Electron-transfer equations, balancing

We can make the following general statement. To balance any electron-transfer equation, you must subtract the reducing half-reaction equation from the oxidizing half-reaction equation after the two equations have first been written to show the same number of electrons. Simplify the final equation, if needed. 

The oxidation half-reaction involves one electron, and the reduction half-reaction involves five electrons. Now we balance the electron transfer and then add the two equations term by term. This gives the balanced net ionic equation. 

The N03 /N0 reduction half-reaction has the more positive value, so we write it first and write the Sn +/Sn + half-reaction as an oxidation. We balance the electron transfer and add the two half-reactions to obtain the equation for the spontaneous reaction. Then we add the half-reaction potentials to obtain the overall cell potential. 

A few redox reactions have more than one oxidation half-reaction or more than one reduction half-reaction. Balancing the equations for these reactions is more complicated. However, the multiple half-reactions are often stoichiometricaUy hnked. Maintain the correct ratio of the elements and balance the electron transfer by multiplying them both by the same integer. Balance the following net ionic equation for a reaction in basic solution. OH" or HjO (but not H" ") may be added as necessary. 

First we find the appropriate half-reactions. As the equation is written, Cu is oxidized to Cu, so we write the Cu /Cu couple as an oxidation and reverse the sign of its tabulated value. We balance the electron transfer and then add the half-reactions. The resulting value can be used to calculate the equilibrium constant, K, for the reaction as written. 

K.23 A mixture of 5.00 g of Cr(N03)2 and 6.00 g of C11SO4 is dissolved in sufficient water to make 250.0 mL of solution, where the cations react. In the reaction, copper metal is formed and each chromium ion loses one electron, (a) Write the net ionic equation, (b) What is the number of electrons transferred in the balanced equation written with the smallest whole-... 

A note on good practice The value of n depends on the balanced equation. Check to ensure that n matches the number of moles of electrons transferred in the balanced equation. 

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. 

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. 

The theory on the level of the electrode and on the electrochemical cell is sufficiently advanced [4-7]. In this connection, it is necessary to mention the works of J.Newman and R.White s group [8-12], In the majority of publications, the macroscopical approach is used. The authors take into account the transport process and material balance within the system in a proper way. The analysis of the flows in the porous matrix or in the cell takes generally into consideration the diffusion, migration and convection processes. While computing transport processes in the concentrated electrolytes the Stefan-Maxwell equations are used. To calculate electron transfer in a solid phase the Ohm s law in its differential form is used. The electrochemical transformations within the electrodes are described by the Batler-Volmer equation. The internal surface of the electrode, where electrochemical process runs, is frequently presented as a certain function of the porosity or as a certain state of the reagents transformation. To describe this function, various modeling or empirical equations are offered, and they... 

The formula you need for this problem is AG° = -ncSSE°. The Faraday constant, <3, is equal to 9.65 x 104 joules volt-1 mole n is the number of electrons transferred between oxidizing and reducing agents in a balanced redox equation. 

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. 

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. 

A redox reaction involves the transfer of electrons between reactants. A reactant that loses electrons is oxidized and acts as a reducing agent. A reactant that gains electrons is reduced and acts as an oxidizing agent. Redox reactions can be represented by balanced equations. 

For a general formulation of the Zintl-Klemm concept, consider an intermetallic AmX phase, where A is the more electropositive element, t3 pically an alkali or an alkaline earth metal. Both A and X, viewed as individual atoms, are assumed to follow the octet rule leading to transfer of electrons from A to X, i.e., A AF, X —> X , so that mp = nq. The anionic unit X arising from this electron transfer is considered to be a pseudoatom, which exhibits a structural chemistry closely related to that of the isoelectronic elements [11]. Since bonding also is possible in the cationic units, the numbers of electrons involved in A-A and X-X bonds of various types (caa and exx> respectively) as well as the number of electrons e not involved in localized bonds can be generated from the numbers of valence electrons on A and X, namely and ex, respectively, by the following equations of balance ... 

From the data in Appendix C, calculate the theoretical maximum EMF of a methane/oxygen fuel cell with an acidic electrolyte under standard conditions. Assume the products to be liquid water and aqueous CO2. [Hint You need to know the number of electrons transferred per mole CH4 consumed. Write a balanced equation for the net reaction, and obtain the number of electrons from Eq. 15.47.] [Answer 1.05 V.]... 

You should note that Equations 17-4 and 17-5 apply only to chemical equations that are complete and balanced and that, for a given electron-transfer reaction, n... 

The basic principles discussed at the beginning of Chapter 17 (in connection with the construction of simple electrochemical cells) are exactly the ones used to write and balance chemical equations for electron-transfer reactions. These principles also enable you to predict whether or not a given electron-transfer reaction will actually take place. 

This chapter concerns the application of these four principles to the balancing of equations for electron-transfer reactions. 

The simplest situation that exists for balancing electron-transfer equations is the one in which a table of standard electrode potentials is at hand, and the two needed half-reactions are included in it. The following problem illustrates this situation. 

The general method of balancing electron-transfer equations requires that halfreaction equations be available. Short lists of common half-reactions, similar to Table 17-1, are given in most textbooks, and chemistry handbooks have extensive lists. However, no list can provide all possible half-reactions, and it is not practical to carry lists in your pocket for instant reference. The practical alternative is to learn to make your own half-reaction equations. There is only one prerequisite for this approach you must know the oxidation states of the oxidized and reduced forms of the substances involved in the electron-transfer reaction. In Chapter 8 you learned the charges on the ions of the most common elements now we review the method of determining the charge (the oxidation state) of an element when it is combined in a radical. 

It should be evident that with a little practice you can very quickly, efficiently, and infallibly balance the most complicated electron-transfer equations. It is a straightforward mechanical process. This statement is true IF you know what the products of oxidation and reduction are. The most difficult situation that exists for balancing equations is the one characterized by the following request "Write a balanced ionic equation for the reaction, if any, that occurs when you mix A and B. You know the potential reactants because they are given, but that is all. 

If both of these requirements are met, the reaction will be electron-transfer, and the equation will be balanced by the principles outlined in this chapter. If only one (or neither) of these requirements is met, the reaction (if any) will be limited to such reactions as double decomposition, association, or dissociation as described in Chapter 27. 

First, decide whether an electron-transfer reaction is possible, using approximate half-reaction potentials (p 301) and/or the characteristics of electron-transfer reactions (p 300). If it is possible, follow the equation-balancing procedure outlined on pp 295-299. 

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