In which of the following acids N-atom has its highest oxidation state? (a) \(\mathrm{H}_{2} \mathrm{~N}_{2} \mathrm{O}_{4}\) (b) \(\mathrm{HNO}_{2}\) (c) \(\mathrm{HNO}_{3}\) (d) \(\mathrm{H}_{4} \mathrm{~N}_{2} \mathrm{O}_{4}\)

Understanding the chemical oxidation number is essential in chemistry, as it helps us keep track of electron shifts during chemical reactions. The oxidation number, often simply called the oxidation state, is a theoretical charge that an atom would have if all bonds to atoms of different elements were fully ionic. This concept allows chemists to speak about the oxidation and reduction of elements, even when the actual charge on the atoms is not changing in whole numbers. In essence, the oxidation number is the count of electrons an element has gained or lost to achieve its current state.

For finding the oxidation number, certain rules are applied: for instance, the oxidation number of oxygen is usually -2, and hydrogen is +1 (except in metal hydrides where it is -1). In a neutral molecule, the sum of the oxidation numbers must equal zero, while in polyatomic ions, the sum should match the ion's charge. Recognizing these patterns helps students to identify changes in the oxidation states of elements in redox reactions and balance chemical equations more confidently.

The nitrogen oxidation state can vary widely, from -3 in ammonia (NH_3) to +5 in nitric acid (HNO_3). This broad range makes nitrogen a versatile element in various chemical reactions, especially redox processes. By applying the rules for calculating oxidation numbers, one can determine nitrogen's oxidation state within compounds. Generally, a more positive oxidation state indicates a higher degree of oxidation of the nitrogen atom.

As the step-by-step example shows, calculating the nitrogen oxidation state involves setting up an equation based on known oxidation numbers and solving for the unknown. In polyatomic molecules like H_2N_2O_4 and HNO_2, it's important to account for all atoms' contributions to understand the overall charge distribution. This knowledge is not only useful for answering textbook questions but also underpins understanding more complex topics such as nitrogen fixation and the biochemical cycles of nitrogen.

Redox reactions, short for reduction-oxidation reactions, are a family of reactions that involve the transfer of electrons between chemical species. In such reactions, one species will lose electrons (oxidized) and another will gain electrons (reduced). Understanding the oxidation numbers of the elements involved in a reaction is crucial for identifying which species is being oxidized and which is reduced.

In the exercise provided, figuring out the highest oxidation state of nitrogen in various compounds relied on applying redox concepts. These reactions are pivotal in many biological systems, industrial processes, and environmental chemistry. For example, combustion, respiration, corrosion, and photosynthesis are all natural redox reactions. In the classroom, gaining proficiency with redox reactions aids in tackling a wide range of chemistry problems and fortifies a conceptual grasp of electron movement in chemical processes.