The oxidation number of sulphur in \(\mathrm{S}_{8}, \mathrm{~S}_{2} \mathrm{~F}_{2}, \mathrm{H}_{2} \mathrm{~S}\) respectively, are: (a) \(0,+1\) and \(-2\) (b) \(+2,+1\) and \(-2\) (c) \(0,+1\) and \(+2\) (d) \(-2,+1\) and \(-2\).

Oxidation states, also known as oxidation numbers, play a crucial role in the arena of chemistry, especially in understanding redox (reduction-oxidation) reactions. Each atom in a molecule can be assigned an oxidation state that represents its degree of oxidation or reduction. Typically, the oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were completely ionic.

For instance, in the molecular form of sulfur, \( \mathrm{S}_8 \), the atoms are not combined with different elements. As a consequence, each sulfur atom is considered to have an oxidation state of 0. It’s a standard convention to assign an oxidation number of 0 to elements in their pure, elemental state. This fundamental concept allows chemists to balance chemical equations and understand how electrons are transferred between atoms in redox reactions. To enrich learning, a helpful visualization would be using Lewis dot structures to show the transfer of electrons and the resulting oxidation number changes.

Chemical bonding forms the foundation of matter and its interactions. In a chemical bond, atoms are linked by their valence electrons. The type of bond, whether it's ionic or covalent, influences the oxidation numbers of the atoms involved. In ionic bonding, electrons are transferred from one atom to another, leading to positive or negative ions that have clear oxidation states. Covalent bonding usually involves sharing electrons, and sometimes the sharing isn't equal. Electronegative atoms, like fluorine in the molecule \( \mathrm{S}_2\mathrm{F}_2 \), pull electrons closer to themselves. In our example, fluorine has a stronger pull on electrons, so it maintains an oxidation number of -1. The sulfur, having a less electronegative character, compensates by having a positive oxidation state of +1 for each sulfur atom to maintain balance within the molecule.

Understanding chemical bonding is essential to making sense of oxidation numbers. An exercise improvement suggestion is to practice determining oxidation states in a variety of chemical compounds, to gain a firm grasp on how different types of bonds affect them.

Redox reactions are essential chemical reactions where one substance transfers electrons to another. These reactions are composed of two parts: oxidation, where an element loses electrons, and reduction, where an element gains electrons. The oxidation number of an atom will increase when it loses electrons during oxidation, and decrease when it gains electrons during reduction.

For example, in the compound \( \mathrm{H}_2\mathrm{S} \), hydrogen is oxidized with an oxidation state of +1 because it is less electronegative than sulfur. This results in sulfur being reduced to an oxidation state of -2. Redox reactions are omnipresent, from biological systems like cellular respiration to industrial processes like the rusting of iron. Diving deeper, one can perform a series of redox titration experiments to truly grasp the practical applications and nuances of redox chemistry in different settings.