Arrange the following species in order of increasing oxidation number of the sulfur atom: (a) \(\mathrm{H}_{2} \mathrm{~S},\) (b) \(\mathrm{S}_{8}\), (c) \(\mathrm{H}_{2} \mathrm{SO}_{4},\) (d) \(\mathrm{S}^{2-}\) (e) \(\mathrm{HS}^{-}\) (f) \(\mathrm{SO}_{2},(\mathrm{~g}) \mathrm{SO}_{3}\)

Understanding oxidation states is essential in mastering redox chemistry, as they tell us about how electrons are distributed in compounds and which atoms are undergoing changes in redox reactions. Assigning oxidation states involves several rules:

• The oxidation state of pure elements is always zero.
• For monoatomic ions, the oxidation state is equal to the ionic charge.
• In most compounds, hydrogen has an oxidation state of +1, while oxygen has an oxidation state of -2.
• The sum of oxidation states in a neutral compound must be zero, and in ions, it must equal the charge of the ion.

In our exercise, these rules enable us to assign oxidation states to sulfur in various compounds and ions. For instance, in hydrogen sulfide ($H\_2S$), hydrogen's +1 state and the compound's neutral charge lead us to give sulfur a -2 oxidation state to balance the equation. In a compound like sulfuric acid ($H\_2SO\_4$), accounting for hydrogen and oxygen's usual states and the compound's neutrality, we deduce that sulfur must have a +6 oxidation state. These practices are vital for students to master in order to analyze and predict the behavior of different chemical species in reactions.

Redox chemistry is the branch of chemistry that studies oxidation-reduction reactions, where the oxidation states of atoms are changed. Oxidation involves the loss of electrons, leading to an increase in oxidation state, while reduction involves the gain of electrons, with a corresponding decrease in oxidation state.

Understanding redox reactions requires not only knowing how to assign oxidation states but also recognizing the signs of oxidation and reduction processes. In the given exercise, identifying the oxidation states allows us to infer the reduction or oxidation tendencies of sulfur across different species. For example, when sulfur goes from an oxidation state of -2 in $H\_2S$ to +6 in sulfuric acid ($H\_2SO\_4$), it indicates that it has lost electrons, undergoing an oxidation process. Redox reactions are common in many chemical processes, including metabolism in living organisms, industrial synthesis of chemicals, and even the rusting of iron.

Sulfur is a versatile element that exhibits a wide range of oxidation states, from -2 in sulfide ions to +6 in sulfate ions. This flexibility is seen in the exercise where sulfur's oxidation state varies across several compounds.

• $S^\{2-\}$ and $H\_2S$: Sulfur has the lowest oxidation state of -2, compatible with the sulfur ion and hydrogen sulfide.
• $S\_8$: As an elemental form of sulfur, the oxidation state is 0.
• $SO\_2$ and $SO\_3$: These represent oxidation states of +4 and +6 for sulfur respectively, corresponding to sulfur dioxide and sulfur trioxide.

Having a grasp on these different states is crucial for students as they reveal how sulfur can act either as an oxidizing agent or a reducing agent depending on the chemical environment. Such knowledge is not only theoretically interesting, but it also has practical implications in fields like environmental science and materials chemistry, where sulfur compounds play significant roles.

Balancing redox equations is a key skill in understanding chemical reactions. This process ensures that the mass and charge are conserved during a reaction. To balance redox equations, one generally follows these steps:

• Determine the oxidation states of atoms to identify the oxidized and reduced species.
• Write half-reactions for the oxidation and reduction processes, balancing all atoms except oxygen and hydrogen.
• Balance oxygen atoms by adding water molecules and hydrogen atoms by adding hydrogen ions.
• Balance the charges by adding electrons.
• Combine the half-reactions, ensuring that the number of electrons lost in oxidation equals the number of electrons gained in reduction.
• Add any further necessary species to balance the atoms in the combined equation.

When students correctly apply these steps, as we did implicitly in our exercise by ensuring that the sulfur atoms' oxidation numbers in various compounds and ions were correctly assigned, they can confidently approach the balance of any redox equation. Mastering the balancing of redox equations empowers students to predict the outcome of chemical reactions and understand the underlying principles of topics such as energy production, electrochemistry, and industrial processes.