Skip to content
BY-NC-ND 4.0 license Open Access Published online by De Gruyter January 13, 2022

Balancing redox equations through zero oxidation number method

Shengping Zheng ORCID logo


Many high school students and first-year undergraduate students find it difficult to balance redox reactions. A method using zero oxidation number to balance redox equations is presented herein. This method may shorten the balancing time and lessen the effort. It is a helpful complement to the traditional oxidation number method and half-reaction method.

For high school students and first year undergraduate students, balancing oxidation-reduction (redox) equations is a good training for understanding gain/loss of electrons and half-reaction in electrochemistry (Andraos, 2016; Herndon, 1997; Jensen, 2009). It could be challenging for balancing organic reactions such as exhaustive oxidations of organic compounds because it might involve different oxidation numbers for same type of atoms or a fractional oxidation number on average. As a special case of Ludwig’s unconventional oxidation number method (Ludwig, 1996), a strategy using zero oxidation number to balance some redox equations is presented herein.

When encountering a compound that is hard to assign oxidation number for all atoms in it, we can assign zero oxidation number for them in such redox-active compound in one side (reactant side or product side) of a reaction, in case it is easy to assign oxidation numbers for the molecules in the other side. We use exhaustive oxidation of glucose (C6H12O6) by KMnO4 in acidic conditions (Guo, 1997) to illustrate this balancing process. ↑ denotes the sum of increase of oxidation numbers and ↓ denotes the sum of decrease of oxidation numbers. Since a redox reaction requires the same amount of gain/loss of electrons, we first find out the increase/decrease of the oxidation numbers, which represents the number of loss/gain of electrons; then we use common multiple to balance the equation with minimum integral coefficients. It should be noted that assigning zero oxidation numbers is solely for the balancing purpose. It by no means suggests the real oxidation numbers for the compound(s) (Karen, 2015).

For the exhaustive oxidation of glucose, no matter what relative oxidation numbers are assigned to C, H, and O in glucose, the net increase of oxidation numbers is always the same, as shown below. Therefore, assigning zero oxidation number for balancing the equation is mathematically relevant. In general, assign C, H, and O the oxidation number a, b, and c respectively, then chemically, 6a + 12b + 6c = 0 (Eq. (1)). A simple calculation can prove that the total change of the oxidation number is not related to the relative oxidation number of C, H, and O in the exhaustive oxidation of glucose (Eq. (2)).

Herein we present several examples to show the convenience of this method in balancing redox reactions (see Supplementary Material for more examples and its scope of application). For example, oxidation of glycerine (C3H8O3) by KMnO4 in basic conditions (Kennedy, 1982) and combustion of an energetic salt (Li et al., 2016) based on furazan derivative and melamine (C9H10N18O4) can be balanced without assigning fractional oxidation numbers or solving algebraic equations.

This method can easily find the optimal ratio of two explosive mixtures for larger relative explosive power. For example, the optimal mixture of pentaerythrityl tetranitrate (PETN, C5H8N4O12) and glyceryl trinitrate (GTN, C3H5N3O9) must contain four moles of GTN for every mole of PETN (ten Hoor, 2003).

Unlike combustion (Yuen & Lau, 2021), many oxidations of organic compounds only involve a certain part of the compound. Simply letting the reacting part’s oxidation number be zero, we can still use this method to balance the equation. For example, propene oxidation by KMnO4 gave potassium acetate and carbonate as the oxidation products (Burrell, 1959). During the oxidation, one carbon was oxidized to carboxylate, and the other was transformed into carbonate.

For oxidation of nicotine by CrO3 (Thomas, 2014), only the atoms in the pyrrolidine ring got oxidized, so the redox could be balanced by assigning zero oxidation number to the side ring.

For a more complicated oxidation of a tetrahydroquinoline compound in basic solution (Klemm, 1996), assigning zero oxidation number to the reacting part will facilitate the balancing process. During the oxidation, four carbons in the tetrahydroquinoline ring got oxidized to carboxylate, one phenyl ring (six carbons) was oxidized to carbonate (see the circled part, the partial formula is C10H10).

Oxidation of a double complex salt, [Cr(H2NCONH2)6]4[Cr(CN)6]3, by potassium permanganate in acidic conditions (Stout, 1995) can be balanced readily using this method.

For some disproportionation reactions, assigning zero oxidation number for specific compound(s) on one side (but keep at least one compound regular oxidation number on that side, then balancing the equation from the other side) could simplify the balancing process. For example, letting oxidation number of P and I in P2I4 be zero and keeping H2O be normal would facilitate the balancing of the following disproportionation reaction (Giomini, Marrosu, & Cardinali, 1995; Kolb, 1979, 1981).

For the double redox reaction (Tóth, 1997) of ethanol and potassium iodide in water (an electrolysis reaction), letting oxidation number of C, H, and O in both ethanol and water be zero simplifies the balancing process. This way, balancing from the products side only involves the redox between K2CO3 and CHI3.

This method is also good for balancing redox equations involving Zintl phases (Bohme et al., 2007).

Application of this methodology in balancing organic redox equations was briefly covered in my undergraduate Organic Chemistry-II lecture. Before presenting this method, only a quarter of the class could balance ethanol oxidation by Na2Cr2O7 reaction; after explaining this method, about half of the class could balance oxidation of p-picoline to p-picolinic acid equation (for detail, see the Supplementary Material).

In summary, balancing complex redox equations using zero-oxidation number method may shorten the time and lessen the effort. It is a versatile method for balancing many redox reactions, especially disproportionation and double redox reactions. It is a helpful complement to the traditional oxidation number method and half-reaction method.

Corresponding author: Shengping Zheng, Department of Chemistry, Hunter College, New York, NY, USA; and Ph.D. Program in Chemistry, The Graduate Center of City University of New York, New York, NY, USA, E-mail:

Funding source: PSC-CUNY

Award Identifier / Grant number: 60835-00 48


This paper is dedicated to my high school chemistry teacher Mr. Fu Quan-an (Huanggang High School). We are grateful to the support from the PSC-CUNY award.

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

  2. Research funding: This work was funded by PSC-CUNY (60835-00 48).

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


Andraos, J. (2016). Using balancing chemical equations as a key starting point to create green chemistry exercises based on inorganic syntheses examples. Journal of Chemical Education, 93(7), 1330–1334. in Google Scholar

Bohme, B., Guloy, A., Tang, Z., Schnelle, W., Burkhardt, U., Baitinger, M., & Grin, Y. (2007). Oxidation of M4Si4 (M = Na, K) to clathrates by HCl or H2O, Journal of the American Chemical Society, 129(17), 5348–5349. in Google Scholar

Burrell, H. P. C. (1959). Balancing organic redox equations. Journal of Chemical Education, 36(2), 77. in Google Scholar

Giomini, C., Marrosu, C., & Cardinali, M. E. (1995). Double disproportionations. Journal of Chemical Education, 72(8), 716. in Google Scholar

Guo, C. (1997). A new inspection method for balancing redox equations. Journal of Chemical Education, 74(11), 1365–1366. in Google Scholar

Herndon, W. C. (1997). On balancing chemical equations: Past and present. Journal of Chemical Education, 74(11), 1359–1362. in Google Scholar

Jensen, W. B. (2009). Balancing redox equations. Journal of Chemical Education, 86(6), 681–682. in Google Scholar

Karen, P. (2015). Oxidation state, a long-standing issue! Angewandte Chemie International Edition, 2015(54), 4716–4726.10.1002/anie.201407561Search in Google Scholar

Kennedy, J. H. (1982). Balancing chemical equations with a calculator. Journal of Chemical Education, 59(6), 523. in Google Scholar

Klemm, L. H. (1996). A classification of organic redox reactions and writing balanced equations for them, with special attention to heteroatoms and heterocyclic compound. Journal of Heterocyclic Chemistry, 33, 569–574. in Google Scholar

Kolb, D. (1979). More on balancing redox equations. Journal of Chemical Education, 56(3), 181. in Google Scholar

Kolb, D. (1981). Balancing complex redox equations by inspection. Journal of Chemical Education, 58(8), 642. in Google Scholar

Li, X., Liu, X., Zhang, S., Wu, H., Wang, B., Yang, Q., … Gao, S. (2016). A low sensitivity energetic salt based on Furazan derivative and melamine: Synthesis, structure, density functional theory calculation, and physicochemical property. Journal of Chemical & Engineering Data, 61(1), 207–212. in Google Scholar

Ludwig, O. G. (1996). On balancing “redox challenges”. Journal of Chemical Education, 73(6), 507. in Google Scholar

Stout, R. (1995). Redox challenges: Good times for puzzle fanatics. Journal of Chemical Education, 72(12), 112. in Google Scholar

ten Hoor, M. J. (2003). The relative explosive power of some explosives. Journal of Chemical Education, 80(12), 1397–1400. in Google Scholar

Thomas, J. M. (2014). The concept, reality and utility of single-site heterogeneous catalysts (SSHCs). Physical Chemistry Chemical Physics, 16, 7647–7661. in Google Scholar

Tóth, Z. (1997). Double redox reactions. Journal of Chemical Education, 74(7), 744.10.1021/ed074p744.4Search in Google Scholar

Yuen, P. K., & Lau, C. M. D. (2021). Application of stoichiometric hydrogen atoms for balancing organic combustion reactions. Chemistry Teacher International, 3(3), 313–323. in Google Scholar

Supplementary Material

The online version of this article offers supplementary material (

Received: 2021-06-08
Accepted: 2021-12-30
Published Online: 2022-01-13

© 2022 Shengping Zheng, published by De Gruyter, Berlin/Boston

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