A Drinking Water Relevant Water Chemistry Model for the Free Chlorine and Cyanuric Acid System from 5°C to 35°C

Abstract

Abstract

In the United States, approved methods to measure free chlorine concentrations in drinking water systems adding sodium dichloroisocyanurate (dichlor) or trichloroisocyanuric acid (trichlor) as chlorine sources exhibit measurement bias from the presence of chlorinated cyanurates, leading to overestimated free chlorine concentrations for regulatory compliance. One option to overcome this limitation is to estimate free chlorine concentrations using an established water chemistry model (full model), but the full model has only been determined for 25°C. The current research used a simplified version of the full model (simple model) and estimated the unknown temperature dependence (5°C to 35°C) of the two remaining equilibrium constants (K_7a and K_9a) required for the simple model. At 0 M ionic strength (μ), \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\ln { { \rm { K } } _ { 7 { \rm { a } } } } = - { \frac { 4 , 671 } { { { \rm { T } } _ { \rm { K } } } } } + 4.95$$ \end{document} or \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$ { \rm { p } } { { \rm { K } } _ { 7 { \rm { a } } } } = { \frac { 2 , 028 } { { { \rm { T } } _ { \rm { K } } } } } - 2.15$$ \end{document} , \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\Delta { \rm{H}}_{7{ \rm{a}}}^0$$ \end{document}  = 38.8 ± 6.0 kJ/mol (95% confidence interval [CI]), \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\ln { { \rm { K } } _ { 9 { \rm { a } } } } = - { \frac { 5 , 133 } { { { \rm { T } } _ { \rm { K } } } } } + 3.79$$ \end{document} or \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$ { \rm { p } } { { \rm { K } } _ { 9 { \rm { a } } } } = { \frac { 2 , 229 } { { { \rm { T } } _ { \rm { K } } } } } - 1.65$$ \end{document} , and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\Delta { \rm{H}}_{9{ \rm{a}}}^0$$ \end{document}  = 42.7 ± 3.0 kJ/mol (95% CI). At 25°C and μ of 0 M, the simple model estimated pK_7a and pK_9a are 4.65 ± 0.059 (95% CI) and 5.83 ± 0.020 (95% CI), respectively. As an example of the impact of temperature, the free chlorine concentration for a 2 mg Cl₂/L dichlor addition (pH 7.0) decreases from 0.90 mg Cl₂/L at 25°C to 0.60 mg Cl₂/L at 5°C. If temperature was not considered, a system operating at 5°C would overestimate their free chlorine concentration by 50%, which could have significant implications for understanding disinfection efficacy, illustrating the developed model's significance.