Using Mean Oxidation Number of Organic Carbons to Count Theoretical Chemical Oxygen Demand

,


Introduction
Chemical oxygen demand (COD) is one of the important analytical parameters for counting pure or mixed organic matters in aqueous solution (ASTM D1252-06, 2020ISO 15705, 2002;IUPAC, 2019;Baker et al., 1999).It is widely used in wastewater, aerobic digestion, and anaerobic digestion (Contreras et al., 2002;Brouckaert et al., 2021;Ahnert et al., 2021;Brouckaert et al., 2022;Angelidaki & Sanders, 2004;Tamis et al., 2021).The quantity of COD of organic matter is relevant to the quantitative amount of molecular oxygen (O 2 ).Currently the calculation of COD of neutral organic matter is based on the number of moles of molecular oxygen (nO 2 ) (Baker et al., 1999;Ahnert et al., 2021).However, the calculation of theoretical chemical oxygen demand of ionic organic matter has seldom been studied.
The mean oxidation number of organic carbons (ONc) of organic matter is a redox metric for environmental chemistry (Kroll et al., 2011), water treatment (Vogel et al., 2000;Li et al., 2022), organic combustion (Yuen & Lau, 2023a), and anaerobic digestion (Yuen & Lau, 2024a).Although the mathematical relationship between ONc and the ratio of COD to total organic carbon (TOC) (Vogel et al., 2000), and the relationship between ONc and nO 2 have already been established (Yuen & Lau, 2023a), the relationships among ONc, nO 2 , and theoretical COD have not been explored yet.
In this article ONc is developed as a metric for determining COD of organic matter.The exploration of mathematical equations for counting COD is based on the chemical formula of organic matter.The chemical formula can be structural or empirical and the organic matter can be in molecular or ionic form.Through the integration of ONc, nO 2 , and COD, the relationships among COD, ONc, number of organic carbons (nc or x), and formula mass of organic matter (μ) are identified.The relationships among ONc, COD, TOC (TCEQ, 2022), and COD TOC are also established.Most importantly, a mathematical equation which uses ONc to count theoretical COD is developed.

Methods and Materials
The methodology of the article is shown in Figure 1.
For organic matters: C x H y O z X w N v S u P t charge  x Chemical formulas of biomasses, biowastes, or unknown structures of pure and mixed organic matters are considered empirical formulas.For any given empirical formula, its ONc of an organic matter can be counted either by the molecular formula method (Yuen & Lau, 2022) or non-carbon atom method (Yuen & Lau, 2023c).All ON inc in empirical formulas are assumed to be ON H = +1, ON O = −2, ON X = −1, ON N = −3, ON S = −2, ON P = +5 (Yuen & Lau, 2024b).
In the empirical formula: The mathematical equation for calculating ONc of an empirical formula is established as x

Chemical Oxygen Demand (COD)
Generally, COD is a measure of the mass of molecular oxygen that can be consumed by organic matters in a measured solution.The unit of COD is commonly expressed in grams of molecular oxygen to liters of aqueous solution or wastewater.It is represented as COD (unit, g/L) = mO 2 V solution .
In the study of volatile solids in anaerobic digestion or sludges in wastewater treatment, COD is a measure of the grams of molecular oxygen that can be consumed by per gram of organic matters.It is defined as COD (unit, g/g) = mO 2 m OM .

Relationship between ONc and nO 2
According to the general organic combustion reaction,

Mole Relationship between n organic matter and nO 2
Two organic combustion equations are provided as examples.
There is a complete reaction between 1 mole of organic matter and moles of molecular oxygen.All ON inc remain the same before and after any combustion reaction (Yuen & Lau, 2023a).Organic combustion equations can be used to calculate theoretical COD of any organic matter.

Mass Relationships
Based on the definitions of COD, TOC, and

4
, three mathematical equations are attained.Since the connection between mass relationships and mole relationships has been found, the mathematical equations for theoretical COD, theoretical TOC, and theoretical COD TOC can be derived.

Triangular Relationships Among ONc, nO 2 and COD
Through the integration of ONc and mole-mass relationship, the triangular relationships among ONc, nO 2 , and COD, and their mathematical equations are shown in Figure 2. ONc

Procedures and Examples
The operating procedures for counting COD, TOC, and

Calculation of ONc
For any given structural formula: x For any given empirical formula:

Examples
The calculated data for carbon atom, molecules, and ions are summarized in  , but same value of TOC.The same set of isomers will have the same TOC value.The more negative the value of ONc is, the greater the value of COD will become.Based on the selected empirical formulas of organic matters (Ahnert et al., 2021), the calculated organic carbon's relevant parameters are summarized in Table 4.  Single molecule Example 1.Given multiple molecules which contain 3.000 mole of H 3 C-S-S-CH 3 , 2.000 moles of and 1.000 moles of , count the values of nO 2 , COD, TOC, and COD TOC of the multiple molecules.
(i) Determine the values of n OM , x, μ, and ONc of three different types of molecules

Conclusion
ONc and theoretical COD of organic matter are two important redox parameters.In this article, ONc is developed as a metric for quantifying theoretical COD.Based on any given formula, empirical or structural, of an organic matter which can either be in molecular or ionic form, the relationships among ONc, , μOM, COD, TOC, and respectively.

Figure 1 .
Figure 1.The methodology: from organic matter to COD, TOC, and COD TOC

X
= halogen atoms charge = electrical charge of organic matter ON inc = individual oxidation number of non-carbon atom ONc = mean oxidation number of carbons nc = x = number of organic carbons When charge = 0, it is a neutral organic matter, ONc = −ΣON inc nc .When charge ≠ 0, it is a charged organic matter, ONc = charge−ΣON inc nc .In the structural formula: C x H y O z X w N v S u P t charge

Figure 2 .
Figure 2. Mathematical relationships among ONc, nO 2 and COD , , μOM → COD, TOC, COD TOC any single organic matter when n OM = 1 mole.Furthermore, the total values of nO 2 , COD, Calculation of  and μ OMBoth the structural and empirical formula can identify the number of organic carbon (x) and calculate the formula mass (μ OM ).
CODTOC can be calculated by using the following mathematical equations.COD is dependent on x, ONc, and μ OM .TOC is related to x and μ OM , but not to ONc.

Table 2 .
The molecular CH 3 COOH and ionic CH 3 COO − have same values of ONc and COD TOC, but different values of COD and TOC.An organic acid and its organic salt have the same ONc, but different electrical charges and formula masses.

Table 2 .
ONc, COD, and parameters of simple atom, molecules, and ions

Table 3
shows the calculated data for structural formulas of organic molecules.Isomers of HS-CH 2 -CH 2 -SH (ON S = −2) and H 3 C-S-S-CH 3 (ON S = −1) have different values of ONc and COD TOC

Table 3 .
ONc, COD, and parameters of structural formulas of organic molecules

Table 4 .
ONc, COD, and parameters of empirical formulas of organic matters

Table 4 .
Mathematical equations for counting total values of nO 2 , COD, TOC, and Table 4, any biomass, biowaste, or biomaterial can be represented by an empirical formula.Any complicated biomass is considered a single molecule or an organic matter.The calculation of the total values of nO 2 ,