Quantitative ¹⁴N NMR with Monte Carlo Uncertainty Analysis of Nitrate/Nitrite in Alkaline Nuclear Waste

Quantification of nitrate and nitrite concentrations is important for the management of radioactive tank waste chemistry, as these species influence solubility and corrosion. However, existing analytical methods are potentially hindered by turbidity, spectral interference, and delays from sample handling. We demonstrate quantitative ¹⁴N nuclear magnetic resonance (qNMR) spectroscopy as a direct, matrix-tolerant approach for nitrate and nitrite detection at natural abundance. Monte Carlo resampling was integrated into the workflow to quantify marginal uncertainty, establish precision-time trade-offs, and separate noise-limited uncertainty from systematic bias arising from shimming, transmitter offset, or excitation pulse conditions. Quantification of nitrate and nitrite was validated in controlled alkaline matrix challenges and in five multicomponent simulants of Hanford Waste. These results establish ¹⁴N qNMR as a practical, uncertainty-bounded tool for quantifying redox-active nitrogen species in chemically complex environments and provide an approach for quantitative analysis of solution-state quadrupolar nuclei.