Balancing Simple Redox Equations

To learn how to balance redox equations, let s revisit the practice of balancing equations. In Chapter 3, you learned to balance equations by counting the number of each kind of atom on each side of the equation arrow. For the purpose of balancing redox equations, it is also necessary to count electrons. For example, consider the net ionic equation for the reaction of chromium metal with nickel ion  

Although this equation has equal numbers of each type of atom on both sides, it is not balanced because there is a charge of +2 on the reactant side and a charge of -1-3 on the product side. In order to balance it, we can separate it into its half-reactions. 

When we add half-reactions to get the overall reaction, the electrons must cancel. Because any electrons lost by one species must be gained by the other, electrons may not appear in an overall chemical equation. Therefore, prior to adding these two half-reactions, we must multiply the chromium half-reaction by 2 

Then when we add the half-reactions, the electrons cancel and we get the balanced overall equation. 

This is known as the half-reaction method of balancing redox equations. We will use this method extensively when we examine more complex redox reactions in Chapter 19. 

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Some redox reactions have relatively simple stoichiometry and can be balanced by inspection. Others are much more complicated. Because redox reactions involve the transfer of electrons from one species to another, electrical charges must be considered explicitly when balancing complicated redox equations. 

Many simple redox equations may be balanced by inspection. The oxidation-number method can be used to balance more difficult reactions. 

Many simple redox equations can be balanced readily by inspection, or by trial and error ... 

J 3 Write and balance chemical equations for simple redox reactions (Self-Test K.4). 

We have seen how analytical calculations in titrimetric analysis involve stoichiometry (Sections 4.5 and 4.6). We know that a balanced chemical equation is needed for basic stoichiometry. With redox reactions, balancing equations by inspection can be quite challenging, if not impossible. Thus, several special schemes have been derived for balancing redox equations. The ion-electron method for balancing redox equations takes into account the electrons that are transferred, since these must also be balanced. That is, the electrons given up must be equal to the electrons taken on. A review of the ion-electron method of balancing equations will therefore present a simple means of balancing redox equations. 

So that you can work out titrations involving redox reactions, you will find it necessary to balance redox equations, and while it is easy for simple reactions such as those above, more complex redox reactions, such as the one below, require more thought and work. 

In many simple chemical equations, such as Equation 20.2, balancing the electrons is handled automatically in the sense that we can balance the equation without explicitly considering the transfer of electrons. Many redox equations are more complex than Equation 20.2, however, and caimot be balanced easily without taking into account the number of electrons lost and gained. In this section we examine the method of halfreactions, a systematic procedure for balancing redox equations. 

In any balanced redox equation, the total increase in oxidation numbers must equal the total decrease in oxidation numbers. Our procedures for balancing redox equations are constructed to make sure this equivalence results. Many redox equations can be balanced by simple inspection, but you should master the systematic method presented here so that you can use it to balance difficult equations. 

Equations for simple redox reactions can be balanced by inspection. Most redox equations, however, require more systematic methods. The equation-balancing process requires the use of oxidation numbers. In a balanced equation, both charge and mass are conserved. Although oxidation and reduction half-reactions occur together, their reaction equations are balanced separately and then combined to give the baianced redox-reaction equation. 

To balance equations for redox reactions in a basic solution, a step or two must be added to the procedure used in Example 5-6. In basic solution, OH , not H, must appear in the final balanced equation. (Recall that, in basic solutions, OH ions are present in excess.) Because both OH and H2O contain H and O atoms, at times it is hard to decide on which side of the halfequations to put each one. One simple approach is to treat the reaction as though it were occurring in an acidic solution, and balance it as in Example 5-6. Then, add to each side of the overall redox equation a number of OH ions equal to the number of H ions. Where H and OH appear on the same side of the equation, combine them to produce H2O molecules. If H2O now appears on both sides of the equation, subtract the same number of H2O molecules from each side, leaving a remainder of H2O on just one side. This method is illustrated in Example 5-7. For ready reference, the procedure is summarized in Table 5.6. 

We need to be able to write balanced chemical equations to describe redox reactions. It might seem that this task ought to he simple. However, some redox reactions can be tricky to balance, and special techniques, which we describe in Sections 12.1 and 12.2, have been developed to simplify the procedure. 

This equation is rather simple and requires no procedure as described. However, those redox reactions that cannot be directly overseen will certainly require a well-defined stepwise procedure to establish stoichiometry and a corresponding mass balance. 

We conventionally cite the oxidized form first within each symbol, which is why the general form is o,r> so pb4+ Pb + is correct, but 2+ 4+ is not. Some people experience difficulty in deciding which redox state is oxidized and which is the reduced. A simple way to differentiate between them is to write the balanced redox reaction as a reduction. For example, consider the oxidation reaction in Equation (7.1). On rewriting this as a reduction, i.e. Al3+(aq) + 3e = A Em, the oxidized redox form will automatically precede the reduced form as we read the equation from left to right, i.e. are written in the correct order. For example, o,r for the couple in Equation (7.1) is Ai3+,ai-... 

Oxidation-reduction reactions are often complicated, which means that it can be difficult to balance their equations by simple inspection. Two methods for balancing redox reactions will be considered here (1) the oxidation states method and (2) the half-reaction method. 

Depending on the nature of the class, the instructor may wish to spend more time with the basics, such as the mass balance concept, chemical equilibria, and simple transport scenarios more advanced material, such as transient well dynamics, superposition, temperature dependencies, activity coefficients, redox energetics, and Monod kinetics, can be skipped. Similarly, by omitting Chapter 4, an instructor can use the text for a water-only course. In the case of a more advanced class, the instructor is encouraged to expand on the material suggested additions include more rigorous derivation of the transport equations, discussions of chemical reaction mechanisms, introduction of quantitative models for atmospheric chemical transformations, use of computer software for more complex groundwater transport simulations, and inclusion of case studies and additional exercises. References are provided... 

Most simple reactions can be balanced in this fashion. But one class of reactions is so complex that this method doesn t work well when applied to them. They re redox reactions. A special method is used for balancing these equations, and I show it to you in Chapter 9. 

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