Urea-Nitrate-Cell · urea oxidation ‖ nitrate reduction · pH 14, 25 °CCan a urea–nitrate cell clean water and make power?

Urea is oxidized at the anode and nitrate reduced to ammonia at the cathode. Move the catalyst and operating parameters on the left and the cell is solved again in the browser with the model of urea_nitrate_cell: both electrode potentials from current balances, Faradaic efficiencies, a comparison with the published LSV data, and a batch treatment run. Potentials are V vs RHE.

Repository Validation table

Cell voltage

V_cell = E_c − E_a − jR_Ω; above zero the cell delivers power, below it needs an external bias

Power

V_cell · j: positive is delivered, negative is required

Electrode potentials

Each solved from its current balance; dashed: standard potentials

Faradaic efficiency

Share of the current carried by the wanted reaction; the rest goes to OER (anode) or HER (cathode)

Model

kinetics: j = 10 (10^η/b − 1) / (10^η₁₀/b − 1) mA cm⁻², anchored at the potential E₁₀ where j = 10 mA cm⁻²

nitrate: j_NO₃ = j_k j_lim / (j_k + j_lim), j_k ∝ (C/100 mM)^γ, j_lim = 8FDC/δ (Koutecký–Levich)

full cell: j_UOR(E_a) + j_OER(E_a) = j, j_NO₃(E_c) + j_HER(E_c) = j, V_cell = E_c − E_a − jR_Ω

batch: dC/dt = −FE_NO₃ I / (8 F V), explicit Euler with 10 s steps until 90 % is removed

Against the data, the electrode potential seen by the potentiostat includes the uncompensated resistance R_u (and a background current at the cathode), both fitted in calibration.py; the curves on the data tab use those fitted values with the parameters on the left.

Parameters now and in the fitted scenario S1

Checks

The JavaScript model of this page is a line-by-line copy of urea_nitrate_cell/model.py and of the measured-curve functions of calibration.py. scripts/verify_web_page.py runs it in Node.js for random parameter sets and compares cell voltages, electrode potentials, Faradaic efficiencies, limiting currents, measured LSV currents and whole batch runs with the Python package; the test (part of the pytest suite) passes only if they agree to a relative 10⁻⁸. The model itself is checked by the 36 validation checks of the repository; the fit to the LSV data is reported there as metrics, without a pass/fail threshold.

Calibration is not independent validation: S1 is fitted to the same LSV curves, and no full-cell data exist yet to test the absolute cell voltage. S2, S3 and R_Ω are assumptions.

Limitations and sources

Single Tafel slopes, a fixed diffusion layer, HER kinetics unaffected by nitrate; no by-products (nitrite, urea over-oxidation), pH drift or membrane potentials; urea is taken to be in excess at the anode.

Data: LSV curves digitized from M. Yao et al., Sustainability 17, 3835 (2025), CC BY 4.0. Thermodynamics: NBS tables (Wagman et al., 1982). Nitrate diffusion coefficient: CRC Handbook of Chemistry and Physics.

Code: github.com/Shuruyue/Urea-Nitrate-Cell. The data block of this page is written by scripts/build_web_page.py from the package. Style shared with the ethanol–water page.