Half-cells and the Nernst equation

Why does sodium react with water yet copper doesn t  

Sodium reacts with in water almost explosively to effect the reaction 

The protons on the left-hand side come from the water. Being spontaneous, the value of AGr for Equation (7.25) is negative. The value of AGr comprises two components  

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. 

By contrast, copper metal does not react with water to liberate hydrogen in a reaction like Equation (7.35) on the contrary, black copper(II) oxide reacts with hydrogen gas to form copper metal  

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Referring to the discussion of the fundamental concepts regarding half cells and the Nernst equation in Chapter 5 (Section 5.3.1) it is possible to briefly summarize the similarities and differences of these two sets of systems. It is important to recognize the ways in which they are different when considering the behavior of complex multivariate systems such as the oceans and clouds, or a lake-river system. 

At this point we describe briefly some important kinds of electrodes, and present the half-cell reactions and the Nernst equation for each. 

A SHE is a platinum wire immersed in acidified aqueous solution (HCl) and surrounded by a tube through which bubbles dihydrogen gas at standard pressure. The reduction reaction and the Nernst equations for this half-cell are given as... 

Write the cell symbol, the cell reaction equation, and the Nernst equation for the cell with the half-reactions... 

The Nernst equation shows the relationship between the concentration of aqueous ions in each half-cell and the electrode potential. 

It is very often necessary to characterize the redox properties of a given system with unknown activity coefficients in a state far from standard conditions. For this purpose, formal (solution with unit concentrations of all the species appearing in the Nernst equation its value depends on the overall composition of the solution. If the solution also contains additional species that do not appear in the Nernst equation (indifferent electrolyte, buffer components, etc.), their concentrations must be precisely specified in the formal potential data. The formal potential, denoted as E0, is best characterized by an expression in parentheses, giving both the half-cell reaction and the composition of the medium, for example E0,(Zn2+ + 2e = Zn, 10-3M H2S04). 

Electrode and therefore cell potentials are very important analytically as their magnitudes are determined by the activities of the reactants and products involved in the electrode reactions. The relation between such activities and the electrode potential is given by the Nernst equation. For a general half-cell reaction written as a reduction, i.e. aA + bB +. .. ne = xX + yY +. . ., the equation is of the form... 

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. 

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... 

Both half- and overall reaction tendencies change with temperature, pressure (if gases are involved), and concentrations of the ions involved. Thus far, we have only been concerned with standard conditions. Standard conditions, as stated previously, are 25°C, 1 atm pressure, and 1 M ion concentrations. An equation has been derived to calculate the cell potential when conditions other than standard conditions are present. This equation is called the Nernst equation and is used to calculate the true E (cell potential)... 

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,... 

From the Nernst equation, calculate the pressure of hydrogen involved if alHsO ) = 0.011, and Eh+,h2 = 0.008 V. Take p = 10 Pa. (Remember from the balanced half-cell reaction that n = 2.)... 

The values of the standard emf in eqs 2.24 and 2.24 are slightly different.) Since a half-reaction represents a cell involving a standard hydrogen electrode, the Nernst equation may also be applied to electrode potentials. Thus for the half-reaction... 

One important application of the Nernst equation is the measurement of pH (and, through pH, acidity constants). The pH of a solution can be measured electrochemically with a device called a pH meter. The technique makes use of a cell in which one electrode is sensitive to the H30+ concentration and the second electrode serves as a reference. An electrode sensitive to the concentration of a particular ion is called an ion-selective electrode. One combination is a hydrogen electrode connected through a salt bridge to a calomel electrode. The reduction half-reaction for the calomel electrode is... 

The Nernst equation applies to both cell reactions and half-reactions. For the conditions specified, calculate the potential for the following half-reactions at 25°C ... 

Potentiometric measurements are based on the Nernst equation, which was developed from thermodynamic relationships and is therefore valid only under equilibrium (read thermodynamic) conditions. As mentioned above, the Nernst equation relates potential to the concentration of electroactive species. For electroanalytical purposes, it is most appropriate to consider the redox process that occurs at a single electrode, although two electrodes are always essential for an electrochemical cell. However, by considering each electrode individually, the two-electrode processes are easily combined to obtain the entire cell process. Half reactions of electrode processes should be written in a consistent manner. Here, they are always written as reduction processes, with the oxidised species, O, reduced by n electrons to give a reduced species, R ... 

In (19-6), n has been made dimensionless. For a half-reaction, n is the number of electrons in the half-equation for the whole-cell reaction, n is the number of electrons in one of the multiplied half-equations before canceling the electrons. The Nernst equation is closely related to the laws of chemical equilibrium. Le Chatelier s principle applies to the potential of a cell in the same sense as it applies to the yield of an equilibrium process. Since Q is a fraction that has product concentrations in the numerator (top) and reactant concentrations in the denominator (bottom), an increased concentration of the product reduces the potential and an increased concentration of reactant raises the potential. 

The standard states to which this E° value refers are 1 atm for oxygen gas and 1 mol/L for H+. We can calculate E for the above half-cell for neutral solutions, in which [H+] = 10-7, by using the Nernst equation. Assuming the oxygen remains at its standard state, P(O2) = 1 atm,... 

The Nernst Equation accurately predicts half-cell potentials only when the equilibrium quotient term Q is expressed in activities. Ionic activities depart increasingly from concentrations when the latter exceed 10-10-3 M, depending on the size and charge of the ion. 

Half-cell reaction — The redox reaction (- electrode reaction) proceeding in a half-cell. The half-cell reaction changes the ratio of the activities of the reduced and oxidized forms. When the half-cell reaction is electrochemically reversible (see reversibility), the -> Nernst equation will describe the dependence of the -> electrode potential on the ratio of the activities of the reduced and oxidized forms. 

In voltaic cells, it is possible to carry out the oxidation and reduction halfreactions in different places when suitable provision is made for transporting the electrons over a wire from one half-reaction to the other and to transport ions from each half-reaction to the other in order to preserve electrical neutrality. The chemical reaction produces an electric current in the process. Voltaic cells, also called galvanic cells, are introduced in Section 17.1. The tendency for oxidizing agents and reducing agents to react with each other is measured by their standard cell potentials, presented in Section 17.2. In Section 17.3, the Nernst equation is introduced to allow calculation of potentials of cells that are not in their standard states. 

The first and third half-reactions have half-cell potentials (AgCl CH Ag) and (Hg2Cl2 cr Hg)that can be combined and called A ef because they make a constant contribution to the cell voltage. The second reaction is the source of a variable potential in the cell, corresponding to the free energy of dilution of H30 from a concentration of 1.0 M to an unknown and variable concentration, and its potential exists across the thin glass membrane of the glass electrode. The Nernst equation for the cell can therefore be written as... 

Recall that the Nernst equation is the mathematical model describing the relationship between cell potential and concentrations and is readily derived from the fact that cell potential shows a concentration dependence due to its relationship to free energy, equations (A.2.2) and (A.2.3), where Q is the concentration ratio of oxidized (e.g., [Fe3+L ]) to reduced (e.g., [Fe2+L ]) species. In our system, E° is the reduction potential for the one electron transfer half reaction [equation (5.4.4)]. 

The electrode potential (reduction potential) for a redox couple is defined as the couple s potential measured with respect to the standard hydrogen electrode, which is set equal to zero (see hydrogen electrode later). This potential, by convention, is the electromotive force of a cell, where the standard hydrogen electrode is the reference electrode (left electrode) and the given half-cell is the indicator electrode (right electrode). The reduction potential for a given redox couple is given by the Nernst equation ... 

Formal potentials are empirically derived potentials that compensate for the types of activity and competing equilibria effects that we have just described. The formal potential of a system is the potential of the half-cell with respect to the standard hydrogen electrode measured under conditions such that the ratio of analytical concentrations of reactants and products as they appear in the Nernst equation is exactly unity and the concentrations of other species in the system are all carefully specified. For example, the formal potential for the half-reaction... 

Ox refers to the oxidized species and Red to the reduced species x and y are their coefficients, respectively, in the balanced equation. The Nernst equation for any cathode half-cell reduction half-reaction) is... 

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