of electron flow and the energetics of chemical reactions.