Ap Chemistry, Chapter 20, Electrochemistry

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Section 20.1 • • • • • • •

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In an oxidation-reduction reaction electron transfer occurs between a reducing agent and an oxidizing agent. In any electron transfer reaction: One reactant is oxidized and one is reduced. The extent of oxidation and reduction must balance. The oxidizing agent (the chemical species causing oxidation) is reduced. The reducing agent (the chemical species causing reduction) is oxidized. Oxidation numbers can be used to determine whether a substance is oxidized or reduced. An element is oxidized if its oxidation number increases. The oxidation number decreases in reduction. All equations for oxidation-reduction reactions must be balanced for both mass and charge. The same number of atoms appear in the products and reactants of an equation, and the sum of electric charges of all the species on each side of the equation arrow must be the same. Charge balance guarantees that the number of electrons produced in oxidation equals the number of electrons consumed in reduction. The half-reaction method is a procedure that involves writing separate, balanced equations for the oxidation and reduction processes called halfreactions. The equation for the overall reaction is the sum of the two half-reactions, after adjustments have been made (if necessary) in one or both half-reaction equations so that the numbers of electrons transferred from reducing agent to oxidizing agent balance. When balancing equations for redox reactions in aqueous solution, it is sometimes necessary to add water molecules (H2O) and either H+ (aq) in acidic solution or OH- (aq) in basic solution to the equation.

Section 20.2 • •

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Devices that use chemical reactions to produce an electric current are called voltaic cells or galvanic cells. All voltaic cells use product-favored redox reactions composed of an oxidation and a reduction. The cell is constructed so that electrons produced by the reducing agent are transferred through an electric circuit to the oxidizing agent. Chemical energy is converted to electrical energy in a voltaic cell. The opposite process, the use of electric energy to effect a chemical change, occurs in electrolysis. Electrochemistry is the field of chemistry that considers chemical reactions that produce or are caused by electrical energy. A salt bridge allows cations and anions to move between the two half-cells connected by the bridge.

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The electrolyte chosen for the salt bridge should contain ions that will not react with chemical reagents in both half-cells. In all electrochemical cells the anode is the electrode at which oxidation occurs. The electrode at which reduction occurs is always the cathode. A minus sign can be assigned to the anode in a voltaic cell, and the cathode is marked with a positive sign. The chemical oxidation occurring at the anode, which produces electrons, gives it a negative charge. Electric current in the external circuit of a voltaic cell consists of electrons moving from the negative to the positive electrode. In all electrochemical cells, electrons flow in the external circuit from the anode to the cathode. Not all half-reactions involve a metal as a reactant or product. With the exception of carbon in the form of graphite, most nonmetals are unsuitable as electrode materials because they do not conduct electricity. It is not possible to make an electrode from a gas, a liquid, or a solution. Ionic solids do not make satisfactory electrodes because the ions are locked tightly in a crystal lattice, and these materials do not conduct electricity. In situations where reactants and products cannot serve as the electrode material, an inert electrode must be used. Such electrodes are made of materials that conduct an electric current but that are neither oxidized nor reduced in the cell. The hydrogen electrode is particularly important in the field of electrochemistry because it is used as a reference in assigning cell voltages. When using shorthand for simplifying cell descriptions, the anode and information with respect to the solution with which it is in contact are always written on the left. A single vertical line (|) indicates a phase boundary, and double vertical lines (||) indicate a salt bridge. For example: Cu(s)|Cu2+(aq, 1.0 M)||Ag+(aq, 1.0 M)|Ag(s)

Section 20.3 • •

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Cells being compact or robust are high priorities for most applications. In most situations, it is also important that the cell produce a constant voltage. Attempting to draw a large current results in a drop in voltage because the current depends on how faster ions in solution migrate to the electrode. Ion concentrations near the electrode become depleted if current is drawn rapidly, resulting in a decline in voltage. The amount of current that can be drawn from a voltaic cell depends on the quantity of reagents consumed. A voltaic cell must have a large mass of reactants to produce current over a prolonged period. In addition, a voltaic cell that can be recharged is attractive. Recharging a cell means returning the reagents to their original sites in the cell. Batteries can be classified as primary and secondary. Primary batteries use redox reactions that cannot be returned to their original state by recharging, so when the reactants are consumed, the battery is “dead” and must be discarded. Secondary batteries are often called storage batteries or rechargeable batteries. The reactions in these batteries can be reversed; thus, the batteries can be recharged.

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If you buy an inexpensive flashlight battery or dry cell battery, it will probably be a modern version of a voltaic cell invented by George LeClanché in 1866. Zinc serves as the anode, and the cathode is a graphite rod placed down the center of the device. These cells are often called “dry cells” because there is no visible liquid phase. However, the cell contains a moist paste of NH4Cl, ZnCl2, and MnO2. The moisture is necessary because the ions present must be in a medium in which they can migrate from one electrode to the other. LeClanché cells are widely used because of their low cost, but they have several disadvantages. If current is drawn from the battery rapidly, the gaseous products cannot be consumed rapidly enough, so the cell resistance rises and the voltage drops. In addition, the zinc electrode and ammonium ions are in contact in the cell, and these chemicals react slowly. These voltaic cells cannot be stored indefinitely. When the zinc outer shell deteriorates, the battery can leak acid and perhaps damage the flashlight or other appliance in which it is contained. Alkaline cells can be purchased for a little more money, generating current up to 50% longer than a dry cell of the same size. Alkaline cells use the oxidation of zinc and the reduction of MnO2 to generate a current, but NaOH or KOH is used in the cell instead of the acidic salt NH4Cl. They have the further advantage that the cell potential does not decline under high current loads because no gases are formed. An automobile battery—the lead storage battery—is probably the bestknown rechargeable battery. The 12-V version of this battery contains six voltaic cells, each generating 2.04 V. It can produce a large initial current, an essential feature to start an automobile engine. The anode of a lead storage battery is metallic lead. The cathode is also made of lead, but it is covered with a layer of compressed, insoluble lead (IV) oxide, PbO2. The electrodes, arranged alternately in a stack and separated by thin fiberglass sheets, are immersed in aqueous sulfuric acid. When current is generated, sulfuric acid is consumed and water is formed. Because water is less dense than sulfuric acid, the density of the solution decreases during this process. A lead storage battery is recharged by supplying electrical energy. The PbSO4 coating the surfaces of the electrodes is converted back to metallic lead and PbO2, and sulfuric acid is regenerated. The lifetime of a lead storage battery is limited, however, because the coatings of PbO2 and PbSO4 flake off of the surface and fall to the bottom of the battery case. Nickel-cadmium (“Ni-cad”) batteries are lightweight and rechargeable. The chemistry of the cell utilizes the oxidation of cadmium and the reduction of nickel (III) oxide under basic conditions. As with the lead storage battery, the reactants and products formed when producing a current are solids that adhere to the electrodes. Ni-cad batteries produce a nearly constant voltage. However, their cost is relatively high and there are restrictions on their disposal because cadmium compounds are toxic and present an environmental hazard.

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The reactants in fuel cells can be supplied continuously to the cell from an external reservoir, eliminating the limitation of a voltaic cell not being able to generate a current once the reactants are completely consumed.

Section 20.4 •

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Electrons generated at the anode of an electrochemical cell move through the external circuit toward the cathode, and the force needed to move the electrons arises from a difference in potential energy of electrons at the two electrodes. This difference in potential energy per electrical charge is called the electromotive force or emf, for which the literal meaning is “force causing electrons to move”. Emf has units of volts (V); one volt is the potential difference needed to impart one joule of energy to an electric charge of one coulomb (1 J=1 V×1 C). One coulomb is the quantity of charge that passes a point in an electric circuit when a current of one ampere flows for one second (1 C=1 A×1 s). The emf of a voltaic cell is equated with the cell voltage, Ecell, which can be measured. So that we can later compare the potential of one half-cell with another, we measure all cell voltages under standard conditions: Reactants and products are present in their standard states. Solutes in aqueous solution have a concentration of 1.0 M. Gaseous reactants or products have a pressure of 1.0 bar. A cell potential measured under these conditions is called the standard potential and is denoted by E°cell. Unless otherwise specified, all values of E°cell refer to measurements at 298 K (25 °C). In a voltaic cell, electrodes always flow from the anode (negative electrode) to the cathode (positive electrode). That is, electrons move from the electrode of higher potential energy to the one of lower potential energy. E°cell=E°cathode-E°anode Here, E°cathode and E°anode are the standard reduction potentials for the half-cell reactions that occur at the cathode and anode, respectively. If we have values for E°cathode and E°anode, we can calculate the standard potential, E°cell, for a voltaic cell. When the calculated value of E°cell is positive, the reaction is predicted to be product-favored as written. Conversely, if the calculated value of E°cell is negative, the reaction is predicted to be reactant-favored. The reaction will be product-favored in a direction opposite to the way it is written. If we measure E°cell and know either E°cathode or E°anode, we can calculate the other value. This value would tell us how one half-cell reaction compares with others in terms of relative oxidizing or reducing ability. All potentials are for reduction reactions. The more negative the value of the reduction potential, E°, the less likely the half-reaction will occur as a reduction, and the more likely the reverse halfreaction will occur (as an oxidation).

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If a reaction is product-favored in one direction, it is reactant-favored in the opposite direction. Electrochemical potentials depend on the nature of the reactants and products and their concentrations, not on the quantities of material used. Therefore, changing the stoichiometric coefficients for a half-reaction does not change the value of E°. Tables or “ladders” of standard reduction potentials are immensely useful. They allow you to predict the potential of a new voltaic cell, provide information that can be used to balance redox equations, and help predict which redox reactions are product-favored. The standard reduction potentials for half-reactions were obtained by measuring cell potentials. It makes sense, therefore, that these values can be combined to give the potential of some new cell.

Section 20.5 • • • • •

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Electrochemical cells seldom operate under standard conditions in the real world. Even if the cell is constructed with all dissolved species at 1 M, reactant concentrations decrease and product concentrations increase in the course of the reaction. Based on both theory and experimental results, it has been determined that cell potentials are related to concentrations of reactants and products, and to temperature, as follows: E=E°-RTnFlnQ In this equation, known as the Nernst equation, R is the gas constant, T is the temperature (K), and n is the number of moles of electrons transferred between oxidizing and reducing agents (as determined by the balanced equation for the reaction). The symbol F represents the Faraday constant (9.6485338×104 C/mol). One Faraday is the quantity of electric charge carried by one mole of electrons. The term Q is the reaction quotient, an expression relating the concentrations of the products and reactants raised to an appropriate power as defined by the stoichiometric coefficients in the balanced, net equation. Using 298 K as the temperature gives: E=E°-0.0257nlnQ at 25 °C In essence, this equation “corrects” the standard potential E° for nonstandard conditions or concentrations. In the real world, using a hydrogen electrode in a pH meter is not practical. The apparatus is clumsy, it is anything but robust, and platinum (for the electrode) is costly. Common pH meters use a glass electrode, so-called because it contains a thin glass membrane separating the cell from the solution whose pH is to be measured. Common pH meters give a direct readout of pH. Collectively, the electrodes used to measure ion concentrations are known as ion-selective electrodes.

Section 20.6 • • • •

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The first law of thermodynamics states that the internal energy change in a system is related to heat and work: ∆E=q+w This also applies to chemical changes that occur in a voltaic cell. As current flows, energy is transferred from the system (the voltaic cell) to the surroundings. In a voltaic cell, the decrease in internal energy in the system will manifest itself ideally as electrical work done on the surroundings by the system. In practice, however, some heat evolution by the voltaic cell is usually observed. The maximum work done by an electrochemical system (ideally, assuming no heat is generated) is proportional to the potential difference (volts) and the quantity of charge (coulombs): wmax=nFE In this equation, E is the cell voltage and nF is the quantity of electric charge transferred from anode to cathode. The free energy change for a process is, by definition, the maximum amount of work that can be obtained. Because the maximum work and the cell potential are related, E° and ∆G° can be related mathematically (taking care to assign signs correctly). The maximum work done on the surroundings when electricity is produced by a voltaic cell is +nFE, with the positive sign denoting an increase in energy in the surroundings. The energy content of the cell decreases by this amount. Thus, ∆G for the voltaic cell has the opposite sign. ∆G=-nFE Under standard conditions, the appropriate equation is: ∆G°=-nFE° This expression shows that, the more positive the value of E°cell, the larger and more negative the value of ∆G° for the reaction. That is, the farther apart the half-reactions on the potential ladder, the more strongly product-favored the reaction. When a voltaic cell produces an electric current, the reactant concentrations decrease and the product concentrations increase. The cell voltage also changes; as reactants are converted to products, the value of Ecell decreases. Eventually the cell potential reaches zero, no further net reaction occurs, and equilibrium is achieved. lnK=nE°0.0257 at 25 ℃ Where K is the equilibrium constant.

Section 20.7 • •

The electrolysis of water is used to illustrate stoichiometry and gas laws and to show how an energetically disfavored reaction can be carried out. Electroplating is another example of electrolysis. Here, an electric current is passed through a solution containing a salt of the metal to be plated. The

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object to be plated is a cathode. When metal ions in solution are reduced, the metal deposits on its surface. All electrolysis experiments are the same. The material to be electrolyzed, either a molten salt or a solution, is contained in an electrolysis cell. As was the case with voltaic cells, ions must be present in the liquid or solution for a current to flow. The movement of ions constitutes the electric current within the cell. The cell has two electrodes that are connected to a source of DC (direct-current) voltage. If a high enough voltage is applied, chemical reactions occur at the two electrodes. Reduction occurs at the negatively charged cathode, with electrons being transferred from that electrode to a chemical species in the cell. Oxidation occurs at the positive anode, with electrons from a chemical species being transferred to that electrode. Water is an electroactive substance; that is, it can be oxidized or reduced in an electrochemical process. The concentration of electroactive species in solution must be taken into account when discussing electrolyses. The potential at which a species in solution is oxidized or reduced depends on concentration. Unless standard conditions are used, predictions based on E° values are merely qualitative. In addition, the rate of a half-reaction depends on the concentration of the electroactive substance at the electrode surface. At a very low concentration, the rate of the redox reaction may depend on the rate at which an ion diffuses from the solution to the electrode surface.

Section 20.8 • • • •

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The number of moles of electrons consumed or produced in an electron transfer reaction is obtained by measuring the current flowing in the external electric circuit in a given time. The current flowing in an electrical circuit is the amount of charge (in units of coulombs, C) per unit time, and the usual unit for current is the ampere (A). Current, I amperes, A=electric charge coulombs, Ctime seconds, s The current passing through an electrochemical cell and the time for which the current flows are easily measured quantities. Therefore, the charge (in coulombs) that passes through a cell can be obtained by multiplying the current (in amperes) by the time (in seconds). Knowing the charge, and using the Faraday constant as a conversion factor, we can calculate the number of moles of electrons that passed through an electrochemical cell. In turn, we can use this quantity to calculate the quantities of reactants and products.