Defining and balancing redox reaction requires both chemical knowledge and mathematical skills. The prevalent approach is to use the concept of oxidation number to determine the number of transferred electrons. However, the task of calculating oxidation numbers is often challenging. In this article, the H-atom method and O-atom method are developed for balancing redox equations. These two methods are based on the definition of redox reaction, which is the gain and loss of hydrogen or oxygen atoms. They complement current practices and provide an alternate path to balance redox equations. The advantage of these methods is that calculation of oxidation number is not required. Atoms are balanced instead. By following standard operating procedures, H-atom, O-atom, and H2O molecule act as artificial devices to balance both inorganic and organic equations in molecular forms. By using the H-atom and O-atom methods, the number of transferred electrons can be determined by the number of transferred H-atoms or O-atoms, which are demonstrated as electron-counting concepts for balancing redox reactions. In addition, the relationships among the number of transferred H-atom, the number of transferred O-atom, the number of transferred electrons, and the change of oxidation numbers are established.

Oxidation number (ON) is taught as an electron-counting concept for redox reactions in chemistry curriculum. The molecular formula method, the Lewis formula method, and the structural formula method have all been used to determine ON. However, the task of assigning ON still poses problems for some teachers and students. This paper explores a new method, the fragmentation method, which is a visual approach for counting the individual ON of any atom according to its structural formula. The critical step is to break the carbon-heteroatom bond into organic fragments and inorganic fragments. The individual ON of carbon atoms and heteroatoms can be determined by the bond cleavages in the organic and biological compounds. The mean ON of carbons can be calculated by the arithmetic mean of all individual ON of carbons in a molecule or molecular ion. The step-by-step operating procedures and examples are provided. When comparing corresponding molecules in organic conversions, the change of individual ON of atoms can be used as a tool for determining the number of transferred electrons. Furthermore, a reaction site can be identified by their changes of individual ON, chemical composition, and bond order in metabolic redox reactions.

The oxidation number and number of transferred electrons are two paramount parameters in the study of redox reactions. Their calculations are both important and challenging. The oxidation number of organic carbons is used in organic chemistry, biochemistry, and applied chemistry. Combustion reaction is a classical type of redox reaction, in which the oxygen molecule (O2) is the oxidizing agent. In this article, the integration of three sets of relations is explored by using the method of balancing organic combustion: (i) number of transferred electrons and oxidation number of organic carbons, (ii) mole of oxygen molecule and number of transferred electrons, and (iii) oxidative ratio, oxidation number of organic carbons, and number of transferred electrons. This method can also establish the relationships among the stoichiometric coefficients, mole of oxygen molecule, oxidative ratio, number of transferred electrons, and oxidation number of organic carbons. Furthermore, the oxidation number of organic carbons and the number of transferred electrons of a given organic compound can be determined by the derived mathematical equations.