Redox reactions half-equations

Plan Because this is a redox reaction, the equation can be balanced by the method of half-reactions discussed in Section 20.2. Thus, we begin with two half-reactions, one involving the NH2OH and N2 and the other involving Cu and Cu. 

Redox reactions, such as that shown in equation 6.22, can be divided into separate half-reactions that individually describe the oxidation and the reduction processes. 

Because E° is a positive quantity, +0.165 V, a redox reaction should occur. The balanced half-equations are... 

Only one method for balancing redox reactions, the half-equation method introduced in Chapter 4. 

We consider oxidation first. To show the removal of electrons from a species that is being oxidized in a redox reaction, we write the chemical equation for an oxidation half-reaction. A half-reaction is the oxidation or reduction part of the reaction considered alone. For example, one battery that Volta built used silver and zinc plates to carry out the reaction... 

Balancing the chemical equation for a redox reaction by inspection can be a real challenge, especially for one taking place in aqueous solution, when water may participate and we must include HzO and either H+ or OH. In such cases, it is easier to simplify the equation by separating it into its reduction and oxidation half-reactions, balance the half-reactions separately, and then add them together to obtain the balanced equation for the overall reaction. When adding the equations for half-reactions, we match the number of electrons released by oxidation with the number used in reduction, because electrons are neither created nor destroyed in chemical reactions. The procedure is outlined in Toolbox 12.1 and illustrated in Examples 12.1 and 12.2. 

The general procedure for balancing the chemical equation for a redox reaction is first to balance the half-reactions separately. 

The chemical equation for a reduction half-reaction is added to the equation for an oxidation half-reaction to form the balanced chemical equation for the overall redox reaction. 

Redox reactions are more complicated than precipitation or proton transfer reactions because the electrons transferred in redox chemishy do not appear in the balanced chemical equation. Instead, they are hidden among the starting materials and products. However, we can keep track of electrons by writing two half-reactions that describe the oxidation and the reduction separately. A half-reaction is a balanced chemical equation that includes electrons and describes either the oxidation or reduction but not both. Thus, a half-reaction describes half of a redox reaction. Here are the half-reactions for the redox reaction of magnesium and hydronium ions ... 

The key to balancing complicated redox equations is to balance electrons as well as atoms. Because electrons do not appear in chemical formulas or balanced net reactions, however, the number of electrons transferred in a redox reaction often is not obvious. To balance complicated redox reactions, therefore, we need a procedure that shows the electrons involved in the oxidation and the reduction. One such procedure separates redox reactions into two parts, an oxidation and a reduction. Each part is a half-reaction that describes half of the overall redox process. 

The first step In balancing a redox reaction is to divide the unbalanced equation into half-reactions. Identify the participants in each half-reaction by noting that each half-reaction must be balanced. That Is, each element In each half-reaction must be conserved. Consequently, any element that appears as a reactant In a half-reaction must also appear among the products. Hydrogen and oxygen frequently appear in both half-reactions, but other elements usually appear In just one of the half-reactions. Water, hydronium ions, and hydroxide ions often play roles In the overall stoichiometry of redox reactions occurring in aqueous solution. Chemists frequently omit these species in preliminary descriptions of such redox reactions. 

Remember that the number of electrons transferred is not explicitly stated in a net redox equation. This means that any overall redox reaction must be broken down into its balanced half-reactions to determine n, the ratio between the number of electrons transferred and the stoichiometric coefficients for the chemical reagents. 

The coefficients of any balanced redox equation describe the stoichiometric ratios between chemical species, just as for other balanced chemical equations. Additionally, in redox reactions we can relate moles of chemical change to moles of electrons. Because electrons always cancel in a balanced redox equation, however, we need to look at half-reactions to determine the stoichiometric coefficients for the electrons. A balanced half-reaction provides the stoichiometric coefficients needed to compute the number of moles of electrons transferred for every mole of reagent. 

Most of the redox reactions can be expressed using two half-reactions as described for zinc and copper. However, for the complete reaction, the number of electrons lost must be equal to the number gained. This requirement sometimes needs adjustment for instance, in case of aluminum metal taking out silver from a solution of silver nitrate, the following equations are set out ... 

This reaction is a redox reaction, and so we will define the number of equivalents of H2S04 in terms of the number of moles of electrons with which it reacts. Since no electrons appear explicitly in an overall equation, we will write the half-reaction in which the H2S04 appears ... 

The net ionic equation is obtained by balancing the redox reaction. First we determine the half-reactions ... 

The electrons lost by the zinc atoms are the same electrons as those gained by the copper (II) ions. Addition of the two ionic half-equations gives the overall redox reaction ... 

If the above half-equation is combined with that for the oxidation of iron (II) to iron (III) ions, Fe2+half-equations, the second is multiplied by 6, giving an overall equation for the redox reaction as ... 

Reactions involving the creation, destruction, and elimination of defects can appear mysterious. In such cases it is useful to break the reaction down into hypothetical steps that can be represented by partial equations, rather akin to the half-reactions used to simplify redox reactions in chemistry. The complete defect formation equation is found by adding the partial equations together. The mles described above can be interpreted more flexibly in these partial equations but must be rigorously obeyed in the final equation. Finally, it is necessary to mention that a defect formation equation can often be written in terms of just structural (i.e., ionic) defects such as interstitials and vacancies or in terms of just electronic defects, electrons, and holes. Which of these alternatives is preferred will depend upon the physical properties of the solid. An insulator such as MgO is likely to utilize structural defects to compensate for the changes taking place, whereas a semiconducting transition-metal oxide with several easily accessible valence states is likely to prefer electronic compensation. 

Since these two equations represent redox reactions, we have effectively separated a cell into its constituent half-cells, each of which is a single redox couple. 

When using the Nernst equation on a cell reaction in which the overall reaction is not supplied, only the half-reactions and concentrations, there are two equivalent methods to work the problem. The first way is to write the overall redox reaction based upon E° values and then apply the Nernst equation. If the Ecell turns out to be negative, it indicates that the reaction is not a spontaneous one (an electrolytic cell) or that the reaction is written backwards if it is supposed to be a galvanic cell. If it is supposed to be a galvanic cell, then all you need to... 

When using the Nernst equation on a cell reaction in which the overall reaction is not supplied, only the half-reactions and concentrations, there are two equivalent methods to work the problem. The first way is to write the overall redox reaction based upon E° values,... 

To monitor the transfer of electrons in a redox reaction, you can represent the oxidation and reduction separately. A half-reaction is a balanced equation that shows the number of electrons involved in either oxidation or reduction. Because a redox reaction involves both oxidation and reduction, two half-reactions are needed to represent a redox reaction. One half-reaction shows oxidation, and the other half-reaction shows reduction. 

In section 10.1, you learned to divide the balanced equations for some redox reactions into separate oxidation and reduction half-reactions. You will now use the reverse approach, and discover how to write a balanced equation by combining two half-reactions. To do this, you must first understand how to write a wide range of half-reactions. 

As shown above, you can use half-reactions to write balanced net ionic equations for redox reactions. In doing so, you use the fact that no electrons are created or destroyed in a redox reaction. Electrons are transferred from one reactant (the reducing agent) to another (the oxidizing agent). 

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. 

This is a redox reaction. Use the half-reaction method to balance the equation. 

In this section, you learned the half-reaction method for balancing equations for redox reactions. You investigated the redox reactions of metals with acids, and the combustion of two hydrocarbons. After applying the half-reaction method in the following review problems, you will learn a different method in section 10.4. This method will make greater use of oxidation numbers. 

In section 10.2, you learned that a redox reaction involves changes in oxidation numbers. If an element undergoes oxidation, its oxidation number increases. If an element undergoes reduction, its oxidation number decreases. When balancing equations by the half-reaction method in section 10.3, you sometimes used oxidation numbers to determine the reactant(s) and product(s) in each half-reaction. 

The zinc anode and copper cathode of a Daniell cell are both metals, and can act as electrical conductors. However, some redox reactions involve substances that cannot act as electrodes, such as gases or dissolved electrolytes. Galvanic cells that involve such redox reactions use inert electrodes. An inert electrode is an electrode made from a material that is neither a reactant nor a product of the cell reaction. Figure 11.6 shows a cell that contains one inert electrode. The chemical equation, net ionic equation, and half-reactions for this cell are given below. 

The following redox reactions occur in acidic solution. Balance the equations using the half-reaction method. 

Equations 7.2 and 7.3 are examples of electrochemical half-cell reactions. Since free electrons are not found in nature, half-cell reactions always occur in pairs such that the electrons generated by one are consumed by the other. The half-cell reaction that releases electrons is referred to as an oxidation reaction. The half-cell reaction that consumes electrons is referred to as a reduction reaction. For the redox reaction shown in Eq. 7.1, the oxidation and reduction half-cell reactions are given by Eqs. 7.2 and 7.3,... 

---