\(\mathrm{KMnO}_{4}\) can be prepared from \(\mathrm{K}_{2} \mathrm{MnO}_{4}\) as per the reaction : \(3 \mathrm{MnO}_{4}^{2-}+2 \mathrm{H}_{2} \mathrm{O} \rightleftharpoons 2 \mathrm{MnO}_{4}^{-}+\mathrm{MnO}_{2}+4 \mathrm{OH}^{-}\) The reaction can go to completion by removing \(\mathrm{OH}^{-}\)ions by adding : (1) \(\mathrm{KOH}\) (2) \(\mathrm{CO}_{2}\) (3) \(\mathrm{SO}_{2}\) (4) \(\mathrm{HCl}\)

Equilibrium reactions are dynamic processes where the forward and reverse reactions occur at the same rate. As a result, the concentrations of reactants and products remain constant over time. This balance is described by the equilibrium constant, denoted as \(K_{eq}\). The value of \(K_{eq}\) depends on the nature of the reaction and the conditions such as temperature.
Shifting an equilibrium reaction towards the products or reactants can be influenced by changes like concentration, pressure, and temperature, according to Le Chatelier's Principle. For instance, in the given exercise reaction, adding a substance that removes \(OH^{-}\) ions will shift the equilibrium towards the products, favoring the formation of \(KMnO_{4}\).
It's essential to understand how equilibrium reactions behave and how we can manipulate them. This knowledge helps in various applications, including chemical manufacturing and biological systems.

Neutralization is a chemical process where an acid and a base react to form water and a salt. In the context of the given problem, \(HCl\) is used to neutralize \(OH^{-}\) ions. This reaction can be represented by: \[ \mathrm{HCl} + \mathrm{OH}^{-} \rightarrow \mathrm{H_{2}O} + \mathrm{Cl^{-}} \] This is a typical neutralization reaction where the strong acid (HCl) reacts with a base (OH⁻) to form water, reducing the concentration of hydroxide ions in the solution.
Neutralization reactions are crucial in various industrial processes, environmental applications, and even in our daily lives (like antacids neutralizing stomach acid).
It’s helpful to know which substances are effective at neutralizing others. Strong acids are particularly good at neutralizing strong bases, which is why \(HCl\) was determined to be the most effective choice in the problem.

Chemical kinetics is the study of the rates of chemical reactions. Understanding reaction rates helps us control how fast a reaction occurs, which is particularly useful in industrial chemistry. Several factors influence the rate of a reaction: concentration of reactants, temperature, presence of catalysts, and surface area of solid reactants.
In the given equilibrium reaction involving \(KMnO_{4}\), the rate at which \(OH^{-}\) ions are removed impacts how quickly the equilibrium shifts towards the products. By adding \(HCl\), which rapidly reacts with \(OH^{-}\) ions, we can speed up the shifting of equilibrium to produce more \(KMnO_{4}\).
Learning and applying the principles of chemical kinetics helps in optimizing reactions to obtain desired products efficiently. Controlling reaction rates is fundamental in fields such as pharmaceuticals, environmental science, and materials engineering.