Startseite Exploring the relationships among stoichiometric coefficients, number of transferred electrons, mean oxidation number of carbons, and oxidative ratio in organic combustion reactions
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Exploring the relationships among stoichiometric coefficients, number of transferred electrons, mean oxidation number of carbons, and oxidative ratio in organic combustion reactions

  • Pong Kau Yuen ORCID logo EMAIL logo und Cheng Man Diana Lau
Veröffentlicht/Copyright: 28. Dezember 2021
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Abstract

Combustion reactions, stoichiometry, and redox reactions are some of the basic contents in chemistry curriculum. Although the counting of transferred electrons is critical in redox reactions, assigning mean oxidation number of organic carbons (ONc) is not always easy. Even though the relationship between the oxidative ratio (OR) and ONc is known, the relationship between the number of transferred electrons (Te−) and OR has not been thoroughly studied. The H-atom method has already been developed to balance and deduct organic combustion reactions. It can be used further to help establish the relationships among the stoichiometric coefficients (SC), the number of transferred hydrogens (TH), and Te−. This article uses the procedures of the H-atom method for balancing and deducting, and the known relationships among SC, TH, and Te− for exploring the relationships among SC, Te−, ONc, and OR in organic combustion reactions. By integrating three sets of relationships: (i) SC and Te−, (ii) Te− and ON, and (iii) SC and OR, the interconversions among SC, Te−, ONc, and OR can be mathematically formulated. Furthermore, Te−, ONc, and OR can be assigned by SC and the general molecular formula of CxHyOzXw.

Keywords: mean oxidation number of organic carbons; molecular formula; number of transferred electrons; organic combustion reaction; oxidative ratio; stoichiometric coefficients

Introduction

Combustion reactions, stoichiometry, and redox reactions are some of the basic contents in general chemistry curriculum (Chang & Goldsby, 2013; Tro, 2014). Redox reactions can be defined in four different models: electron transfer, H-atom transfer, O-atom transfer, and oxidation number (IUPAC, 2019). Oxidation number is an electron-counting concept (IUPAC, 2019; Karen, McArdle & Takats, 2014, 2016) for balancing redox reactions. It is counted by using chemical formula methods (Bentley, Franzen & Chasteen, 2002; Halkides, 2000; Jurowski, Krzeczkowska & Jurowska, 2015; Kauffman, 1986). Although counting oxidation number is critical for balancing organic redox reactions, assigning oxidation number of organic carbons is not always easy.

The mean oxidation number of organic carbons (or the mean oxidation state of organic carbons; ONc) is used as a redox indicator in the fields of ecosystem (Masiello, Gallagher, Randerson, Deco & Chadwick, 2008), environmental chemistry (Kroll et al., 2011), geochemistry (Dick & Shock, 2011), and water biochemical treatment (Li et al., 2018).

Oxidative ratio (OR) is a reaction-based parameter which is defined by the ratio of the number of moles of O2 to one mole of CO2 in a chemical reaction (Hockaday et al., 2015; Worrall, Clay, Masiello & Mynheer, 2013). The relationship between OR and ONc has already been known (Hockaday et al., 2015; Masiello et al., 2008; Worrall, Clay, Masiello & Mynheer, 2013). OR is a macroscopic concept which can be determined by the stoichiometric coefficients (SC) of an overall balanced combustion equation. ONc is a microscopic concept which can be used for counting the number of transferred electrons (Te−). Although an organic combustion reaction is an electron transfer reaction, the relationships among Te−, ONc, and OR have not been revealed. The H-atom method (Yuen & Lau, 2021) has been developed to balance and deduct organic combustion reactions, and has also been used to establish the relationships among SC, the number of transferred hydrogens (TH), and Te− in organic combustion reactions. This article applies the procedures of the H-atom method for balancing and deducting, and the known relationships among SC, TH and Te− for exploring the relationships among the SC, Te−, ONc, and OR in organic combustion reactions. An organic compound containing the general chemical formula of CxHyOzXw is chosen as an exemplar.

By integrating three sets of relationships: (i) SC and Te−, (ii) Te− and ONc in a half combustion reaction, and (iii) SC and OR in an overall combustion reaction, the interconversions among these four parameters can be demonstrated by using the H-atom method.

Assigning Te− and ONc in a half combustion reaction

By using the organic compound, CCl3COOH, which contains halogen and oxygen atoms, as an example, the H-atom method shows how Te− is counted. Then ONc is assigned by the derived mathematical formula.

Example 1:

Balancing a half combustion reaction of CCl3COOH.

C 2 HO 2 Cl 3 → CO 2 + HCl
C 2 HO 2 Cl 3 → 2 CO 2 + 3 HCl
C 2 HO 2 Cl 3 + 2 H + 2 O → 2 CO 2 + 3 HCl
C 2 HO 2 Cl 3 + 2 H + 2 O + 2 H → 2 CO 2 + 3 HCl + 2 H
C 2 HO 2 Cl 3 + 2 H 2 O → 2 CO 2 + 3 HCl + 2 H

The above balanced half reaction shows that there are two carbon atoms (nc = 2) involved in the oxidation reaction. That means there is either a loss of two H atoms (TH = +2) or a loss of two protons and two electrons (2H → 2H+ + 2e−; Te− = +2).

The relationship between the change of mean oxidation number of organic carbons (ΔONc) and Te− is established in a half redox reaction (Yuen & Lau, 2022). Then by deducting the mathematical equations, ONc can be assigned by Te−.

Te − = nc  Δ ONc

Δ ONc = ONc ( CO 2 ) − ONc ( C 2 HO 2 Cl 3 )

ONc ( C 2 HO 2 Cl 3 ) = ONc ( CO 2 ) − Te − nc

ONc CO 2 = + 4 ; Te − = + 2 ;  nc = 2

ONc ( C 2 HO 2 Cl 3 ) = ONc ( CO 2 ) − Te − nc = 4 − ( + 2 ) 2 = + 3

The calculated ONc of C2HO2Cl3 is equal to +3.

Counting OR in an overall combustion reaction

The H-atom method can balance an overall organic combustion reaction and consequently count OR.

Example 2:

Balancing an overall organic combustion reaction of “ C 2 HO 2 Cl 3 + O 2 → CO 2 + H 2 O + HCl ” .

Step 1. C 2 HO 2 Cl 3 → CO 2 + HCl
O 2 → H 2 O
Step 2. C 2 HO 2 Cl 3 + 2 H 2 O → 2 CO 2 + 3 HCl + 2 H (from Example 1)
O 2 + 4 H → 2 H 2 O
Step 3. ( C 2 HO 2 Cl 3 + 2 H 2 O → 2 CO 2 + 3 HCl + 2 H ) × 2
( O 2 + 4 H → 2 H 2 O ) × 1
Step 4. 2 C 2 HO 2 Cl 3 + 4 H 2 O + O 2 + 4 H → 4 CO 2 + 6 HCl + 4 H + 2 H 2 O
Step 5. 2 C 2 HO 2 Cl 3 + 2 H 2 O + O 2 → 4 CO 2 + 6 HCl

According to the above reaction, the OR which goes through the combustion of C2HO2Cl3 can be counted by the molar ratio of oxygen gas to carbon dioxide.

nO 2 = 1 ;  nCO 2 = 4 O R = nO 2 nCO 2 = 1 4

Deducting relationship between SC and Te− in a half combustion reaction

To deduct the stoichiometric relationship between SC and Te− in a half oxidation combustion reaction, a general molecular formula of CxHyOzXw is chosen to demonstrate the operating procedures.

Example 3:

Given CxHyOzXw → CO2 + HX.

C x H y O z X w + ( 2 x − z ) O → xCO 2 + wHX + ( y − w ) H
C x H y O z X w + ( 2 x − z ) O + 2 ( 2 x − z ) H → xCO 2 + wHX + ( y − w ) H + 2 ( 2 x − z ) H
C x H y O z X w + ( 2 x − z ) H 2 O → xCO 2 + wHX + ( 4 x + y − 2 z − w ) H
C x H y O z X w + ( 2 x − z ) H 2 O → xCO 2 + wHX + ( 4 x + y − 2 z − w ) H
( 4 x + y − 2 z − w ) H → ( 4 x + y − 2 z − w ) H + + ( 4 x + y − 2 z − w ) e −
C x H y O z X w + ( 2 x − z ) H 2 O → xCO 2 + wHX + ( 4 x + y − 2 z − w ) H + + ( 4 x + y − 2 z − w ) e −

Regarding CxHyOzXw, the x number of carbons (nc = x) has participated. TH is equal to Te− (TH = Te−) and Te− are lost (Te− > 0) in the half oxidation reaction.

TH = 4 x + y − 2 z − w

Te − = 4 x + y − 2 z − w

Deriving relationships among SC, Te−, and ONc

According to the relationship between SC and Te−, to complement the mathematical equation of Te− = nc ΔONc, the relationship between SC and ONc of CxHyOzXw is shown. The triangular relationships among SC, Te−, and ONc are established in a half redox reaction and exhibited in Figure 1.

Te − = nc  Δ ONc

Δ O N c = Te − nc

Δ ONc = ONc ( product ) − ONc ( reactant )

Figure 1: Triangular relationships among SC, Te−, and ONc in a half redox reaction.
Figure 1:

Triangular relationships among SC, Te−, and ONc in a half redox reaction.

For the balanced half oxidation reaction:

C x H y O z X w + ( 2 x − z ) H 2 O → xCO 2 + wHX + ( 4 x + y − 2 z − w ) H

Te − = ( 4 x + y − 2 z − w ) ;  nc = x

Δ O N c = Te − nc

Δ O N c = 4 x + y − 2 z − w x

Δ ONc = ONc ( product ) − ONc ( reactant )

Δ ONc = ONc ( CO 2 ) − ONc ( C x H y O z X w )

ONc ( C x H y O z X w ) = ONc ( CO 2 ) − ΔONc

ONc ( C x H y O z X w ) = ONc ( CO 2 ) − Te − nc = 4 − Te − x = 4 − 4 x + y − 2 z − w x = − y + 2 z + w x

Deriving relationships among SC, OR, and ONc

The stoichiometric relationship between SC and ONc of CxHyOzXw is deducted by balancing two half reactions. Then the stoichiometric relationship between SC and OR is derived by the balancing overall combustion.

nO 2 = 4 x + y − 2 z − w 4 ; nCO 2 = nc = x

OR = nO 2 nCO 2 = 4 x + y − 2 z − w 4 x

Example 4:

Given CxHyOzXw + O2 → CO2 + H2O + HX.

Step 1. C x H y O z X w → CO 2 + HX
O 2 → H 2 O
Step 2. C x H y O z X w + ( 2 x − z ) H 2 O → xCO 2 + wHX + ( 4 x + y − 2 z − w ) H (from Example 3)
O 2 + 4 H → 2 H 2 O
Step 3. ( C x H y O z X w + ( 2 x − z ) H 2 O → xCO 2 + wHX + ( 4 x + y − 2 z − w ) H ) × 4
( O 2 + 4 H → 2 H 2 O ) × ( 4 x + y − 2 z − w )
Step 4. 4 C x H y O z X w + 4 ( 2 x − z ) H 2 O + ( 4 x + y − 2 z − w ) O 2 + 4 ( 4 x + y − 2 z − w ) H
→ 4 xCO 2 + 4 wHX + 4 ( 4 x + y − 2 z − w ) H + 2 ( 4 x + y − 2 z − w ) H 2 O
Step 5. 4 C x H y O z X w + ( 4 x + y − 2 z − w ) O 2 → 4 xCO 2 + 4 wHX + 2 ( y − w ) H 2 O
C x H y O z X w + 4 x + y − 2 z − w 4 O 2 → xCO 2 + y − w 2 H 2 O + wHX

Based on the relationship of ONc = - y  +  2 z  +  w x which is derived from the balanced half reactions and OR = 4 x  +  y  −  2 z  −  w 4 x which is derived from the balanced overall reaction, the relationship of OR = 1 − O N c 4 can be derived correspondingly. The relationships among SC, OR, and ONc for CxHyOzXw are shown in Figure 2.

Figure 2: Triangular relationships among SC, OR, and ONc in an overall redox reaction.
Figure 2:

Triangular relationships among SC, OR, and ONc in an overall redox reaction.

From molecular formula to counting Te−, ONc, and OR

Based on the general molecular formula of CxHyOzXw, the relationships among SC, Te−, and ONc in a half reaction and the relationships among SC, OR, and ONc in an overall reaction are integrated. Then the established mathematical formulas and triangular relationships are shown in Figure 3.

Figure 3: From molecular formula to counting Te−, ONc, and OR.
Figure 3:

From molecular formula to counting Te−, ONc, and OR.

Te−, ONc, and OR can be assigned by SC and the given chemical formula of CxHyOzXw. An example is shown below.

Example 5:

Determining Te−, ONc, and OR of CCl3COOH in a combustion reaction.

When comparing CCl3COOH (C2HO2Cl3) to CxHyOzXw, x = 2; y = 1; z = 2; w = 3

Te − = 4 x + y − 2 z − w = 4 ( 2 ) + ( 1 ) − 2 ( 2 ) − ( 3 ) = + 2 ONc = − y + 2 z + w x = − ( 1 ) + 2 ( 2 ) + ( 3 ) 2 = + 3 OR = 4 x + y − 2 z − w 4 x = 4 ( 2 ) + ( 1 ) − 2 ( 2 ) − ( 3 ) 4 ( 2 ) = 1 4

To determine Te−, ONc, and OR of the CCl3COOH compound, the H-atom balancing equations method has been applied in Example 1 and Example 2, and the molecular formula method has been applied in Example 5. In comparison, Te−, ONc, and OR can be counted by a given molecular formula effectively in Example 5.

Interconversions among SC, Te−, ONc, and OR

By combining the half reaction to an overall organic combustion reaction, the relationships among SC, Te−, ONc, and OR can be derived accordingly. The interconversions are summarized in Table 1 and graphically demonstrated in Figure 4.

Table 1:

Mathematical relationships among Te−, ONc, and OR in organic combustion reactions.

Te− and ONc Te− and OR ONc and OR
nc = x nCO2 = nc = x OR = Te − 4 x
ONc = 4 − Te − nc nO 2 = Te − 4 ONc = 4 − Te − x
ONc = 4 − Te − x OR = nO 2 nCO 2 ONc 4 = 1 − Te − 4 x
Te− = x (4 − ONc) OR = Te − 4 x ONc = 4 (1 − OR)
Te− = 4x (OR) OR = 1 − ONc 4
Figure 4: Interconversions among SC, Te−, ONc, and OR.
Figure 4:

Interconversions among SC, Te−, ONc, and OR.

Based on the given molecular formula of CxHyOzXw, the OR can be calculated by using SC, Te−, or ONc. Examples are shown below.

Example 6:

Determining Te−, ONc, and OR of C6H5COCl in a combustion reaction.

When comparing C6H5COCl (C7H5OCl) to CxHyOzXw, x = 7; y = 5; z = 1; w = 1

By using x, y, z, w → Te − = 4 x + y − 2 z − w = 4 ( 7 ) + ( 5 ) − 2 ( 1 ) − ( 1 ) = + 30 ONc = − y + 2 z + w x = − ( 5 ) + 2 ( 1 ) + ( 1 ) 7 = − 2 7 OR = 4 x + y − 2 z − w 4 x = 4 ( 7 ) + ( 5 ) − 2 ( 1 ) − ( 1 ) 4 ( 7 ) = 15 14
By using Te− → ONc = 4 − Te − x = 4 − ( + 30 ) 7 = − 2 7 OR = Te − 4 x = ( + 30 ) 4 ( 7 ) = 15 14
By using ONc → OR = 1 − ONc 4 = 1 − ( − 2 7 × 1 4 ) = 15 14

Example 7:

Determining Te−, ONc, and OR of CH3COOH in the combustion reaction.

When comparing CH3COOH (C2H4O2) to CxHyOzXw, x = 2; y = 4; z = 2; w = 0

By using x, y, z, w → Te − = 4 x + y − 2 z − w = 4 ( 2 ) + ( 4 ) − 2 ( 2 ) − ( 0 ) = + 8 ONc = − y + 2 z + w x = − ( 4 ) + 2 ( 2 ) + ( 0 ) 2 = 0 OR = 4 x + y − 2 z − w 4 x = 4 ( 2 ) + ( 4 ) − 2 ( 2 ) − ( 0 ) 4 ( 2 ) = 1
By using Te− → ONc = 4 − Te − x = 4 − ( + 8 ) 2 = 0 OR = Te − 4 x = ( + 8 ) 4 ( 2 ) = 1
By using ONc → OR = 1 − ONc 4 = 1 − 0 = 1

Conclusions

In this article, a reaction-based approach is explored to establish the relationships among SC, Te−, ONc, and OR in organic combustion reactions by using the H-atom method. Firstly, the triangular relationships among SC, Te−, and ONc are derived in the half organic combustion reaction. Secondly, the relationships among SC, OR, and ONc are revealed in the overall organic combustion reaction. Then the interconversions among SC, ONc, OR, and Te− are established and mathematically formulated. Furthermore, Te−, ONc, and OR are counted by using SC as well as the general molecular formula of CxHyOzXw.

Corresponding author: Pong Kau Yuen, Department of Chemistry, Texas Southern University, Houston, TX 77004 USA, E-mail:

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-07-27
Accepted: 2021-12-11
Published Online: 2021-12-28

© 2021 Pong Kau Yuen and Cheng Man Diana Lau, published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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https://doi.org/10.1515/cti-2021-0020
Schlagwörter für diesen Artikel
mean oxidation number of organic carbons; molecular formula; number of transferred electrons; organic combustion reaction; oxidative ratio; stoichiometric coefficients
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Artikel in diesem Heft

  1. Frontmatter
  2. Research Article
  3. New approach for assigning mean oxidation number of carbons to organonitrogen and organosulfur compounds
  4. Good Practice Report
  5. Measuring the mass of an electron: an undergraduate laboratory experiment with high resolution mass spectrometry
  6. Research Articles
  7. A new spin on electrochemistry in the undergraduate lab
  8. Exploring the relationships among stoichiometric coefficients, number of transferred electrons, mean oxidation number of carbons, and oxidative ratio in organic combustion reactions
  9. A simple theoretical, quantitative approach to help understand the titration of weak acids and bases
  10. Good Practice Report
  11. Balancing redox equations through zero oxidation number method
  12. Research Articles
  13. Simple and easy way for students to develop a dynamic model on Excel sheet
  14. Development and validation of customized pedagogical kits for high-school chemistry teaching and learning: the redox reaction example
  15. Good Practice Report
  16. Leaded or unleaded? Homemade microscale tin electroplating
  17. Research Article
  18. Incorporating research literature and chemistry textbooks in 5E instructional model to reveal ambiguous oxidation state formalism of CuS for pre-service science teachers
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