Electrochemical cell half-reactions

Review of Oxidation-Reduction Concepts Half-Reaction Method for Balancing Redox Reactions Electrochemical Cells... 

This is a reduction reaction because the positively charged metal ions have gained electrons, lost their charge, and become neutral atoms. The neutral atoms deposit on the electrode, a process called electrodeposition. This electrode is termed a cathode. At the cathode, reduction of an electroactive species takes place. An electroactive species is one that is oxidized or reduced during reaction. Electrochemical cells also contain nonelectroactive (or inert) species such as counterions to balance the charge, or electrically conductive electrodes that do not take part in the reaction. Often these inert electrodes are made of Pt or graphite, and serve only to conduct electrons into or out of the half-cell. 

The essential features of the electrochemical mechanism of corrosion were outlined at the beginning of the section, and it is now necessary to consider the factors that control the rate of corrosion of a single metal in more detail. However, before doing so it is helpful to examine the charge transfer processes that occur at the two separable electrodes of a well-defined electrochemical cell in order to show that since the two half reactions constituting the overall reaction are interdependent, their rates and extents will be equal. 

In an electrochemical cell, these two half-reactions occur at two different electrodes, which most often consist of metal plates or wires. Reduction occurs at the cathode a typical half-reaction might be... 

The overall reaction describes what goes on in the entire electrochemical cell. In half of the cell, the right beaker, reaction (7) occurs. In the other half of the cell, the left beaker, reaction (2) occurs. Hence, reactions (7) and (2) are called half-cell reactions or half-reactions. 

The two half-reactions are written separately. In our electrochemical cell the half-reactions occur in separate beakers. As the name implies, there must be two such reactions. 

We see that the overall chemical reaction that occurs in an electrochemical cell is conveniently described in terms of two types of half-reactions. In one, electrons are lost in the other, they are gained. To distinguish these half-reactions we need two identifying names. 

The value of this list is obvious. Any half-reaction can be combined with the reverse of another half-reaction (in the proportion for which electrons gained is equal to electrons lost) to give a possible chemical reaction. Our list permits us to predict whether equilibrium favors reactants or products. We would like to expand our list and to make it more quantitative. Electrochemical cells help us do this. 

The usefulness of Table 12-1 is clear. Qualitative predictions of reactions can be made with the aid of the ordered list of half-reactions. Think how the value of the list would be magnified if we had a quantitative measure of electron losing tendencies. The voltages of electrochemical cells furnish such a quantitative measure. 

We can use the electrochemical series to predict the thermodynamic tendency for a reaction to take place under standard conditions. A cell reaction that is spontaneous under standard conditions (that is, has K > 1) has AG° < 0 and therefore the corresponding cell has E° > 0. The standard emf is positive when ER° > Et that is, when the standard potential for the reduction half-reaction is more positive than that for the oxidation half-reaction. 

This is a quantitative problem, so we follow the standard strategy. The problem asks about an actual potential under nonstandard conditions. Before we determine the potential, we must visualize the electrochemical cell and determine the balanced chemical reaction. The half-reactions are given in the problem. To obtain the balanced equation, reverse the direction of the reduction half-reaction with the... 

Ab initio atomic simulations are computationally demanding present day computers and theoretical methods allow simulations at the quantum mechanical level of hundreds of atoms. Since an electrochemical cell contains an astronomical number of atoms, however, simplifications are essential. It is therefore obvious that it is necessary to study the half-cell reactions one by one. This, in turn, implies that a reference electrode with a known fixed potential is needed. For this purpose, a theoretical counterpart to the standard hydrogen electrode (SHE) has been established [Nprskov et al., 2004]. We will describe this model in some detail below. 

Analytical methods based upon oxidation/reduction reactions include oxidation/reduction titrimetry, potentiometry, coulometry, electrogravimetry and voltammetry. Faradaic oxidation/reduction equilibria are conveniently studied by measuring the potentials of electrochemical cells in which the two half-reactions making up the equilibrium are participants. Electrochemical cells, which are galvanic or electrolytic, reversible or irreversible, consist of two conductors called electrodes, each of which is immersed in an electrolyte solution. In most of the cells, the two electrodes are different and must be separated (by a salt bridge) to avoid direct reaction between the reactants. 

In case (c), a voltage opposite to and higher than the emf of the galvanic cell is imposed as a consequence, the current flow and hence also the electrochemical reactions are reversed, which means that half-reaction 1 becomes an anodic oxidation and half-reaction 2 is a cathodic reduction, so that Zn is deposited instead of Cu. 

The electrochemical cell can again be of the regenerative or electrosynthetic type, as with the photogalvanic cells described above. In the regenerative photovoltaic cell, the electron donor (D) and acceptor (A) (see Fig. 5.62) are two redox forms of one reversible redox couple, e.g. Fe(CN)6-/4 , I2/I , Br2/Br , S2 /S2, etc. the cell reaction is cyclic (AG = 0, cf. Eq. (5.10.24) since =A and D = A ). On the other hand, in the electrosynthetic cell, the half-cell reactions are irreversible and the products (D+ and A ) accumulate in the electrolyte. The most carefully studied reaction of this type is photoelectrolysis of water (D+ = 02 and A = H2)- Other photoelectrosynthetic studies include the preparation of S2O8-, the reduction of C02 to formic acid, N2 to NH3, etc. 

A reaction in an electrochemical cell comprises two half-cell reactions. Even when we want to focus on a single half-cell, we must construct a whole cell and determine its cell emf, which is dehned as (positive electrode) - E(negative electrode) - Only when we know both the emf and the value of one of the two electrode potentials can we calculate the unknown electrode potential. 

Electrode reactions are inner-sphere reactions because they involve adsorption on electrode surfaces. The electrode can act as an electron source (cathode) or an electron sink (anode). A complete electrochemical cell consists of two electrode reactions. Reactants are oxidized at the anode and reduced at the cathode. Each individual reaction is called a half cell reaction. The driving force for electron transfer across an electrochemical cell is the Gibbs free energy difference between the two half cell reactions. The Gibbs free energy difference is defined below in terms of electrode potential,... 

In these redox reactions, there is a simultaneous loss and gain of electrons. In the oxidation reaction part of the reaction (oxidation half-reaction), electrons are being lost, but in the reduction half-reaction, those very same electrons are being gained. Therefore, in redox reactions there is an exchange of electrons, as reactants become products. This electron exchange may be direct, as when copper metal plates out on a piece of zinc or it may be indirect, as in an electrochemical cell (battery). 

R is the ideal gas constant, T is the Kelvin temperature, n is the number of electrons transferred, F is Faraday s constant, and Q is the activity quotient. The second form, involving the log Q, is the more useful form. If you know the cell reaction, the concentrations of ions, and the E°ell, then you can calculate the actual cell potential. Another useful application of the Nernst equation is in the calculation of the concentration of one of the reactants from cell potential measurements. Knowing the actual cell potential and the E°ell, allows you to calculate Q, the activity quotient. Knowing Q and all but one of the concentrations, allows you to calculate the unknown concentration. Another application of the Nernst equation is concentration cells. A concentration cell is an electrochemical cell in which the same chemical species are used in both cell compartments, but differing in concentration. Because the half reactions are the same, the E°ell = 0.00 V. Then simply substituting the appropriate concentrations into the activity quotient allows calculation of the actual cell potential. 

The rules of stoichiometry also apply in this case. In electrochemical cells, we must consider not only the stoichiometry related to chemical formulas, but also the stoichiometry related to electric currents. The half-reaction under consideration not only involves 1 mol of each of the copper species, but also 2 mol of electrons. We can construct a mole ratio that includes moles of electrons or we could construct a mole ratio using faradays. A faradav (F) is a mole of electrons. Thus, we could use either of the following ratios for the copper half-reaction ... 

The more the two half-reactions are separated in the table, the greater is the tendency for the net reaction to occur. This tendency for an overall redox reaction to occur, whether by direct contact or in an electrochemical cell, is determined from the standard reduction potentials, E° values, of the half-reactions involved, and the value of this potential are indications of the tendency of the overall redox reaction to occur. We will now present a scheme for determining this potential, which is symbolized E"d. ... 

Consequently, a wealth of information on the energetics of electron transfer for individual redox couples ("half-reactions") can be extracted from measurements of reversible cell potentials and electrochemical rate constant-overpotential relationships, both studied as a function of temperature. Such electrochemical measurements can, therefore, provide information on the contributions of each redox couple to the energetics of the bimolecular homogeneous reactions which is unobtainable from ordinary chemical thermodynamic and kinetic measurements. 

Let us continue with the example of copper ions in contact with copper metal and zinc ions in contact with zinc metal. This combination is usually referred to as the Darnell cell or zinc/copper couple(Fig. 6.5a). For this electrochemical cell the reduction and oxidation processes responsible for the overall reaction are separated in space one half reaction taking place in one electrode compartment and the other takes place in the other compartment. 

SHE, standard hydrogen electrode The electrode used as a standard against which aU other half-cell potentials are measured. The following reaction occurs at the platinum electrode when immersed in an acidic solution and cormected to the other half of an electrochemical cell 2H (aq) -H 2e —> H2(g). The half- cell potential of this reaction at 25°C, 1 atm and 1 m concentrations of aU solutes is agreed, by convention, to be OV... 

Methanol is one of the few alcohols that can be fed directly into a fuel cell and can be converted electrochemically at the anode. The DMFC can be fed with a gaseous or liquid fuel feed. The liquid DMFC generally uses a diluted methanol in water mixture (ty pically 1-2 molar) and only a fraction of the methanol is used at the anode (Collins, 2001). The DMFC, like an ordinary battery, provides DC electricity according to the following half reactions. 

The two half reactions of any redox reaction together make up an electrochemical cell. This cell has a standard potential difference, E , which is the voltage of the reaction at 25 °C when all substances involved are at unit activity. E refers to the potential difference when the substances are not in the standard state. E for a particular reaction can be found by subtracting one half cell reaction from the other and also subtracting the corresponding voltages. For example for reduction of Fe to Fe by H2, E° = 0.77 - 0 = 0.77 V. A further example is the oxidation of Fe " by solid Mn02 in acid solution. The half cell reactions are. 

E is the standard equilibrium potential, i. e. the potential corresponding to unit activity and RTF. The dissolution reaction leads to the development of an electrical double layer at the iron-solution interface. The potential difference of the Fe/Fe " half cell cannot be measured directly, but if the iron electrode is coupled with a reference electrode (usually the standard hydrogen electrode, SHE), a relative potential difference, E, can be measured. This potential is termed the single potential of the Fe/Fe electrode on the scale of the standard hydrogen couple H2/H, the standard potential of which is taken as zero. The value of the equilibrium potential of an electrochemical cell depends upon the concentrations of the species involved. 

The reaction produces hydroxyl ions which react directly with the Fe ions to produce an oxide precipitate. The combined anodic and cathodic reactions form the corrosion cell, the electrochemical potential of which lies between the single potential of the two half reactions. This mixed potential is termed the corrosion potential, corr> and for corrosion to proceed beyond the equilibrium state, the corrosion potential must be more positive than the equilibrium single potential of iron. For iron in water at pH 7 and with [Fe j = 10" M, for example, the potential of the anodic reaction is. 

The left half of this electrochemical cell, containing a zinc electrode and zinc sulfate solution, engages in an oxidation reaction. This reaction liberates electrons and turns zinc atoms into zinc ions (Zn, which is a zinc atom that has lost two electrons and therefore has a net positive charge of 2). The zinc atoms come from the electrode, which is gradually depleted the zinc ions that are produced in the reaction enter the solution. In the right half of the cell, a reduction reaction occurs electrons combine with copper ions to produce neutral atoms of copper. Copper ions leave the solution in the process and collect at the copper electrode. Over time, the zinc electrode and copper solution will run out of material, causing the reaction to cease unless the material is replenished. 

In each compartment of the electrochemical cell a half reaction occurs. The two half reactions result in an overall reaction that generates a flow of electrons or current. In one cell compartment, zinc is oxidized according to the reaction Zn Zn + 2e . The reduction of copper takes place in the other cell s compartment Cu +,, + 2e Cu,.. Notice that these reactions are the same ones that take place... 

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