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Electrochemistry translates the chemical energy of a reduction–oxidation reaction into electrical energy. Reduction–oxidation reactions (Chapter 5) involve the transfer of electrons. Electrical energy comes from the movement of electrons through a wire.

When the substances involved in oxidation and reduction half–reactions are physically separated, it is called an electrochemical cell. Each half reaction occurs on the surface of an electrically conductive solid called an electrode. Each electrode is immersed in a solution containing ions needed for the half–reaction. The electrodes are connected by a wire so that electrons can move from the oxidation half–reaction to the reduction half–reaction. The solutions are connected by a salt bridge so that ions can move between solutions. In an electrochemical cell the chemical potential energy can be harnessed as the substances undergoing oxidation push electrons through the wire to the substances undergoing reduction. The force moving electrons through the wire is called the electromotive force, electrochemical potential, or voltage (E). In fact, the units for this force are volts (V). The rate at which the electrons move is current with units of amperes (A). Since electrons are negative, a negative charge might build up with the reduction and a positive charge with the oxidation. The salt bridge moves ions into those solutions to maintain electric neutrality without mixing of solutions.

Another characteristic of an electrochemical cell is that the oxidation and reduction half–reactions occur at surfaces called electrodes. The electrode where oxidation occurs is the anode. The electrode where reduction occurs is called the cathode. Sometimes the electrode acts as a reactant or product in the reaction. At other times it only provides a conductive surface on which the reaction occurs. If it does not participate in the reaction, it is called an inert electrode.

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Another characteristic of electrochemical cells is that the redox reaction may occur spontaneously (voltaic cell), or nonspontaneous reactions can be forced to occur (electrolytic cell). Voltaic cells are typically used to produce electrical energy. In fact, batteries are a voltaic cell. Electrolytic cells are used to produce some substance. This process is called electrolysis.

In a voltaic cell, electrons are spontaneously emerging at the cathode so that reduction can occur. Therefore the cathode is often denoted with a negative sign. The term cathode comes from the observation that cations (positively charged ions) are attracted to the cathode, so the cathode must be negative. Since electrons are being removed from the anode, it is given a positive sign. However, in an electrolytic cell, the electrons are being forced to move in a direction opposite of spontaneous. Therefore in an electrolytic cell the cathode is labeled "+" and the anode is labeled "–."

Since electrochemical potential (E) measures the driving force of a reaction, it is similar in concept to Gibbs free energy (G). The relationship is

G = –nFE         (Equation 17.6)

where n is the number of electrons transferred in the redox reaction and F is Faraday's constant, 9.65 x 10⁴ C/mol e^–. Thus a positive potential represents a spontaneous reaction and voltaic cell. A negative potential denotes a nonspontaneous reaction and an electrolytic cell.

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Like free energy, electrochemical potential is related to the equilibrium constant (K), where

E°

=

RT nF

ln K

where R is the gas constant (8.314 J/mol•K), T is the temperature (K), n is the number of electrons transferred, F is Faraday's constant, and the superscript 0 refers to standard conditions of 25 °C, 10⁵ Pa and a 1 M concentration of each reactant and product. Using the actual values for the constants at 25 °C and rearranging, the equation becomes

log K

=

nE°cell 0.0592

(Equation 17.19)

Positive values of standard potential (E°) indicate that the forward process is favored, and K > 1. Negative values of E° indicate reactants are favored with K < 1.

In electrolysis, a substance is generated by the addition or removal of electrons. Often a metal is produced by reducing its ion. In this process, the half–reaction shows the relationship between the moles of electrons and moles of substance. Michael Faraday determined the relationship between charge (Q) in coulombs (C) and moles of electrons. This relationship is expressed in Faraday's constant (F), where 9.65 x 10⁴ C = 1 mole electrons. Current measures the rate of electron flow in amperes, or amps (A), where 1 A = 1 C/s. Using these relationships, the amount of substance produced can be determined from current, time, and the half–reaction, and vice versa.

Cell potentials (E) depend primarily on the identity of the reaction. Since cells separate the half–reactions, it is often convenient to talk about the potential of the half–reaction or the electrode potential. Unfortunately, since one–half of a reaction does not occur without the other half, it is impossible to measure electrode potentials directly. Instead, only potential differences can be measured. So that electrode potentials could be tabulated, one half–cell was defined as having an electrode potential of exactly 0 V. This half–cell is called the standard hydrogen electrode (SHE). It uses an inert platinum electrode with 1 M H⁺ and 1 atm H₂ for the following reaction

2 H⁺ + 2 e^– H₂

By tradition, tables list potentials for reduction half–reactions at standard state (1 M, 25 °C and 10⁵ Pa) with SHE as the oxidation half–reaction. These are called standard reduction potentials. To obtain standard oxidation potentials, the opposite sign is used. (As with Hess's law for H and G, reverse the reaction, change the sign.) These tabulated values can be used to determine the standard cell potential for any electrochemical cell. The standard cell potential is the difference between the reduction potential of the cathode and the reduction potential of the anode.

E°_cell = E°_c – E°_a         (Equation 17.11)

The minus in the equation changes the reduction potential to an oxidation potential, so a separate step is not necessary.

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To correct for nonstandard conditions, the Nernst equation is used to determine the cell potential (E_cell).

Ecell

=

E°cell

–

RT nF

ln Q         (Equation 17.17)

where R is the gas constant, T is temperature, n is the moles of electrons in the reaction, F is Faraday's constant, and Q is the reactant quotient (Chapter 15), where all solutions are in units of molarity and concentration of gases are expressed as the partial pressure in atmospheres.

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Because the temperature effect is relatively small and most cells operate at room temperature, the cell potential in volts is often determined from a more convenient form of the Nernst equation, which assumes a temperature of 25 °C

Ecell

=

E°cell

–

0.0592 n

log Q         (Equation 17.18)

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