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Chapter 7 | Electrochemistry

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Chapter 7 | Electrochemistry C h a p t e r 7 Electrochemistry “There is a powerful agent, obedient, rapid, easy, which conforms to every use, and reigns supreme on board my vessel. Everything is done by means of it. It lights, warms, and is the soul of my mechanical apparatus. This agent is electricity.” — Jules Verne, 1870, in Twenty Thousand Leagues under the Sea, translated by Gerard Harbison C o n c e p t s The first clear human records of bioelectricity are inscribed on 5 th dynasty tombs in Egypt, dating from about 2400 BCE. These carvings show depictions of the electric catfish, Malaptererus electricus , native to the Nile. Our first encounter with bioelectric- ity, therefore, was likely painful; these fish can deliver jolts of up to 350 V. Somewhat later, mysterious earthen jars found in middle-eastern archaeological sites may have been the first chemical batteries, possibly used to do electroplating. However, systematic study of the interaction of electric currents with biological organisms had to wait until the 18 th century and the famous experiments of Luigi Galvani, who showed that electric shocks applied to frog legs caused the muscles to contract, and inspired Mary Shelley’s novel Frankenstein, and later an entire genre of horror movies. Galvani’s compatriot, Alessandro Volta, was one of the first to appreciate that, while biological organisms generate and are influenced by electricity, electric phenomena are not exclusive to life, and can be generated by an apparatus as simple as two disks of different metal in contact with each other and with an ionic solution. These simple electrochemical cells possess a characteristic potential. Under standard conditions, the electrochemical potential is an unvarying property of a specific pair of metals or other chemical substances, one of which is oxidized and one reduced, and it is proportional to the standard free energy of the redox (reduction oxidation) reaction. There is in fact an identity between the electri- > cal work done by an electrochemical cell and the free energy. The Nernst equation is the second link between thermodynamics and electricity, and relates the concentrations of chemical compounds at equilibrium and their electrochemical potential under nonstandard conditions. This link underpins the generation of bioelectrical potentials; cells pump ions across cell membranes, leading to electrical potentials, which are in turn sustained by equilibria with ion concentration gradients across these membranes. Biological organisms do not merely do chemistry; they also do electrochemistry. Applications The large voltages electric eels and catfish produce are generated by stacking literally thousands of cell membranes, each of which individually creates a potential of the order of 100 mV. The spectacular (one might even say shocking) voltages these electric fishes create are a bizarre evolutionary adaptation of a much more general phenomenon: the 238 Basic Electricity | 239 membrane potential. All cells carry membrane potentials. These potentials are the foun- dation of nerve transmission, and also drive the transport of most chemical compounds across biological membranes. Frogs, seaweed, and other organisms that live in contact with water have semiper- meable skins. Water and some ions and small molecules pass through the skins; macro- molecules generally do not. The frog or the seaweed can selectively concentrate certain molecules inside and selectively exclude or excrete other molecules. How do they do it? If a molecule can easily pass through the skin, how can the inside concentration be main- tained at a value that is different from the outside concentration, and still be consistent with thermodynamics? The answer is to ensure that the free-energy change for transport- ing the molecule inside is negative. For example, the presence of a protein inside seaweed that strongly binds the iodide ion ensures that the iodide concentration in the seaweed is always higher than in the seawater. If the concentration of free iodide is the same inside and outside, the bound iodide would account for the concentrating effect of the seaweed. This effect, known as passive transport , does not depend on whether the seaweed is alive or dead. Similarly, metabolism is not involved in the transport of ligands like O 2 through the walls of the alveoli to bind to macromolecules like hemoglobin in the blood. Cells, however, also perform active transport . A number of different kinds of ion pumps, of which the most important is the sodium potassium ATPase, actively transport > ions across cell membranes, using the chemical energy provided by ATP hydrolysis to over- come unfavorable electrical and chemical potential gradients. The negative potential across the cell membrane allows positive ions such as Ca2+ and Mg2+ to accumulate by simple equilibration; it can also drive the transport of other, sometimes uncharged molecules using specialized membrane proteins such as symporters and antiporters. The electrical potential itself is exquisitely sensitive to the movement of small numbers of ions, and can under the right circumstance change rapidly, allowing the phenomenon of nerve conduction. It can also be brought into and out of equilibrium with much more robust ion concentration gradients, allowing long-term maintenance of stable cell potentials. Even more fundamentally, the processes of respiration and photosynthesis drive hydro- gen ions across the cell membranes of bacteria and the inner membranes of mitochondria and chloroplasts. This gradient of potential and of hydrogen ion concentration is, in turn, used to drive the energetically unfavorable synthesis of ATP from ADP and an inorganic phosphate. Thus the transduction of energy in all but a few organisms uses electrical transmembrane potentials as intermediates. Finally, humans have learned to use the Nernst equation to build sensors to convert chemical concentrations of oxidizable or reducible molecules, such as glucose, into electrical potentials, and thus build sensitive chemical sensors that allow rapid and reliable measure- ments of concentration of single chemical compounds in chemically complex mixtures such as blood; this is the basis of the glucose meters used in management of diabetes. Development of electrochemical sensors is an important contemporary area of applied chemical research. Basic Electricity The base electrical SI unit is the ampere or amp (A), which is technically defined as the electrical current which, passing through two infinitely long parallel wires a meter apart, gives a force between the wires of 2 * 10-7 N per meter of length. The amp is really not a fundamental unit, however; rather, it corresponds to a current or flow of electrical charge Q , which can be expressed as a differential: dQ I = . (7.1) dt The SI unit of electrical charge is the coulomb (C): 1 A = 1 C s -1 . 240 Chapter 7 | Electrochemistry The smallest known quantity of charge on a free particle is the charge on the electron, which is often given the special abbreviation e. This charge has been measured to high accuracy; the best current estimate is 1.60217656 * 10-19 C. Even though the electron is a negatively charged particle, e is defined as a positive quantity; the charge on an electron, strictly speaking, is therefore - e . Ions have charges Z which are integer multiples of e ; the charge on a Mg2 + ion, for example, is Ze = 2e. What about a mole of ions, instead of 1 ion? If a single ion has a charge of e (in other = = = -1 words, Z 1), the charge of a mole of ions, Qm NAe 96485.3 C mol . T h i s q u a n t i t y of charge is given a special designation, the Faraday constant, or F . Just as moving a mass in the Earth’s gravity requires work, so does moving charge in an electrical potential. The SI unit of electrical potential is the volt (V). 1 joule of work is required to bring a charge of one coulomb from an infinitely distant point (which is assumed to have a potential of zero) to a point with an electrical potential of 1 V. In other = words, wE -QV. Electrical potential is a state variable, as is charge, and therefore electrical work wE , unlike mechanical work, is a state variable. We can also define electric power P as electrical work done per second: dw P = E . (7.2) dt = = Combining this with wE QV a n d E q . 7 . 1 , w e o b t a i n P VI. The SI unit of power is the watt (W). Capacitance and Electrical Neutrality Just as a mass carries with it its own gravitational field, so a charge creates an electrical potential around it. For example, walking across a carpet in your socks rubs some electrons onto you from the carpet, or onto the carpet from you, so that you become charged up to a potential of perhaps thousands of volts, enough to cause sparks when you touch an object at a different potential and to give you a shock. It is truly ‘shocking’ how few electrons it takes to give you a potential of thousands of volts. The quantity that determines the potential on an object per unit of charge it carries is the capacitance ( C ): C = Q V . The SI unit of capacitance is the farad (F); as you might expect, > 1 F = 1 C 1 V. Calculating capacitances of real objects is beyond the scope of this book, > but a simple formula gives the capacitance (actually, the self-capacitance) of a conducting = sphere: C 4pe0r, w h e r e r is the radius of the sphere, and e0 is the electric constant: = -12 -1 e0 8.854187817620 * 10 F m . A little math indicates that the capacitance of a liter of a solution of an electrolyte in water, in a round flask that occupies a sphere of radius 0.062 m, is 6.9 * 10-12 F.
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