Balancing chemical equations half-reaction method

When a chemical equation is / V I balanced by the half-reaction method, the number of electrons that occur on both sides of the balanced equation (before canceling) is equal to the value of n. 

Balance the following redox chemical equation. Rewrite the equation in full ionic form, then derive the net ionic equation and balance by the half-reaction method. Give the final answer as it is shown below but with the balancing coefficients. 

A balanced chemical equation must have the same number and types of atoms on both sides of the equation, and the sum of the electric charges must be the same for the reactants as for the products of the reaction. If all the reactants and products are known, the equation for a redox reaction may be balanced by the half-reaction method. (Another method, called the oxidation-number method, may also be used, but for our purposes knowledge of one method is sufficient.)... 

A half-reaction is a chemical equation representing only the oxidation or only the reduction of an oxidation-reduction reaction. Redox equations, which must be balanced for both mass and charge, can be balanced using the half-reaction method... 

You could balance the chemical equation for the reaction of magnesium with aluminum nitrate by inspection, instead of writing half-reactions. However, many redox equations are difficult to balance by the inspection method. In general, you can balance the net ionic equation for a redox reaction by a process known as the half-reaction method. The preceding example of the reaction of magnesium with aluminum nitrate illustrates this method. Specific steps for following the half-reaction method are given below. 

Balance chemical equations for redox reactions by the half-reaction method, Toolbox 12.1 and Examples 12.1 and 12.2. 

In lesson C the student must know the definition of molarity and moles, the quantitative relationship of a chemical equation to determine quantities of reactants and products for reactions. Lesson D has the following objectives Assignment of oxidation numbers to elements according to a set of rules balancing oxidation-reduction equations by the half-reaction method and identification of oxidizing and reducing agents. 

In Chapter 7, we learned how to balance chemical equations by inspection. Some redox reactions can be balanced in this way. However, redox reactions occurring in aqueous solutions are usually difficult to balance by inspection and require a special procedure called the half-reaction method of balancing. In this procedure, the overall equation is broken down into two half-reactions one for oxidation and one for reduction. The half-reactions are balanced individually and then added together. For example, consider tiie redox reaction ... 

However, because a balanced chemical equation must have a charge balance as well as a mass balance, this equation is not balanced it has a total charge of +1 for the reactants and +2 for the products. Let us apply the half-reaction method for balancing this equation. 

Redox equations are often so complex that the inspection method (the fiddling-with-coefficients method) of balancing chemical equations doesn t work well with them. (See Chapter 7 for a discussion of this balancing method.) So chemists developed other methods of balancing redox equations, such as the ion electron (half-reaction) method. 

In many simple chemical equations, such as Equation 20.2, balancing the electrons is handled automatically —that is, we balance the equation without explicitly accounting for the transfer of electrons. Many redox equations are more complex than Equation 20.2, however, and cannot be balanced easily without taking into account the number of electrons lost and gained. In this section, we examine the method of half-reactions, a systematic procedure for balancing redox equations. 

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