Propagation of Uncertainty in Aqueous Equilibrium Calculations:  Non-Gaussian Output Distributions

The propagation of uncertainty in aqueous equilibrium calculations is examined using a derivative method and Monte Carlo simulations. Simulations of 10⁴ trials provide both good reproducibility and reasonably short simulation times (<100 s on a 90 MHz Pentium microcomputer) for simple systems of up to seven components. Independent Gaussian uncertainty distributions of input constraints can lead to bimodal and/or skewed output distributions of pH, pM, and species concentrations. Gaussian input uncertainties of ≤10% can lead to much larger output uncertainties (95% confidence interval in pH or pM over 2 log units). While derivative methods of uncertainty prediction are faster than Monte Carlo simulations and reasonably accurate for some solution conditions, they are inappropriate if the output distribution is non-Gaussian. Consequently, Monte Carlo simulations are an essential complement to derivative methods for evaluating the uncertainty of calculated equilibrium concentrations.