CHEM331 Physical Chemistry Revision 2.0 A Review of the Construction of Electrochemical Cells Electrochemical cells provide us with our first real example of a system which performs non-PV work. The work is associated with a transfer of charge from one electrode of the cell to the other. Generally, an Electrochemical Cell is a system which produces electrical energy using the chemical energy of an oxidation-reduction reaction or can cause an oxidation-reduction reaction to occur by using electrical energy. In the case of a Primary Cell, also known as a Voltaic or Galvanic Cell, the system generates an electric current which spontaneously flows (G < 0) through an external device, thereby "powering" the device. In contrast, work must be done on a Secondary Cell, also known as a Storage Cell, in order to drive a current through the system, thereby causing a non-spontaneous (G > 0) chemical reaction to occur. The consequence of driving the non-spontaneous chemistry forward is the storage of electrical energy as chemical energy within the system. An Electrolytic Cell is typically a secondary cell configured to cause an electrolysis reaction to occur within the system. P age |2 The Lead Storage Battery used in automobiles is an example of a commercially available secondary cell. During discharge, as the battery drives a car's starter, the battery is behaving as a Voltaic Cell. Once the car has started and the alternator kicks in, the battery is being recharged by the alternator and it is behaving as a secondary cell. (Lead Storage Battery) Starter Leads to Battery Leads to Battery Alternator When its electrodes are disconnected from any device, a cell is in an Open Circuit configuration. When the electrodes are shorted with a wire, the cell is Short Circuited. A short circuited Voltaic Cell discharges irreversibly without doing any work, much like a gas expanding against zero pressure does no work. P age |3 It is the purpose of this review to consider the construction and operation of electrochemical cells. Once we have an understanding of their operation, we can then apply a thermodynamic analysis to these cells. The first electrochemical cell constructed was invented by Alessandro Volta, which he described in a communication on 20 March 1800 to Sir Joseph Banks, President of the Royal Society of London. His cell was a Pile of pairs of Zinc and Silver disks separated by paper disks soaked in salt water. With a tall Pile, he could detect a weak electric shock when he touched its two ends. (Volta's Pile) How was Volta's Pile was able to produce an electric shock and more generally, how do electrochemical cells work? Electrochemical cells are built using the chemistry of Oxidation-Reduction reactions. Voltaic Cells use the spontaneity of the underlying Cell Reaction to “drive” the cell so that electrons can be shunted through an external device (lightbulb, etc.). On the other hand, the non-spontaneous Cell Reaction of an electrolytic cell must be “driven” by a generator, primary cell (battery) or other source of electromotive force. As a first step in understanding the operation of a Voltaic Cell, consider an oxidation-reduction reaction that occurs spontaneously. A classic example is provided by the resulting chemical reaction when a strip of Zinc metal is dipped into an aqueous solution of Cupric Sulfate, CuSO4. P age |4 Over time, we observe the disappearance of the bluish color of the Cu2+ ion and note the appearance of a dark coppery platting on the Zinc metal. The Zinc metal also appears to dissolve. Hence, we have the following chemical reaction occurring: Zn(s) + CuSO4(aq) Cu(s) + ZnSO4(aq) In Net Ionic form, this is written as: Zn(s) + Cu2+(aq) Cu(s) + Zn2+(aq) Here we note Zinc is being Oxidized while the Cupric Ion is being Reduced. Electrons are being transferred from the Zinc metal to the Cupric Ion and the system behaves like a shorted battery. P age |5 So, this chemical reaction can be used to construct a Voltaic Cell because, first, the reaction proceeds spontaneously and, second, it involves a transfer of electrons which can potentially be shunted through an external device. In order to construct a Voltaic Cell using this Redox Reaction we must first split the reaction into two Half-Reactions; one half-reaction is associated with the Oxidation and the other the Reduction. Oxidation: Zn(s) Reduction: Cu2+(aq) + 2 e- Zn2+(aq) + 2 eCu(s) Then we must arrange things physically so the two Half-Reactions occur in separate regions of the cell; two separate Half-Cells for the present case. This is done such that the electrons are forced to travel through an external device in order for the Cell Reaction to progress forward. In the present example, we can do this by separating the two reactions into two different beakers. A Zinc electrode is used in the beaker on the left. Over time this electrode will oxidize and produce Zinc ions. Copper metal is used as an electrode on which to plate the Cupric ions in the beaker on the right. Any inert metal that is less Active than Copper, such as Platinum (Pt), Silver (Ag) or Gold (Au), can be used as this electrode. The Zn electrode on the left is referred to as the Anode; it involves the cells's oxidation halfreaction and produces electrons. The Cu electrode on the right is the cathode and involves the cells's reduction half-reaction, consuming electrons. This can be generalized: Anode: Electrode supplying electrons; where oxidation occurs. Cathode: Electrode consuming electrons; where reduction occurs. A problem with our cell construction now presents itself. The cathodic half-cell is producing an excess of positive ions and the anodic half-cell is depleting them. This imbalance within both half-cells is rectified by adding a Salt-Bridge to the Cell. A Salt-Bridge can be constructed using P age |6 a glass tube filled with an inert salt such as KCl in high concentration that employs a porous plug at both ends, a saline soaked piece of paper or cardboard, or a fritted-glass disk. In any case, the salt-bridge is arranged so that inert ions can leak into the half-cells, but gross mixing of the halfcell solutions is prevented. Plugged Glass Tube Salt Bridge Fritted Glass Disk Salt Bridge For example, using a glass-tube construction, where the tube is filled with KCl, in our cell, Clwill leak from the Salt-Bridge into the anodic half-cell so as to counter the build-up of positive ions. As a point of cell nomenclature, the two electrodes of our battery are marked (+) or (-) according to: Cathode ===> (+) Anode ===> (-) This is so we can view our Cell in a more abstract way: P age |7 This “+” and “-“ convention is reversed in an electrolytic cell. Our sketch of the cell above can be shortened into a Cell Diagram, where phase boundaries are denoted with a | and the salt-bridge is denoted by ||. The anode, by convention, is placed on the left-hand side of the Diagram and the cathode on the right. The electrodes are always placed on the outside of the Diagram. For our simple cell, the Cell Diagram is: Zn(s) | Zn2+(aq) || Cu2+(aq) | Cu(s) If our cell is a Voltaic Cell, then it is capable of doing work on an external device. In other words, it is capable of delivering electrical energy to the device. A system which delivers electrical energy is referred to as a Seat of Electromotive Force (EMF). Unfortunately a real cell is not a true EMF. Suppose a Voltaic Cell presents two electrodes, or terminals, each with an electric potential, measured in volts, of and '. Then, the Terminal Voltage of the cell is simply the measured Potential Difference across the cell's terminals: TV = ' - It is observed that TV decreases slightly as the current drawn by an external device, or load, increases. This means the cell acts as an ideal EMF in series with a small resistor; the cell's Internal Resistance. In the limit that the current draw is zero, in other words if the cell is operated in an open circuit configuration, the cell's EMF will equal its terminal voltage: P age |8 = TV when I 0 This, then, is the measured Cell Potential. In practical terms, the Cell Potential can be measured using a Voltmeter with a very high internal impedance. If the impedance is high enough, the current flow through the meter is sufficiently low that the cell is effectively operating as an Open-Circuit. Thus, we have: = Voltage across the Meter when I 0 Now to an incredibly subtle point. The possible work which can be performed by the cell is related to its cell potential. The maximum work obtainable will only be available when the cell is being operated reversibly. That is, the cell reaction must take place readily in either direction. If the cell is short-circuited, the reaction should proceed in its spontaneous direction; and if an external potential is applied which overrides the natural cell potential, then the reaction should just as easily proceed in the opposite direction. The reversible electrochemical cell is thus one which may be held in a state of dynamic balance by application of an external counterpotential just equal to . For example, in the case of the Daniel cell is about 1.1 V if m1 = m2 = 1. External application of an opposing 1.1 V will just prevent reaction from occurring; a slightly smaller opposing potential will allow the cell reaction to occur as written, and a slightly larger opposing potential will make the reaction go in the opposite direction. The customary way of determining for a cell is, in fact, to find that opposing emf which puts the cell in balance. The procedure thus defines as the reversible emf of the cell. Arthur W. Adamson A Textbook of Physical Chemistry As Bromberg notes, "As the resistance [of the external circuit] is made larger and larger, the reaction proceeds more and more slowly. In the limit as the resistance gets infinitely large, the reaction proceeds at an infinitesimally low rate and for all practical purposes can be considered reversible." (Physical Chemistry, 2nd Ed.; J. Philip Bromberg) Thus, the cell potential measured with the voltmeter is, for practical purposes, rev. Bromberg, however, does sound a caution: That a process proceeds at an infinitesimally low rate is generally only a necessary but not a sufficient condition for reversibility. That this is not sufficient can be seen by considering the expansion of an ideal gas into a vacuum through an infinitesimally small pinhole. The process proceeds at and infinitesimally low rate, but it is still completely irreversible; no work is done, P age |9 since there is no opposing force. The case of a battery discharging through a very large resistor is a special case in that a potential drop is automatically established in the resistor by the current flow, and work is done. One conceptual difficulty in using a large resistor to establish a reversible process is that the direction of the process cannot be reversed with just a resistor. [There is] an arrangement whereby the direction can be reversed using potentiometers and voltage sources in opposition to the battery. J. Philip Bromberg Physical Chemistry, 2nd Ed. So, our cell's measured potential will provide us with the reversible EMF for the cell. Now, if, for our example Zn|Zn2+||Cu2+|Cu cell, the aqueous solutions are prepared such that the electrolytic solutions are in their Standard State (Unit Activity; 1M concentration and Ideal behavior), then the Standard Potential is found by measurement to be 1.10 Volts and is denoted as Cello. By convention, the Standard Half Cell Potential of electrochemical half-cells is measured relative to the Standard Hydrogen Electrode. The Standard Hydrogen Electrode is built using the following Half-Reaction: H2(fugacity = 1 bar) By convention, we take SHE = 0 Volts. (A Standard Hydrogen Electrode) 2 H+(a = 1M) + 2 e- P a g e | 10 (A Simple Schematic of a SHE) Each Half-Cell in our example cell above can be compared to a Standard Hydrogen Electrode (SHE) and its associated cell potential measured. Zn(s) | Zn2+(a = 1M) || SHE Cello = 0.762 Volt SHE || Cu2+(a = 1M) | Cu(s) Cello = 0.339 Volt P a g e | 11 The measured cell potential can be formally split into an anodic and cathodic contributions. Cello = oxo + redo For our Zinc | Zinc Ion half-cell, we then have: Cello = Zn|Zn2+,oxo + SHE or Zn|Zn2+,oxo = 0.762 Volt since SHE = 0. Likewise, for our Copper | Cupric Ion half-cell, we have: Cello = SHE + Cu|Cu2+,redo or Cu|Cu2+,redo = 0.339 Volt The cell potential for any cell is then simply the sum of the cell potentials for the two half-Cells. For our example: cello = Zn|Zn2+,oxo + Cu|Cu2+,redo = 0.762 V + 0.339 V = 1.10 Volt Half-Cell potentials are always Tabulated as Cathodic Reactions. So, the Electrochemical Potentials for our half cells would be listed as: Cu2+(aq) + 2 e- Cu(s) Cu|Cu2+,redo = 0.339 Volt Zn2+(aq) + 2 e- Zn(s) Zn|Zn2+,redo = - 0.762 Volt More extensive tabulations of half-cell potentials can be found in most reference texts. We now turn our attention to Electrolytic Cells. As mentioned above, electrolytic cells must be electrically driven. They frequently involve an electrolytic break-down of the cell system. For instance, the electrolysis of molten NaCl in a Down's Cell generates liquid Na and gaseous Cl2. 2 NaCl(l) Here, the underlying half-reactions are: 2 Na(l) + Cl2(g) P a g e | 12 Na+ + e2 Cl- Na Cl2 + 2 e- (Cathode is a Steel Electrode) (Anode is a Graphite Electrode) This is useful if the electrolytic breakdown products are commercially desirable. Many commercial cells are available for the electrolysis of Water, Bauxite to form Aluminum via the Hall Process, or electroplating of Chromium, Sliver or other metals. Hall Process P a g e | 13 2 Al2O3 (l) + 3 C(s) 4 Al(l) + 3 CO2(g) With this basic understanding of the operation of electrochemical cells under our belt, we can now turn to a thermodynamic analysis of these systems. Our jumping off point will be the reversible cell potential whose measurement was outlined above. P a g e | 14 Appendix - Batteries In the common parlance, we generally refer to Primary Cells, alternatively known as Voltaic Cells, as Batteries. Historically, "batteries" were constructed from a number of Leyden Jars ganged together as a "Battery of Jars". Leyden Jar Battery of Leyden Jars A Leyden Jar is a glass jar lined with a metal foil and fitted with a metal rod that is used to store electricity, much as a capacitor stores electricity. A battery of jars will then allow for a greater storage capacity. This increase of storage capacity is leveraged in modern batteries, where individual Voltaic Cells are ganged together serially to produce a "battery" of greater potential. A standard Lead Storage Battery is really a series of Voltaic Cells ganged together as a "battery". Pb(s) | PbSO4(s) | H2SO4(aq) | PbSO4(s) | PbO2(s) | Pb(s) P a g e | 15 Each cell that makes up the Lead Storage Battery has an approximate potential of about 2 V. So, six cells are needed to construct a 12 V car battery; all six ganged together in series. In modern usage, the term "battery" generally refers to both a battery of Voltaic Cells and a single Voltaic Cell. P a g e | 16 Appendix - Sign Conventions A short note concerning the signs (+ or -) with which we label the Anode and Cathode of an electrochemical cell. By convention, Current is defined as the direction of flow of positive charge; this is opposite the direction of electron flow. The current naturally flows from a Higher (“+”) Potential to a Lower (“-“) Potential. Hence, for a Voltaic Cell, the Cathode gets a “+” designation and the Anode gets a “-“. Within a Voltaic Cell, chemical energy is converted to electrical energy. This effectively “pumps” positive charge from a low to a high potential. For an Electrolytic Cell, the cathode is sitting at a lower potential, so the Cathode gets a “-“ designation and the Anode a “+”. An external power source is required to “pump” the current from the cathode to the anode. This sign convention is also an aid to indicate how Voltaic and an Electrolytic Cells should be connected. Suppose you wish to drive an Electrolytic (Secondary) Cell with a Voltaic (Primary Cell). In this case you connect the two “+” terminals together and the two “-“ terminals together. This will ensure the all the terminals are connected so that electrons will cycle properly through the two systems. It also allows us to correctly place several cells in Series or in Parallel. Connecting Voltaic Cells in series will increase the voltage; two cells connected in series will have double the voltage of a single cell. P a g e | 17 Connecting cells in parallel will increase the cell capacity but not the volatage. Historical Origin of the Sign Convention An Amber rod, after being rubbed with Cat’s Fur, will pick-up bits of hair, etc. A Glass rod, when rubbed with Silk, will do something similar. Further, touching bits of metal with either the “charged” amber or glass will cause the bits to repel each other. However, a bit of metal touched by a “charged” amber rod will attract a bit of metal touched by the “charged” glass rod. Amber = Gr. (electron) Benjamin Franklin explained these observations with a One Fluid Theory of Electric Charge. The Electric Fluid could flow from one object to another. So, when an amber rod is rubbed with cat’s fur, the electric fluid flows from the rod to the fur, leaving the rod deficient (-) of electric fluid and the fur with an excess (+). In the case of the glass rod, the fluid flows from the silk to the glass. Now the glass rod has an excess (+) of electric fluid and the silk a deficit (-). P a g e | 18 This electric fluid can then flow from the rods to bits of metal. Metal bits with an excess of electric fluid (+) will repel each other. Likewise for bits of metal with a deficiency of electric fluid (-). However, a bit of metal with an excess will be attracted to a bit of metal with a deficiency. We now know that “charge” flow is in the form of a flow of electrons. So, when amber is rubbed by cat’s fur, electrons flow from the fur to the rod. To maintain Franklin’s sign convention, we then designate the sign of the charge of an electron as “-“. As the electrons flow from the fur to the rod, the rob becomes more negative (-) and the fur more positive (+). The sign convention for a Voltaic Cell, then translates as: Anode: Electrode supplying electrons (Has a deficiency of the Electric Fluid) => Stamped with a "-" Cathode: Electrode consuming electrons (Has an excess of the Electric Fluid) => Stamped with a "+" Is this ideal? No. But it is consistent. P a g e | 19 If we had Franklin's choice to make over again today, we would probably reverse his signs to avoid the semantic difficulty of having negative carriers of a positive fluid. In any case, the choice of + and - is consistent throughout the science of electricity. When we say that the copper wire attached to the cadmium electrode in the Weston cell [Anode] is more negative that the copper wire attached to the mercury electrode [Cathode], we mean that it contains an excess of the same kind of electricity found in amber rubbed with cat's fur. Walter J. Moore Physical Chemistry, 4th Ed.