$$ \begin{aligned} &\text { Point out the oxidation number of } \mathrm{C} \text { in the following : }\\\ &\mathrm{CH}_{4}, \mathrm{C}_{3} \mathrm{H}_{8}, \mathrm{C}_{2} \mathrm{H}_{6}, \mathrm{C}_{4} \mathrm{H}_{10}, \mathrm{CO}, \mathrm{CO}_{2} \text { and } \mathrm{HCO}_{3}^{-}, \mathrm{CO}_{3}^{2-} \end{aligned} $$

Oxidation states, also known as oxidation numbers, serve as a bookkeeping tool in chemistry, giving us insight into the electron distribution within compounds. Essentially, an oxidation state indicates the hypothetical charge an atom would possess if all its bonds were ionic in nature, disregarding the actual bond type—it's essentially a measure of electron 'ownership' within a molecule.

When determining the oxidation state of an atom, certain rules are applied consistently. For instance, the oxidation number of a pure element is always 0, and for monoatomic ions, it is equal to the ion's charge. In compounds, hydrogen typically has an oxidation number of +1, and oxygen normally has an oxidation number of -2, with some exceptions, such as in peroxides. The sum of oxidation states for all atoms in a molecule or ion must equal the overall charge of that species.

Understanding compound nomenclature is vital for identifying and communicating chemical substances systematically. It follows specific rules, such as prefixes for the number of atoms (mono-, di-, tri-, etc.), and suffixes for the type of compound, like '-ide' for simple anions or binary compounds. For example, CO is known as carbon monoxide, and CO₂ is carbon dioxide, reflecting the number of oxygen atoms.

Naming ions involves similar methods: anions typically end in '-ide', while polyatomic ions have unique names, such as the bicarbonate (HCO₃^-) and carbonate (CO₃^2-) ions mentioned in the provided exercise. The prefixes and suffixes are essential clues to the composition and structure of the compounds, an essential aspect of effective chemical communication.

Balancing charges is a crucial aspect of writing correct chemical formulas and equations. It's a concept based on the law of conservation of charge, which states that the net charge in an isolated system remains constant. In chemical compounds, the total positive charge (from cations) must balance the total negative charge (from anions) resulting in a neutral entity. For polyatomic ions, the sum of charges of all atoms included must result in the ion's net charge.

For instance, in the bicarbonate ion (HCO₃^-), the positive and negative charges must add up to -1. Similarly, in methane (CH₄), carbon has a -4 oxidation state to neutralize the +1 oxidation states of the four hydrogen atoms. Understanding how to balance charges enables chemists to predict the formulas of compounds formed and to balance chemical equations for reactions.

Redox chemistry, which stands for reduction-oxidation chemistry, involves reactions in which the oxidation states of atoms change. These processes are fundamental to numerous chemical reactions, such as combustion, respiration, corrosion, and energy generation within batteries.

Redox reactions consist of two complementary processes: reduction (gain of electrons, leading to a decrease in oxidation state) and oxidation (loss of electrons, leading to an increase in oxidation state). For a redox process to occur, there must be a transfer of electrons from the reducing agent to the oxidizing agent. The action of assigning oxidation numbers, as demonstrated in the provided exercise, is a preliminary step to identifying redox reactions and understanding the electron transfer that occurs during these chemical processes.