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Black-box Balance

Elemental and electron balances. Pick which rates you measured, let the balances calculate the rest, and check whether carbon and electrons close.

Species and rates, mmol/(L·h)

SpeciesFormulaElectronsMeasuredRate

Consumption is negative. Biomass is in C-mmol/(L·h). “Electrons” is the degree of reduction per mol: 4C + H − 2O − 3N. Untick “Measured” to let the C, H, O and N balances calculate that rate.

Do the balances close?

How it works

A black box has no internal structure. Only what crosses the boundary is counted: substrates in, products and biomass out. Each element (C, H, O, N) gives one balance, so four balances can calculate up to four unmeasured rates.

With three unknowns (O₂, NH₃, H₂O) and four balances, one balance is left over. That redundancy is a check on the data. If carbon or electrons do not close, a measurement is wrong or a product was missed.

The electron balance is the sum of (rate × degree of reduction) over all species. It is a combination of the four element balances. CO₂, H₂O and NH₃ have zero electrons, and O₂ has −4.