12. Electrochemistry

During the course of the reaction, electrons flow from the zinc anode through the wire and to the copper cathode. A voltmeter can be connected to measure this electromotive force. As mentioned earlier, the anions (Cl ) flow externally from the salt bridge into the ZnSO , and the cations (K ) flow externally from the salt bridge into the CuSO . This flow depletes the salt bridge and, along with the finite quantity of Cu in the solution, accounts for the relatively short lifespan of the cell.

A cell diagram is a shorthand notation representing the reactions in an electrochemical cell. A cell diagram for the Daniell cell is as follows: Zn (s) | Zn^2+ (1 M) || Cu^2+ (1 M) | Cu (s) The following rules are used in constructing a cell diagram: 1. The reactants and products are always listed from left to right in this form: anode | anode sol'n (concentration) || cathode sol'n (concentration) | cathode 2. A single vertical line indicates a phase boundary. 3. A double vertical line indicates the presence of a salt bridge or some other type of barrier.

A reduction potential is measured in volts (V) and defined relative to the standard hydrogen electrode (SHE), which is given a potential of 0 V by convention. The species in a reaction that will be oxidized or reduced can be determined from the reduction potential of each species, defined as the tendency of a species to gain electrons and to be reduced.

Each species has its own intrinsic reduction potential; the more positive the potential, the greater the tendency to be reduced.

KEY CONCEPT 1

Electrons move through an electrochemical cell opposite to the flow of current (I).

KEY CONCEPT 8

If Ecell is positive, ln K is positive. This means that K must be greater than one and that the equilibrium lies to the right (products are favored).

KEY CONCEPT 7

If you need to multiply each half-reaction by a common denominator to cancel out electrons when coming up with the net ionic equation, do not multiply the reduction potential, E° , by that number. That would indicate a change in the chemical identity of the electrode, which is not occurring.

KEY CONCEPT 5

In a galvanic cell, the anode is negative and the cathode is positive. In an electrolytic cell, the anode is positive and the cathode is negative. This is because an external source is used to reverse the charge of an electrolytic cell. However, in both types of cells, reduction occurs at the cathode, and oxidation occurs at the anode; cations are attracted to the cathode, and anions are attracted to the anode.

Electrochemical cells are contained systems in which oxidation-reduction reactions occur. There are three fundamental types of electrochemical cells: galvanic cells (also known as voltaic cells), electrolytic cells, and concentration cells.

In addition, there are specific commercial cells such as Ni-Cd batteries through which we can understand these fundamental models.

In spite of this difference in designating charge (sign), oxidation always takes place at the anode and reduction always takes place at the cathode in both types of cells; electrons always flow through the wire from the anode to the cathode and current flows from cathode to anode. Finally, note that— regardless of its charge designation—the cathode always attracts cations and the anode always attracts anions.

In the Daniell cell, for example, the electrons created at the anode by the oxidation of elemental zinc travel through the wire to the copper half-cell. There, they attract copper(II) cations to the cathode, resulting in the reduction of the copper ions to elemental copper, and drawing cations out of the salt bridge into the compartment. The anode, having lost electrons, attracts anions from the salt bridge at the same time that zinc(II) ions formed by the oxidation process dissolve away from the anode.

In this electrolytic cell, molten NaCl is decomposed into Cl (g) and Na (l). The external voltage source—a battery—supplies energy sufficient to drive the oxidation-reduction reaction in the direction that is thermodynamically unfavorable (nonspontaneous).

In this example, Na ions migrate toward the cathode, where they are reduced to Na (l). At the same time, Cl ions migrate toward the anode, where they are oxidized to Cl (g). Notice that the halfreactions do not need to be separated into different compartments; this is because the desired reaction is nonspontaneous. Note that sodium is a liquid at the temperature of molten NaCl; it is also less dense than the molten salt and, thus, is easily removed as it floats to the top of the reaction vessel.

Let's examine the inner workings of a galvanic (voltaic) cell. Two electrodes of distinct chemical identity are placed in separate compartments, which are called half-cells. The two electrodes are connected to each other by a conductive material, such as a copper wire. Along the wire, there may be other various components of a circuit, such as resistors or capacitors, but for now, we'll focus on the battery itself.

Surrounding each of the electrodes is an aqueous electrolyte solution composed of cations and anions. The cations in the two half-cell solutions can be of the same element as the respective metal electrode. Connecting the two solutions is a structure called a salt bridge, which consists of an inert salt. When the electrodes are connected to each other by a conductive material, charge will begin to flow as the result of an oxidation-reduction reaction that is taking place between the two half-cells. The redox reaction in a galvanic cell is spontaneous, and therefore the change in Gibbs free energy for the reaction is negative (ΔG < 0). As the spontaneous reaction proceeds toward equilibrium, the movement of electrons results in a conversion of electrical potential energy into kinetic energy. By separating the reduction and oxidation halfreactions into two compartments, we are able to harness this energy and use it to do work by connecting various electrical devices into the circuit between the two electrodes.

KEY CONCEPT 2

The purpose of the salt bridge is to exchange anions and cations to balance, or dissipate, newly generated charges.

For galvanic cells, the direction of spontaneous movement of charge is from the anode, the site of oxidation, to the cathode, the site of reduction. This is simple enough to remember, but it begs the question: how do we determine which electrode species will be oxidized and which will be reduced?

The relative tendencies of different chemical species to be reduced have been determined experimentally, using the tendency of the hydrogen ion (H ) to be reduced as an arbitrary zero reference point.

A rechargeable cell or rechargeable battery

is one that can function as both a galvanic and electrolytic cell.

So far, we have considered the calculation of a cell's emf only under standard conditions. However, electrochemical cells may have ionic concentrations that deviate from 1 M. Also, for the concentration cell, the concentrations of the ions in the two compartments must be different for there to be a measurable voltage and current. Concentration and the emf of a cell are related: emf varies with the changing concentrations of the species in the cell. When conditions deviate from standard conditions, one can use the Nernst equation:

where Ecell is the emf of the cell under nonstandard conditions, Ecell is the emf of the cell under standard conditions, R is the ideal gas constant, T is the temperature in kelvin, n is the number of moles of electrons, F is the Faraday constant, and Q is the reaction quotient for the reaction at a given point in time. The following simplified version of the equation can be used, assuming T = 298 K. This simplified version of the equation brings together R, T (298 K), and F, and converts the natural logarithm to the base-ten logarithm to make calculations easier.

ΔG° = -RT ln Keq

where R is the ideal gas constant, T is the absolute temperature, and K is the equilibrium constant for the reaction. By extension, if the values for n, T, and Keq are known, then Ecell for the reaction is easily calculated. On the MCAT, you will not be expected to calculate natural logarithm values in your head. That being said, these equations can still be tested but in a conceptual way.

Knowing the effects of concentration on equilibria, we can now derive the change in Gibbs free energy of an electrochemical cell with varying concentrations using the equation

ΔG = ΔG° + RT ln Q where ΔG is the free energy change under nonstandard conditions, ΔG° is the free energy change under standard conditions, R is the ideal gas constant, T is the temperature, and Q is the reaction quotient.

This is the change in the amount of energy available in a chemical system to do work. In an electrochemical cell, the work done is dependent on the number of coulombs of charge transferred and the energy available. Thus, ΔG° and emf are related as follows:

ΔG° = -nFEcell where ΔG° is the standard change in free energy, n is the number of moles of electrons exchanged, F is the Faraday constant, and Ecell is the standard emf of the cell. Keep in mind that, if the Faraday constant is expressed in coulombs then ΔG° must be expressed in J, not kJ. Notice the similarity of this relationship to that expressed in the physics formula W = qΔV for the amount of work available or needed in the transport of a charge q across a potential difference ΔV: n × F is a charge, and Ecell is a voltage. Note the significance of the negative sign on the right side of the equation. ΔG° and Ecell will always have opposite signs. Therefore, galvanic cells have negative ΔG° and positive Ecell values; electrolytic cells have positive ΔG° and negative Ecell values.

Standard reduction potential (Ered ) is measured under standard conditions: 25°C (298 K), 1 atm pressure, and 1 M concentrations. The relative reactivities of different half-cells can be compared to predict the direction of electron flow.

A more positive Ered means a greater relative tendency for reduction to occur, while a less positive E means a greater relative tendency for oxidation to occur.

KEY CONCEPT 6

A reduction potential is exactly what it sounds like. It tells us how likely a compound is to be reduced. The more positive the value, the more likely it is to be reduced—the more it wants to be reduced.

Remember that the reaction quotient, Q, for a general reaction:

Although the expression for the reaction quotient Q has two terms for the concentrations of reactants and two terms for the concentrations of products, remember that only the species in solution are included. The emf of a cell can be measured with a voltmeter. A potentiometer is a kind of voltmeter that draws no current and gives a more accurate reading of the difference in potential between two electrodes.

A lead-acid battery, also known as a lead storage battery, is a specific type of rechargeable battery.

As a voltaic cell, when fully charged, it consists of two half-cells—a Pb anode and a porous PbO2 cathode, connected by a conductive material (concentrated 4 M H2SO4 ). When fully discharged, it consists of two PbSO electroplated lead electrodes with a dilute concentration of H2SO4. Both half-reactions cause the electrodes to plate with lead sulfate and dilute the acid electrolyte when discharging. The lead anode is negatively charged and attracts the anionic bisulfate. The lead(IV) oxide cathode is a bit more complicated. This electrode is porous, which allows the electrolyte (sulfuric acid) to solvate the cathode into lead and oxide ions. Then, the hydrogen ions in solution react with the oxide ions to produce water, and the remaining sulfate ions react with the lead to produce the electroplated lead sulfate.

KEY CONCEPT 3

Because electrolysis is nonspontaneous, the electrode (anode or cathode) can consist of any material so long as it can resist the high temperatures and corrosion of the process.

In a galvanic cell, current is spontaneously generated as electrons are released by the oxidized species at the anode and travel through the conductive material to the cathode, where reduction takes place. Because the anode of a galvanic cell is the source of electrons, it is considered the negative electrode; the cathode is considered the positive electrode. Electrons, therefore, move from negative (low electrical potential) to positive (high electrical potential), while the current—the flow of positive charge—is from positive (high electrical potential) to negative (low electrical potential).

Conversely, the anode of an electrolytic cell is considered positive because it is attached to the positive pole of the external voltage source and attracts anions from the solution. The cathode of an electrolytic cell is considered negative because it is attached to the negative pole of the external voltage source and attracts cations from the solution.

KEY CONCEPT 4

Faraday's laws state that the liberation of gas, and deposition of elements, on electrodes is directly proportional to the number of electrons being transferred during the oxidation- reduction reaction. Here, normality or gram equivalent weight is used. These observations are proxy measurements of the amount of current flowing in a circuit.

Galvanic cells and concentration cells house spontaneous reactions, whereas electrolytic cells contain nonspontaneous reactions. Remember that spontaneity is indicated by the change in Gibbs free energy, ΔG. All three types contain electrodes where oxidation and reduction take place.

For all electrochemical cells, the electrode where oxidation occurs is called the anode, and the electrode where reduction occurs is called the cathode. Other descriptors of electrochemical cells include the electromotive force (emf), which corresponds to the voltage or electrical potential difference of the cell. If the emf is positive, the cell is able to release energy (ΔG < 0), which means it is spontaneous. If the emf is negative, the cell must absorb energy (ΔG > 0), which means it is nonspontaneous.

For galvanic cells, the electrode with the more positive reduction potential is the cathode, and the electrode with the less positive reduction potential is the anode. Because the species with a stronger tendency to gain electrons (that wants to gain electrons more) is actually doing so, the reaction is spontaneous and ΔG is negative.

For electrolytic cells, the electrode with the more positive reduction potential is forced by the external voltage source to be oxidized and is, therefore, the anode. The electrode with the less positive reduction potential is forced to be reduced and is, therefore, the cathode. Because the movement of electrons is in the direction against the tendency or desires of the respective electrochemical species, the reaction is nonspontaneous and ΔG is positive.

Furthermore, we can also state that, for all electrochemical cells, the movement of electrons is from anode to cathode, and the current (I) runs from cathode to anode. This point can be a point of confusion among students. In physics, it is typical to state that current is the direction of flow of a positive charge through a circuit; this model was first proposed by Ben Franklin and continues to be used among physicists. Modern chemists are interested in the flow of electrons, but may discuss the current (a theoretical flow of positive charge) as a proxy for the flow of electrons; the current and the flow of electrons are always of equal magnitude but in opposite directions.

Last, it is important to note that all batteries are influenced by temperature changes. For instance, lead-acid batteries in cars, like most galvanic cells, tend to fail most in cold weather.

When charging, the lead-acid cell is part of an electrolytic circuit. These equations and electrode charge designations are the opposite because an external source reverses the electroplating process and concentrates the acid solution—this external source is very evident when one uses jumper cables to restart a car.

Lead-acid batteries, as compared to other cells, have some of the lowest energy-to-weight ratios (otherwise known as energy density). Energy density is a measure of a battery's ability to produce power as a function of its weight. Lead-acid batteries, therefore, require a heavier amount of battery material to produce a certain output as compared to other batteries.

This cell is used in industry as the major means of sodium and chlorine production. You may wonder why one would do so much work to obtain pure sodium and chlorine. Remember that these elements are never found naturally in their elemental form because they are so reactive. Thus, to use elemental sodium or chlorine gas in a reaction, it must be manufactured through processes such as these.

Michael Faraday was the first to define certain quantitative principles governing the behavior of electrolytic cells. He theorized that the amount of chemical change induced in an electrolytic cell is directly proportional to the number of moles of electrons that are exchanged during the oxidation- reduction reaction. The number of moles exchanged can be determined from the balanced halfreaction. In general, for a reaction that involves the transfer of n electrons per atom M, M^n+ + n e- → M (s)

Nickel-cadmium batteries are also rechargeable cells. They consist of two half-cells made of solid cadmium (the anode) and nickel(III) oxide-hydroxide (the cathode) connected by a conductive material, typically potassium hydroxide (KOH). Most of us are familiar with AA and AAA cells made of Ni-Cd materials, inside of which the electrodes are layered and wrapped around in a cylinder.

Ni-Cd batteries have a higher energy density than lead-acid batteries. The electrochemistry of the Ni-Cd half-reactions also tends to provide higher surge current. Surge currents are periods of large current (amperage) early in the discharge cycle. This is preferable in appliances such as remote controls that demand rapid responses. It is important to note that modern Ni-Cd batteries have largely been replaced by more efficient nickel-metal hydride (NiMH) batteries. These newer batteries have more energy density, are more cost effective, and are significantly less toxic. As the name suggests, in lieu of a pure metal anode, a metal hydride is used instead.

It should be noted that reduction and oxidation are opposite processes. Therefore, to obtain the oxidation potential of a given half-reaction, both the reduction half-reaction and the sign of the reduction potential are reversed.

Note that, in the examples of batteries given above (lead-acid storage batteries and nickel-cadmium batteries), the oxidation half-reaction was given with the reduction potential of the reverse reaction. These two quantities have equal magnitudes but opposite signs. On the MCAT, reduction potentials are generally given rather than oxidation potentials. Therefore, all references in this book (with exception of the thallium example immediately above) are given using reduction potentials—not oxidation potentials.

In the Daniell cell, a zinc electrode is placed in an aqueous ZnSO solution, and a copper electrode is placed in an aqueous CuSO solution. The anode of this cell is the zinc bar where Zn (s) is oxidized to Zn (aq). The cathode is the copper bar, and it is the site of the reduction of Cu (aq) to Cu (s).

The calculation can be accomplished by knowing each half-reaction. If the two half-cells were not separated, the Cu ions would react directly with the zinc bar, and no useful electrical work would be done. Because the solutions and electrodes are physically separated, they must be connected by a conductive material to complete the circuit.

Isoelectric focusing is a technique used to separate amino acids or polypeptides based on their isoelectric points (pI).

The positively charged amino acids (protonated at the solution's pH) will migrate toward the cathode; negatively charged amino acids (deprotonated at the solution's pH) will migrate toward the anode.

According to this equation, one mole of metal M (s) will logically be produced if n moles of electrons are supplied to one mole of M . Additionally, the number of moles of electrons needed to produce a certain amount of M (s) can now be related to the measurable electrical property of charge. One electron carries a charge of 1.6 × 10^ -19 coulombs (C).

The charge carried by one mole of electrons can be calculated by multiplying this number by Avogadro's number, as follows: This number is called the Faraday constant, and one faraday (F) is equivalent to the amount of charge contained in one mole of electrons (1 F = 96,485 C) or one equivalent. On the MCAT, you should round up this number to to make calculations more manageable.

However, if only a wire were provided for this electron flow, the reaction would soon stop because an excess positive charge would build up on the anode, and an excess negative charge would build up on the cathode. Eventually, the excessive charge accumulation would provide a countervoltage large enough to prevent the oxidation-reduction reaction from taking place, and the current would cease. This charge gradient is dissipated by the presence of a salt bridge, which permits the exchange of cations and anions.

The salt bridge contains an inert electrolyte, usually KCl or NH NO , which contains ions that will not react with the electrodes or with the ions in solution. While the anions from the salt bridge (Cl ) diffuse into the solution on the anode side (ZnSO ) to balance out the charge of the newly created Zn ions, the cations of the salt bridge (K ) flow into the solution on the cathode side (CuSO ) to balance out the charge of the sulfate ions left in solution when the Cu ions are reduced to Cu and precipitate onto the electrode. This precipitation process onto the cathode itself can also be called plating or galvanization.

A concentration cell is a special type of galvanic cell. Like all galvanic cells, it contains two halfcells connected by a conductive material, allowing a spontaneous oxidation-reduction reaction to proceed, which generates a current and delivers energy. The distinguishing characteristic of a concentration cell is in its design: the electrodes are chemically identical. For example, if both electrodes are copper metal, they have the same reduction potential.

Therefore, current is generated as a function of a concentration gradient established between the two solutions surrounding the electrodes. The concentration gradient results in a potential difference between the two compartments and drives the movement of electrons in the direction that results in equilibration of the ion gradient. The current will stop when the concentrations of ionic species in the half-cells are equal. This implies that the voltage (V) or electromotive force of a concentration cell is zero when the concentrations are equal; the voltage, as a function of concentrations, can be calculated using the Nernst equation. In a biological system, a concentration cell is best represented by the cell membrane of a neuron. Sodium and potassium cations, and chlorine anions, are exchanged as needed to produce an electrical potential. The actual value depends on both the concentrations and charges of the ions. In this way, a resting membrane potential (V ) can be maintained. Disturbances of the resting membrane potential, if sufficiently large, may stimulate the firing of an action potential.

Analysis of the equations shows us that, for redox reactions with equilibrium constants less than 1 (equilibrium state favors the reactants), the Ecell will be negative because the natural logarithm of any number between 0 and 1 is negative. These properties are characteristic of electrolytic cells, which house nonspontaneous oxidation-reduction reactions. Instead, if the equilibrium constant for the reaction is greater than 1 (equilibrium state favors the products), the Ecell will be positive because the natural logarithm of any number greater than 1 is positive.

These properties are characteristic of galvanic cells, which house spontaneous oxidation-reduction reactions. If the equilibrium constant is equal to 1 (concentrations of the reactants and products are equal at equilibrium), the Ecell will be equal to zero. An easy way to remember this is that Ecell = 0 V for any concentration cell with equimolar concentrations in both half-cells because there is no net ionic equation (both half-cells contain the same ions).

All of the nonrechargeable batteries you own are galvanic cells, also called voltaic cells. Accordingly, because household batteries are used to supply energy to a flashlight or remote control, the reactions in these cells must be spontaneous.

This means that the reaction's free energy is decreasing (ΔG < 0) as the cell releases energy to the environment. By extension, if the free energy change is negative for these cells, their electromotive force (E ) must be positive; the free energy change and electromotive force always have opposite signs.

Standard reduction potentials are also used to calculate the standard electromotive force (emf or E ) of a reaction, which is the difference in potential (voltage) between two half-cells under standard conditions. The emf of a reaction is determined by calculating the difference in reduction potentials between the two half-cells.

When subtracting standard potentials, do not multiply them by the number of moles oxidized or reduced. This is because the potential of each electrode does not depend on the size of the electrode (the amount of material), but rather the identity of the material. The standard reduction potential of an electrode will not change unless the chemical identity of that electrode is changed.

When comparing and contrasting galvanic and electrolytic cells, it is important to keep straight what remains consistent between the two types of cells and what differs. All types of electrochemical cells have a reduction reaction occurring at the cathode, an oxidation reaction occurring at the anode, a current flowing from cathode to anode, and electron flow from anode to cathode. However, electrolytic cells, in almost all of their characteristics and behavior, are otherwise the opposite of galvanic cells.

Whereas galvanic cells house spontaneous oxidation-reduction reactions, which generate electrical energy, electrolytic cells house nonspontaneous reactions, which require the input of energy to proceed. Therefore, the change in free energy for an electrolytic cell is positive. This type of oxidation-reduction reaction driven by an external voltage source is called electrolysis, in which chemical compounds are decomposed. For example, electrolytic cells can be used to drive the nonspontaneous decomposition of water into oxygen and hydrogen gas.