Biological nitrogen fixation and atmospheric composition:

• Dinitrogen ($\text{N}_2$) comprises approximately $78\%$ of the Earth's atmosphere by volume, making it the most abundant atmospheric gas.
• Plants cannot assimilate molecular nitrogen directly due to the highly stable triple covalent bond ($N \equiv N$).
• Symbiotic diazotrophs (such as Rhizobium in legume root nodules) utilize the nitrogenase enzyme complex to reduce atmospheric nitrogen into plant-absorbable ammonium ($\text{NH}_4^+$).

Mechanism and stoichiometry of the nitrogenase enzyme:

• The overall balanced reaction catalyzed by nitrogenase is: $\text{N}_2 + 8\text{H}^+ + 8e^- + 16\text{ ATP} \rightarrow 2\text{NH}_3 + \text{H}_2 + 16\text{ ADP} + 16\text{P}_i$.
• For every molecule of $\text{N}_2$ reduced, the enzyme complex releases exactly two molecules of ammonia ($\text{NH}_3$) and one molecule of hydrogen gas ($\text{H}_2$).
• Nitrogenase is extremely sensitive to oxygen and is irreversibly inactivated by molecular $\text{O}_2$, requiring an anaerobic microenvironment protected by leghemoglobin.

Energetics of biological nitrogen fixation:

• Assertion (A) is true: Diazotrophic bacteria depend on a large supply of host plant carbohydrates (such as sucrose, dicarboxylic acids like malate and succinate) to fuel bacteroid respiration.
• Reason (R) is true: Nitrogenase reduction of one mole of $\text{N}_2$ into two moles of $\text{NH}_3$ is energetically expensive, consuming $16\text{ ATP}$ molecules (plus reducing equivalents). High respiration rates driven by carbohydrate metabolism are necessary to generate this massive pool of ATP, directly explaining Assertion (A).

Dehydrogenase activity in soil:

• Dehydrogenase enzymes are intracellular enzymes that exist only in viable, intact living microbial cells; unlike extracellular hydrolases, they do not accumulate in an active state outside the cell in soil matrices.
• They catalyze oxidation-reduction reactions central to cellular respiration and the oxidative phosphorylation chain, transferring electrons from organic substrates to acceptors. Hence, dehydrogenase assay reflects the total viable microbial respiration and metabolic activity in soil.