Equations, balancing electron-transfer reactions with

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. 

As most of us recall from our struggles with balancing redox equations in our beginning chemistry courses, many electron-transfer reactions involve hydrogen ions and hydroxide ions. The standard potentials for these reactions therefore refer to the pH, either 0 or 14, at which the appropriate ion has unit activity. Because multiple numbers of H+ or OH- ions are often involved, the potentials given by the Nernst equation can vary greatly with the pH. 

For planar or spherical electrodes, where the mass transport is a diffusion function in one dimension, it is possible to solve the diffusion equation as a function of time. In Section 3 the principles of how the cyclic voltammetric peak current could be calculated for a simple electron transfer reaction were presented. It is also possible to solve the material balance equations for the spherical electrode at steady state for a few first-order mechanisms (Alden and Compton, 1997a). In order to tackle second-order kinetics, more complex mechanisms, solve time-dependent equations or model other geometries with... 

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-... 

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.]... 

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. 

Electron transfer in proteins generally involves redox centers separated by long distances. The electronic interaction between redox sites is relatively weak and the transition state for the ET reaction must be formed many times before there is a successhil conversion from reactants to products the process is electronically nonadiabatic. A Eandau-Zener treatment of the reactant-product transition probability produces the familiar semiclassical expression for the rate of nonadiabatic electron transfer between a donor (D) and acceptor (A) held at fixed distance (equation 1). Biological electron flow over long distances with a relatively small release of free energy is possible because the protein fold creates a suitable balance between AG° and k as well as adequate electronic coupling between distant redox centers. 

Here, the number of electrons transferred is 2. This number is obtained by examining the balanced equation and evaluating the change in oxidation numbers. For example, copper ions with +2 oxidation state changed to copper (solid) with an oxidation state of 0. In other words, each half-reaction involves two electrons. 

The stoichiometric form of Eq. 1 is usually quite simple, involving simple numerical ratios of oxidized and reduced forms with perhaps the addition of one or more of the species, hydrogen ions, hydroxyl ions and water, to balance the equation. However, the actual course of the reaction is quite complex since it is at least formally heterogeneous in nature, involving electron transfer between presumably a solution species or its adsorbed or otherwise altered form, and the electrode, and occurring in the interfacial region between bulk solution and electrode, which is distinguished as the electrical double layer. 

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. 

Notice in the balanced equation that two moles of Na were used to react with the two moles of chlorine atoms in one mole of Cl2. Each mole of Na lost one mole of electrons each mole of chlorine atoms gained a mole of electrons. Two moles of electrons were transferred to form two moles of NaCl. The overall reaction is the sum of the two half-reactions the moles of electrons cancel, and the sodium ions and chloride ions combine to form sodium chloride. Note that the sum of the oxidation numbers in sodium chloride is zero (+1) + (—1) = 0. 

Figure 4.13 Displacing one metal by another. More reactive metals displace less reactive metals from solution. In this reaction, Cu atoms each give up two electrons as they become Cu " ions and leave the wire. The electrons are transferred to two Ag" ions that become Ag atoms and deposit on the wire. With time, a coating of crystalline silver coats the wire. Thus, copper has displaced silver (reduced silver ion) from solution. The reaction is depicted as the laboratory view (fop), the atomic-scale view (middle), and the balanced redox equation (bottom).

It is common to treat the semiconductor-electrolyte interface in terms of charge and current density boundary conditions. The total charge held within the electrolytic solution and the interfacial states, which balances the charge held in the semiconductor, is assumed to be constant. This provides a derivative boundary condition for the potential at the interface. The fluxes of electrons and holes are constrained by kinetic expressions at the interface. The assumption that the charge is constant in the space charge region is valid in the absence of kinetic and mass-transfer limitations to the electrochemical reactions. Treatment of the influence of kinetic or mass transfer limitations requires solution of the equations governing the coupled phenomena associated with the semiconductor, the electrolyte, and the semiconductor-electrolyte interface. 

SECTION 20.2 An oxidization-reduction reaction can be balanced by dividing the reaction into two half-reactions, one for oxidation and one for reduction. A half-reaction is a balanced chemical equation that includes electrons. In oxidation half-reactions the electrons are on the product (right) side of the equation we can enviaon that these electrons are transferred from a substance when it is oxidized. In reduction halfreactions the electrons are on the reactant (left) side of the equation. Each half-reaction is balanced separately, and the two are brought together with proper coefficients to balance the electrons on each side of the equation, so the electrons cancel when the half-reactions are added. 

Balanced half-equations (with equal numbers of electrons) can be used to establish the mole ratio of products in electrolysis. Half equations are used to describe redox reactions. These reactions involve the transfer of electrons (Chapter 9). 

This is the basic equation for relating changes in electric potential with changes in energy. This equation also takes advantage of the definition that 1 J = 1 V C. The variable n represents the number of moles of electrons that are transferred in the balanced redox reaction. Because completed redox reactions do not usually show the balanced number of electrons explicitly, we might have to figure this out from the redox reaction itself. 

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