Track nitrogen species without losing nitrogen atoms

Define the community evidence

Microorganisms transform nitrogen among chemical forms. Nitrogen fixation reduces dinitrogen into forms that can enter organic synthesis; ammonification returns organic nitrogen to ammonium. Nitrification oxidizes ammonia/ammonium through nitrite toward nitrate, while denitrification reduces nitrate through intermediates toward gaseous products under suitable electron-donor and acceptor conditions. These mechanisms differ from simply removing nitrogen atoms from existence.

Connect mechanism and boundary

The original record starts with 100 mol of nitrogen atoms in ammonium. A supplied amount n is converted to nitrate, then fraction f of that nitrate nitrogen becomes dinitrogen. The remaining pools are 100−n mol N as ammonium, n(1−f) as nitrate and nf as gaseous nitrogen atoms. Because each N2 molecule contains two N atoms, the dinitrogen amount is nf/2 mol N2.

The restricted ledger omits assimilation, nitrite accumulation and intermediate nitrogen gases. It therefore illustrates an explicit endpoint assumption, not a full environmental model. Nitrification changes oxidation state without itself removing nitrogen from the water-system boundary; gas export changes the aqueous inventory only when the chosen boundary allows it to leave.

Carbon transformations similarly include fixation, decomposition, methane production and oxidation; sulfur transformations include oxidation and reduction of sulfur species. These coupled redox roles depend on available energy and electron partners. A nitrogen-only balance does not establish oxygen consumption or greenhouse-gas performance. No treatment operating conditions or cultivation method are supplied.

Reconstruct the original record

With n=50 and f=0.5, ammonium retains 50 mol N, nitrate retains 25 and dinitrogen contains 25 mol N atoms, equivalent to 12.5 mol N2. The atom total is 100, not 87.5; adding molecule moles without accounting for atoms would mix currencies.

Predict and investigate

Predict first: Why can a correct molecule count appear to violate a nitrogen balance when units are mixed?

Reconstruct all nitrogen pools before and after the second transformation. Separate aqueous retention from gas export, then name one omitted intermediate or coupled resource that prevents a complete ecosystem prediction.

Defend a changed case

Apply the mechanism to a changed boundary

Use n=80 and f=0.75. Find remaining ammonium, nitrate and dinitrogen in both atom and molecule units.

Retain the first response, units, uncertainty and any prior feedback exposure in the notebook before comparing this public explanation.

Compare a worked response

Ammonium 20 mol N, nitrate 20 mol N and gas 60 mol N close 100. The gas is 30 mol N2. The endpoint ledger does not reveal the actual pathway intermediates or energy demand.

Retain bounded evidence

Preserve the original record, first reasoning, units, sources and feedback exposure in the Microbiology evidence workspace. All numerical records are original fictional evidence, not measured field or treatment performance. No culture, process setup, biological handling or safety certification is requested.

Primary mechanism context, checked 31 October 2026. Original teaching and numerical examples; no source operating procedures reproduced.