\(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+6 \mathrm{I}+14 \mathrm{H}^{+} \longrightarrow 2 \mathrm{Cr}^{3+}+7 \mathrm{H}_{2} \mathrm{O}+3 \mathrm{I}_{2}\) Equivalent weight of \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) is: (a) \(\mathrm{M} / 3\) (b) \(\mathrm{M} / 6\) (c) \(\mathrm{M} / 2\) (d) None of these

A redox reaction, short for reduction-oxidation reaction, is a chemical process involving the transfer of electrons between two substances. These reactions are characterized by changes in the oxidation states of atoms.
During a redox reaction, one substance gains electrons (reduction) while another loses electrons (oxidation). Electrons are transferred from the oxidizing agent, causing it to be reduced, to the reducing agent, causing it to be oxidized. This reciprocal process is fundamental to many chemical reactions, such as the one in our exercise:
\[\begin{equation} \mathrm{Cr}_2\mathrm{O}_7^{2-} + 6\mathrm{I} + 14\mathrm{H}^{+} \longrightarrow 2\mathrm{Cr}^{3+} + 7\mathrm{H}_2\mathrm{O} + 3\mathrm{I}_2 \end{equation}\]
The dichromate ion \(\mathrm{Cr}_2\mathrm{O}_7^{2-}\) reduces into \(\mathrm{Cr}^{3+}\), thus showing a loss of electrons. Simultaneously, iodine ions gain electrons to form iodine molecules, \(\mathrm{I}_2\). This highlights the redox characteristic of gaining and losing electrons.

Oxidation state, often referred to as oxidation number, is a concept that provides a way to keep track of electrons in atoms during chemical reactions, particularly redox processes. It's a theoretical number that represents the electric charge an atom would have if the compound was composed of ions.
In redox reactions, the oxidation states of atoms change as electrons are transferred. These changes must be balanced, as the total number of electrons lost by one species must equal the number of electrons gained by another. In the given exercise, the oxidation state of \(\mathrm{Cr}\) in the dichromate ion \(\mathrm{Cr}_2\mathrm{O}_7^{2-}\) is +6, and it becomes +3 in \(\mathrm{Cr}^{3+}\). The change in the oxidation state here is essential for determining the equivalent weight of the compound.

Molecular weight, sometimes referred to as molecular mass, is the sum of the atomic weights of all atoms in a molecule. It's a measure of the total mass of a molecule and is often used in stoichiometry calculations for chemical reactions.
In the context of equivalent weight calculations, the molecular weight becomes a critical factor. Equivalent weight is defined as the mass of a substance that reacts with a given mass of another substance, such as hydrogen or oxygen, or that leads to the transfer of one mole of electrons in a redox reaction.Considering the exercise, we use the symbol \(M\) to represent the molecular weight of the dichromate ion \(\mathrm{Cr}_2\mathrm{O}_7^{2-}\), as the specific value is not given. To calculate the equivalent weight, this molecular weight is divided by the total change in oxidation states, providing a straightforward relationship between these parameters in chemistry.