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Introduction

When we think about the force of gravity, and the spontaneous tendency for a stream to flow or a ball to roll downhill, it is convenient to regard it as a tendency for the water or the ball to go from a region of high to low potential energy. Only when such a drop in potential is possible can useful work be obtained from the process. The attractive force that the Earth exerts on a ball of mass m is F = mg, in which g is the gravitational constant. If we lift the ball to a height h above some starting level, we give it an extra potential energy of Ep = mgh. The ball can convert this potential energy to kinetic energy of motion by rolling downhill to the original level, as represented on the next page. Spontaneous motion occurs from a region of high potential to one of low potential. The same language is useful in studying chemical reactions. We know that a spontaneous chemical reaction at constant overall temperature and pressure is one that leads to a decrease in free energy, G. The combination of hydrogen with oxygen to form water is highly spontaneous, and can be explosively fast:

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Introduction

We can think of this reaction as a process in which the atoms of hydrogen and oxygen move from a state of high chemical potential (H2 and 02 molecules) to a state of lower chemical potential (molecules of water vapor). It is reasonable to think of the free energy per mole of a substance as its chemical potential, and to regard a spontaneous chemical reaction as a rolling of atoms down a chemical potential "slope". The free energy given off in a spontaneous process then is just the change in potential (AG per mole) times the amount of substance undergoing the change (number of moles). In equation form the reaction may be written as follows free energy emitted = change in potential x amount of reaction For the water-vapor reaction, the free energy change per mole of water vapor formed is -54.64 kcal mole-1 H2O. This is the chemical potential drop during the water reaction. If fifty moles of water vapor are produced, then the total free energy given off is DG0 = (-54.64 kcal mol-1) (50 moles) = -2732 kcal In the language of gravitation, this amounts to rolling 50 balls down a 54.64 kcal hill. The concept of a potential of some kind to explain why spontaneous processes take place is a useful one

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Free Energy and Escaping Tendency

Free energy also is a measure of escaping tendency, as the experiment at the bottom left illustrates. Ether and water will not mix; they are mutually insoluble because the polar water molecules can form much stronger interactions by separating from the nonpolar ether molecules into their own phase. If we shake water and ether together in a flask, they divide into two layers upon standing. Iodine crystals are soluble to a limited extent in both ether and water. If we add a small amount of iodine to the ether phase, some of the deep violet color slowly will appear in the water phase as a brown coloration, and if we add iodine to the water, some of it will diffuse into the ether. The free energy per mole, or chemical potential, of a substance in a mixture depends on its concentration; The higher the concentration, the higher the chemical potential. The spontaneous tendency of molecules to diffuse from regions of high concentration to more dilute regions is another example of the tendency to move from high to low potential. In the ether-water experiment, if iodine is added to the ether, its chemical potential in ether initially is higher than in water; hence iodine molecules migrate from ether to water until their chemical potential or free energy per mole is the same in both phases. When this condition is reached; no further change in free energy is produced by moving a molecule of I2 from one phase to the other, D G = O for the transfer, and equilibrium exists

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Free Energy and Escaping Tendency

Because chemical potential or molar free energy determines when a substance will move from one chemical region to another, it often is referred to as an escaping tendency. When I2 is concentrated in the ether layer, it has a high free energy per mole, or a high escaping tendency. If the escaping tendency of I2 in water is lower because the concentration there is low, then iodine will diffuse from ether to water until its escaping tendencies in the two phases are the same. This relationship between free energy and escaping tendency is especially helpful in understanding some of the properties of solutions, and these are the subject of the first part of this chapter. lodine molecules will partition themselves between the ether and water layers until their molar free energy, or escaping tendency, is the same in each layer

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Solutions and Colligative Properties

Liquids are held together by van der Waals attractions, dipole forces if the molecules are polar, hydrogen bonds, and electrostatic attractions between ions of a molten salt. We will be concerned mainly with molecular liquids such as water, in which hydrogen bonds and van der Waals and dipole forces are the most important factors. Not all molecules in a liquid move with the same speed. In general, the higher the temperature, the faster they move; but the molecules in a liquid have a range of speeds rather than one uniform speed. As molecules collide with one another they gain and lose energy, but the liquid as a whole maintains a velocity distribution of the type shown below. Increasing the temperature simply shifts the distribution maximum to higher speeds. Go on to the next page to see this animated.

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Solutions and Colligative Properties

At any temperature, some of the molecules in a liquid will be moving so fast when they encounter the liquid-gas interface that they keep right on going into the gas phase as vapor. Most of the molecules of liquid have too little energy, and are pulled back from the interface into the liquid by the attractions of their neighbors. The overall free energy per mole of liquid rises as the temperature increases, and can be thought of as an average escaping tendency of molecules from the liquid. At the same time, molecules in the vapor above the liquid also have a range of speeds and energies, and the slower-moving among them may be captured when they strike the liquid surface. The likelihood that this will happen increases with the number of gas molecules hitting the liquid surface per second, which in turn depends on the concentration or partial pressure of vapor molecules above the liquid. The higher this partial pressure of vapor, the more frequently the molecules will strike the surface of the liquid, and the greater will be the tendency of vapor molecules to mo ve back into the liquid.

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Solutions and Colligative Properties

At any temperature, equilibrium exists when the escaping tendency (or free energy per mole) of molecules in the liquid and vapor is the same. If the temperature is raised: the escaping tendency of the liquid increases. More liquid will evaporate until the vapor pressure rises to the point at which the escaping tendency of vapor molecules back into the liquid matches the tendency of the liquid molecules to evaporate. This equilibrium partial pressure of vapor above a liquid is known as the equilibrium vapor pressure of the substance. The vapor pressure of water at room temperature (25° C) is 0.0313 atm, or 23.8 mm of mercury (760 mm Hg = 1 atm). This means that if a still body of air over a lake is saturated with moisture at 25° C, there will be 0.0313 atm of water vapor in the air, and 0.969 atm of O2, N2, and other gases. The way in which equilibrium vapor pressure changes with temperature is shown in the graph on the right. At 0° C the molecules of liquid water move slowly, their escaping tendency is small, and the equilibrium vapor pressure above the liquid is only 4.6 mm Hg. At 50° C it increases to 92.5 mm Hg, and at 100° C it equals 760 mm Hg or 1 atm pressure. This is the definition of the boiling point of a liquid -the temperature at which its vapor pressure equals the external pressure.

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Solutions and Colligative Properties

Below the boiling point, atmospheric pressure on the liquid surface is greater than the pressure that bubbles of vapor can develop in the liquid, so these bubbles are prevented from forming. Evaporation takes place only at the liquid-gas interface. But at the boiling point, the vapor pressure becomes as great as the total pressure on the liquid surface. Bubbles of vapor begin to form inside the liquid as well as at its surface, which leads to the rapid agitation that we call boiling. What would happen to the equilibrium vapor pressure of a liquid if some nonvolatile solute molecules or ions were added? In the pure liquid water, every molecule that approaches the surface has a certain chance of escaping into the vapor phase, depending on its kinetic energy. If a nonvolatile material such as sugar is added so that one molecule in ten is sugar and not water, then only 90% of the molecules that formerly were potential escapees have a possibility of getting out of the liquid. The average escaping tendency of water molecules from a given amount of solution is reduced, but the rate of condensation is unaffected since no sugar molecules are present in the vapor. Condensation gets ahead of vaporization, so more vapor condenses. When vapor-liquid equilibrium is established once more, we find that the equilibrium vapor pressure is only 90% as great as it was originally

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Solutions and Colligative Properties

The mole fraction of a substance in a mixture is the number of moles of that substance divided by the total number of moles of all substances present:

If a nonvolatile solute, A, is added to a pure solvent, B, until the mole fraction of the original solvent has decreased from one to XB, then the vapor pressure will be only XB times the vapor pressure of the pure liquid, p°B pB = XBp° B This is Raoult's law. The lowering of vapor pressure of B will be proportional to the mole fraction of the added solute, A: pB=XAp°B You should be able to show that this follows from the previous expression, with the added fact that the sum of mole fractions is unity: XA + XB =1

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Solutions and Colligative Properties

The actual identity of the solute molecules is unimportant to the lowering of vapor pressure. Since theirs is a "spoiling" role in decreasing the frequency with which solvent molecules approach the surface, only their numbers matter. If a substance such as a salt dissociates into two particles or ions in solution, then it is doubly effective. One mole of NaCl lowers the vapor pressure of water by twice as much as a mole of glucose, because it yields twice the number of particles in an aqueous solution. Example. At 35° C the vapor pressure of water is 42.2 mm Hg. What is the vapor pressure of an aqueous solution of glucose that has one glucose molecule for every 100 water molecules?

Lowering of the equilibrium vapor pressure of a liquid by ions or molecules of a solute is known as a colligative property (meaning "collective" or "joint") because the size of the effect depends only on the total number of solute molecules or ions, and not on their identity. There are three other common colligative properties of solutions: boiling point elevation, freezing point lowering, and osmotic pressure. In all four cases, adding solute molecules or ions decreases the escaping tendency of solvent molecules from the liquid. Therefore some adjustment in temperature or pressure must be made to restore equilibrium between the liquid and the other phase

Solution Example. The elemental abundance table in Chapter 8 shows that ocean water can be considered as a solution with 330 NaCl "molecules" for every 33,000 water molecules. The vapor pressure of pure water on a hot summer day (35° C) is 42.2 mm Hg. What is the vapor pressure of water in the middle of the ocean at that temperature? Solution

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Solutions and Colligative Properties

Lowering of the equilibrium vapor pressure of a liquid by ions or molecules of a solute is known as a colligative property (meaning "collective" or "joint") because the size of the effect depends only on the total number of solute molecules or ions, and not on their identity. There are three other common colligative properties of solutions: boiling point elevation, freezing point lowering, and osmotic pressure. In all four cases, adding solute molecules or ions decreases the escaping tendency of solvent molecules from the liquid. Therefore some adjustment in temperature or pressure must be made to restore equilibrium between the liquid and the other phase

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Boiling Point Elevation

Since the boiling point is defined as that temperature at which the vapor pressure equals the atmospheric pressure, anything that lowers the vapor pressure obviously will raise the boiling point. In terms of molar free energies or escaping tendencies, adding sugar molecules to boiling water at 100¡C dilutes the H20 molecules, lowers their escaping tendency, and causes the boiling to cease. To make the solution boil again, we must raise the temperature until the escaping tendency of the remaining H20 molecules is as great as before. We can set up a free energy expression that tells how the escaping tendencydepends on concentration and temperature, and look for conditions under which these two effects cancel. The result for dilute solutions, in which interactions between solute molecules or ions can be neglected, is that the increase in boiling point, DTB, is proportional to the solute concentration

The proportionality constant, kb, varies from one solvent to another but is completely independent of the nature of the solute particles, A. The solute exerts its effect only by virtue of the number of molecules or ions present. As with vapor pressure, salts that produce several ions per molecule are more effective than molecules that do not dissociate. Example. The molal boiling point elevation constant for water is kb =0.512. What is the boiling point (Tb) of a solution of 0.10 mole of glucose in 1000 g of water? Solution Example. What is the boiling point of a 0.10-molal solution of NaCl ? Solution

expressed as molality, or number of moles of solute particles per kilogram of pure solvent: mA = molality of A mA= moles of A per kilogram of pure solvent B

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Boiling Point Elevation

The meaning of a boiling point and the effect of salts can be illustrated by two cooking phenomena. Boiling water is a simple way of attaining a reproducible (constant) high temperature, which at sea level (1 atm pressure) is 100° C. The situation is slightly different at high altitude. At 8000 feet in Aspen, Colorado, atmospheric pressure is 560 mm Hg rather than 760 mm. Water needs to be heated only to 92° C before its vapor pressure equals 560 mm, and the turbulent bubbling away of vapor that we call boiling begins. Indeed, 92° C is as hot as an open pan of water can be heated in Aspen. If more heat is supplied, the temperature remains at 92° C, and the liquid simply boils away faster. Among the practical consequences of this are cold coffee, and hard-boiled eggs that take forever to cook. At the other extreme, in a sealed pressure cooker that can take an overpressure of 3 atm (or total pressure of 4 atm), one can raise the temperature to 134° C, thereby making cooking much faster. The second cooking phenomenon illustrates the influence of salts on boiling point. If a pot of water is brought to a boil, and salt is added, boiling immediately stops. The added ions lower the escaping tendency of water molecules. Only at a higher temperature will the vapor pressure again reach atmospheric pressure, and boiling recommence.

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Boiling Point Elevation

The meaning of a boiling point and the effect of salts can be illustrated by two cooking phenomena. Boiling water is a simple way of attaining a reproducible (constant) high temperature, which at sea level (1 atm pressure) is 100° C. The situation is slightly different at high altitude. At 8000 feet in Aspen, Colorado, atmospheric pressure is 560 mm Hg rather than 760 mm. Water needs to be heated only to 92° C before its vapor pressure equals 560 mm, and the turbulent bubbling away of vapor that we call boiling begins. Indeed, 92° C is as hot as an open pan of water can be heated in Aspen. If more heat is supplied, the temperature remains at 92° C, and the liquid simply boils away faster. Among the practical consequences of this are cold coffee, and hard-boiled eggs that take forever to cook. At the other extreme, in a sealed pressure cooker that can take an overpressure of 3 atm (or total pressure of 4 atm), one can raise the temperature to 134° C, thereby making cooking much faster. The second cooking phenomenon illustrates the influence of salts on boiling point. If a pot of water is brought to a boil, and salt is added, boiling immediately stops. The added ions lower the escaping tendency of water molecules. Only at a higher temperature will the vapor pressure again reach atmospheric pressure, and boiling recommence.

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Freezing Point Depression

Addition of solute molecules also depresses the freezing point of a liquid.The freezing point is the temperature at which freezing and thawing are in equilibrium. If solute ions or molecules are added until only 90% of the particles in the liquid are the original solvent molecules, then only 90% of the collisions of solvent particles with a crystal have a chance of adhering to the solid. Hence the temperature must be lowered, to decrease the tendency for molecules to break loose from the solid and escape into the solution, before freezing and thawing again are in balance. For dilute solutions, the lowering of freezing point is proportional to the molality of the solute: D Tf = -kfmA Example. The molal freezing point depression constant for water is kf = 1.86. What is the freezing point of a solution of 0.10 mole of glucose in 1000 g of water? Solution

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Freezing Point Depression

DTf = -kfmA Example. What is the freezing point of ocean water containing approximately one NaCl per 100 water molecules, or one mole of NaCl per 100 moles of H2O as described previously in this chapter? Solution Colligative properties were the basis for one of the original proofs that salts really did dissociate, and for determining how many ions were produced. For example, one could imagine that the compound potassium ferricyanide, K3Fe(CN)6 dissociates in solution as follows:

Is this true? A freezing-point experiment can settle the matter. Example. When 300 mg of potassium ferricyanide are dissolved in 10 ml of water, the freezing point falls to -0.68° C. How many ions are produced by one K3Fe(CN)6 formula unit? Solution

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Freezing Point Depression

When we add ethylene glycol to automobile radiators as an antifreeze, we are taking advantage of the freezing point lowering of the radiator water. Ethylene glycol evaporates too readily in the summer months, but with other less volatile "year-round" antifreezes, we also make use of the raising of the boiling point of the radiator water to prevent boilover in hot weather. When we scatter salt on icy sidewalks, Na+ and Cl- ions lower the freezing point of water and cause the ice to melt into a concentrated brine. Similarly, home ice cream makers use rock salt and ice to produce a slush at a lower temperature than can be achieved with pure water and ice. All of these are applications of the colligative properties of molecules and ions dissolved in water. Another important application of colligative properties is in determining molecular weights. A freezing point depression measurement can tell us how many moles of a solute are present, and if we already know the number of grams, it is easy to calculate the molecular weight.

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Freezing Point Depression

Example. A saturated solution of glutamic acid (an amino acid) in water has 1.50 g of glutamic acid per 100 g of water. The observed freezing point of the solution is -0.189¡C. What is the molecular weight of glutamic acid? Solution Example. A 200-mg sample of cytochrome c (a protein) is dissolved in 10 ml of water. The molecular weight of cytochrome c is 12,400. What is the expected freezing point depression? Solution The sensitivity of molecular weight measurements can be increased somewhat by choosing solvents with larger kf or kb. Camphor, an organic compound, often is used because it has a kf of 40.0. Using molten camphor as a solvent increases the sensitivity by more than twenty times, but this is practical only if the molecule whose molecular weight is to be found is both soluble in camphor and stable at the camphor melting point of 180° C.

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Osmotic Pressure

The fourth colligative property is osmotic pressure, and it is useful in molecular-weight determinations when freezing point depressions are not.

Picture of a dialysis machine

Many membranes have pores large enough to let some molecules pass through, but too small to pass others. These are known as semipermeable membranes. Some will permit water to pass, but not ions or salts. Others, with larger pores, will be permeable to water, salts, and small molecules, but not to protein molecules with molecular weights in the thousands. This selective passage of ions and small molecules but not proteins is called dialysis, and is a common biochemical method of separation and purification. Our kidneys essentially are fine networks of dialysis tubing, excreting liquids, salts, and small waste molecules, but at the same time preventing the loss of proteins from body fluids. Artificial kidney machines simulate this blood-purification process with man-made dialysis tubing, in which the blood from the patient flows across one side of semi-permeable membranes, and wash fluid flows across the other.

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Osmotic Pressure

Osmotic pressure is particularly easy to understand on the basis of escaping tendencies. It is illustrated by the diagram opposite, which shows a single glass tube with one end covered by a semipermeable membrane, and immersed in a beaker of water. With pure water on both sides of the membrane, the escaping tendency of molecules through the membrane from either side is the same. Now if molecules of some solute that cannot pass through the membrane are added to the tube, but not to the beaker, the escaping tendency of water molecules from the tube is decreased. Although the rate of flow of water molecules through the membrane into the tube is unimpeded, the reverse flow from tube to beaker is hindered, since not every molecule that approaches the membrane from the inside surface will be a water molecule. If only 90% of the molecules in the tube are H2O, then the flow of water out to the beaker will be only 90% as great. More water will flow in than out, and the water level will rise in the tube.

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Osmotic Pressure

An increase in pressure inside the tube increases the escaping tendency of water molecules from within the tube, since their escape through the membrane lowers the pressure. Water initially flows into the tube because the escaping tendency of H2O molecules of the solution inside is less than that of pure water outside. This inflow of water builds up a hydrostatic head of pressure in the tube, which in turn raises the escaping tendency of H2O molecules within the tube. When the pressure is high enough, inward flow is matched by outward flow, and a new equilibrium results. This equilibrium pressure is known as osmotic pressure. The more solute molecules or ions in solution, the higher the osmotic pressure must be to block the inward flow of water molecules. As before, the proper approach to the problem is to set up expressions for the way in which molar free energy or escaping tendency of water molecules depends on concentration and pressure in a solution, and find the conditions under which these two opposing effects exactly cancel. The result for dilute solutions is that the osmotic pressure necessary to balance flow across a membrane is related to the molarity of the solute particles on the side of the membrane to which pressure must be applied: CA= molarity of A = moles of A per litre of solution P = CART = osmotic pressure

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Osmotic Pressure

The molarity of a solution is the number of moles of solute per litre of solution, in contrast to molality, which is the number of moles of solute per kilogram of pure solvent. With water as the solvent (which has a density of 1 kg per litre) and with dilute solutions, in which the change in volume of solvent upon adding solute is small, the difference between molarity and molality also is small. In the above expression, if the osmotic pressure (P ) is measured in atmospheres, concentration (CA) is in moles per litre, and T is the absolute temperature in degrees Kelvin, then R is the gas constant encountered first in Chapter 2: R = 0.0821 litre atm deg-1mol-1. (Notice the similarity between the osmotic pressure law for ideal dilute solutions and the gas law for ideal gases.) Osmotic pressure is more sensitive to concentration than is freezing point depression, and therefore is more useful for molecular-weight determinations of large molecules. Example. A 200-mg sample of cytochrome c is dissolved in 10 ml of water. The molecular weight of cytochrome c is 12,400. What will be the osmotic pressure in the solution when diffusion equilibrium is restored? Solution

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Osmotic Pressure

Osmotic pressure is important in living cells, because they are surrounded by a semipermeable cell membrane through which they communicate with the outside world. Cells are designed to function with a certain internal salt concentration. If they are put in a concentrated brine solution they lose water through the membrane and shrivel; conversely, if they are placed in distilled water they take up more water and swell. If the osmotic pressure inside becomes too great for the membrane strength the cell ruptures. Plant cells have rigid cell walls of cellulose around them to protect them from such osmotic shock. The fundamental idea behind all four colligative properties is that the molar free energy, chemical potential, or escaping tendency of solvent molecules must be the same in two phases if equilibrium is to exist between them. When foreign molecules or ions are added to a liquid phase, the chemical potential of the liquid decreases in that phase. There is less tendency to migrate into a nearby vapor phase, solid phase, or to the other side of a membrane. To redress the balance and reestablish equilibrium, the temperature or the pressure of the solution must be adjusted.

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Redox Reactions and Electrochemical Potential

Oxidations and reductions involve the escape of electrons from molecules or ions of one substance and their capture by other chemical substances. As with the movement of entire molecules discussed in previous sections, free energy is the key to understanding this escaping tendency. Oxidation-reduction (redox) reactions are important because they are the principal sources of energy on this planet, both natural or biological and artificial. Oxidation of molecules by removal of hydrogen or combination with oxygen normally liberates large quantities of energy. The synthesis of reduced organic molecules (sugars) by photosynthetic green plants is the main device for trapping and storing solar energy on this planet. Oxidation either can involve the outright loss of electrons:

or the shifting away of bonding electrons toward a more electronegative atom:

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Redox Reactions and Electrochemical Potential

In the first example, electrons are physically removed from copper atoms to produce positively charged copper ions. In the second example, electrons on hydrogen that originally were shared equally with another hydrogen atom are partially lost by being shared unequally with oxygen atoms. Since electrons are never created or destroyed in chemical reactions, whenever one atom is oxidized, another atom must be reduced .When hydrogen is oxidized by the process above, oxygen is reduced. The copper reaction is incomplete, since some unspecified substance must become reduced by taking up the two electrons indicated on the right side of the equation. In the water reaction, hydrogen is oxidized and oxygen is reduced. Free energy is given off because oxygen is a strong oxidizing agent (meaning that it has a strong attraction for electrons) and hydrogen is a good reducing agent (meaning that it lets go of its electrons easily to something else). The standard free energy change during this reaction is D G° = -54.6 kcal mol-l of water vapor. In general, the oxidation of a substance with a tenuous hold on its electrons, by a strong oxidant with a powerful pull for electrons, is accompanied by the release of free energy. It is a spontaneous process.

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Redox Reactions and Electrochemical Potential

Oxidation does not necessarily require the outright removal of electrons, as we have said. Oxidation-reduction reactions in which electrons are actually moved from one substance to another are especially useful, since if the donor and recipient can be isolated, and the electrons made to flow through an external wire or circuit, some of the free energy of the oxidationreduction process can be harnessed to do useful work. As an example, zinc metal has less of an affinity for its 4 outer electrons than metallic copper does. In a competition between Cu2+ and Zn2+ ions for electrons, copper ions will win. The reaction

is highly spontaneous, with a standard free energy change of -50.7 kcal per mol. If we dip a zinc strip into a copper sulfate solution, as shown opposite, the zinc will be eaten away, a spongy layer of metallic copper will plate out on the zinc strip, and the deep blue color of copper sulfate will gradually fade. (Zinc sulfate, which is formed, is colorless.) In contrast, if we immerse a copper strip in a zinc sulfate solution, no reaction will occur because the reverse reaction is highly nonspontaneous, with a +50.7 kcal per mol free energy barrier to surmount. This spontaneous transfer of electrons from zinc to copper is not useful because the free energy released is dissipated as heat. It is analogous to burning a spoonful of sugar with a match instead of eating it and converting the free energy of oxidation into useful muscle work. If some means could be found to separate the removal of electrons from zinc (oxidation) from the donation of electrons to copper ions (reduction), then the electrons might be made to do something useful along the way.

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Redox Reactions and Electrochemical Potential

This spontaneous transfer of electrons from zinc to copper is not useful because the free energy released is dissipated as heat. It is analogous to burning a spoonful of sugar with a match instead of eating it and converting the free energy of oxidation into useful muscle work. If some means could be found to separate the removal of electrons from zinc (oxidation) from the donation of electrons to copper ions (reduction), then the electrons might be made to do something useful along the way.

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Redox Reactions and Electrochemical Potential

One answer is the simple electrochemical cell. On the left side, a piece of metallic zinc is immersed in zinc sulfate solution, and on the right, copper is immersed in copper sulfate. The two pieces of metal are connected by a wire, and the two solutions are connected by a porous barrier that allows the migration of ions but prevents the bulk mixing of the two solutions. At the left metal rod, called an electrode, zinc atoms give up electrons and enter the solution as zinc ions. This electrode is slowly eaten away. At the copper electrode on the right, copper ions from solution combine with electrons and plate out on the electrode as metallic copper. This electrode slowly increases in bulk as the reaction progresses. The electrons needed to reduce the copper ions at the right come from oxidation of zinc atoms at the left, but to do so they must travel through the external wire circuit. In the two solutions, as zinc ions enter the left compartment and copper ions are removed from the right, negative sulfate ions must migrate slowly through the porous barrier from right to left, and positive zinc ions from left to right, to preserve electrical neutrality in the two solutions. The two electrodes, connecting wire, and porous barrier form a closed circuit, with negative electrons moving from left to right through the wire, and positive and negative ions moving through the porous barrier.

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Redox Reactions and Electrochemical Potential

The main purpose of the barrier is to keep Cu2+ ions away from direct contact with the Zn electrode. The positive Cu2+ ions have no tendency to migrate by electrostatic forces from right to left, but they could be brought up to the zinc metal by stirring or agitation. This is what the barrier prevents. The electrode at which oxidation takes place always is called the anode, and the reducing electrode, the cathode. In the Zn-Cu cell, the zinc electrode is the anode, and the copper is the cathode. Negative ions are called anions because they flow toward the anode in an electrochemical cell, and positive ions are cations because they migrate toward the cathode. Negatively charged sulfate anions, for example, migrate from the copper sulfate compartment, through the porous barrier, and into the zinc sulfate compartment where the anode is found. The logic in naming the anode arises because it is the electrode from which electrons flow up and out of the cell (Greek: ana, meaning up), and the cathode is the pole at which electrons flow back into the cell (Greek: cata, meaning down). This is as hard to remember as the terms themselves. The best memory device is to recall that Anode and Oxidation begin with vowels, Cathode and Reduction with consonants, or that Anode precedes Cathode in the alphabet, and Oxidation precedes Reduction. (It may not be elegant, but it works.)

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Redox Reactions and Electrochemical Potential

Although the zinc rod in copper sulfate and the two-solution cell just described are physically different, the same chemical reaction takes place in both:

In the cell, however, the 51 kcal of free energy released by the reaction can be used for other purposes. Every time a mole of the above reaction occurs in the cell, two moles of electrons flow from the zinc anode, through the external circuit, to the copper cathode. As we saw previously, in chemical reactions and phase changes it is useful to define a chemical potential as the free energy change per mole of a specific reactant, as the equation is written. This chemical potential is the intrinsic capacity of the reaction to do work; and the actual work done, or free energy released, is the product of this potential times the number of moles of a substance undergoing chemical change.

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Redox Reactions and Electrochemical Potential

In exactly the same way, we can define the electrochemical potential of a cell using oxidation-reduction reactions as the free energy change per mole of electrons transferred. If one mole of reaction occurs with the transfer of n moles of electrons (n = 2 in the Zn-Cu cell), and if F is the charge on one mole of electrons, then the electrochemical potential, E, is given by D G0 =-nFE0 The superscript 0 on the potential, E0, has the same meaning as for free energy. It signifies the value when reactants and products all are in standard states of 1-molar concentrations, or 1-atm partial pressures for gases. It usually also refers to a temperature of 25° C. The charge on a mole of electrons, F, is known as Faraday's constant. It has various numerical values, depending on the units involved, but if free energy is in kcal mol-1, n has units of electrons, and potential is expressed in volts, then F= 23.056 kilocalories per mole per electron volt (eV), or 23.056 kcal mol-1 eV-1. Example. What is the standard electrochemical potential of the ZnCu cell? Solution

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Redox Reactions and Electrochemical Potential

The voltage of an electrochemical cell or battery is a familiar concept. It measures the potential for doing useful work with the cell. The actual amount of work done is the product of this potential times the amount of chemical reaction carried out through the cell; just as the amount of work that can be harnessed from a waterfall depends on the height of the waterfall (analogous to potential, E), and the amount of water that flows over the falls (analogous to electrons, nF). For both waterfalls and electrochemical cells, the product of potential drop and quantity of matter reacted is the free energy released in the process, ∆ G.

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Redox Reactions and Electrochemical Potential

The porous barrier between the two solutions can be eliminated in the particularly simple version of the Zn-Cu cell, the Daniell gravity cell. In this cell the lighter zinc sulfate solution is carefully layered on top of a denser copper sulfate solution, and the electrodes are gently lowered into place, with the copper electrode insulated where it passes through the zinc sulfate layer. The Daniell cell delivers a dependable 1.10 volts, and at one time was used widely as a stationary power source for telegraph lines and doorbells. It obviously would be useless in a moving vehicle, for agitation would mix the two solutions. Metallic zinc then could transfer its electrons directly to copper ions in solution, and the electrons would not have to pass through the external wire. The cell would be ruined by an internal short-circuit, and the free energy released would be wasted as heat. As was pointed out previously, the purpose of the salt bridge, or porous barrier, is to permit the migration of counter ions to maintain charge neutrality, while avoiding mixing the solutions and thereby short-circuiting the cell.

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Addition of Cell Reactions

Nickel also is a good electron donor to copper, although not as good as zinc. In a competition between Ni2+ and Cu2+ for electrons, Cu2+ will win, but in a contest between Zn2+ and Ni2+, the nickel ions will take the electrons. The following reaction is spontaneous and has the indicated free energy change:

If an electrochemical cell were made up with a nickel electrode immersed in nickel sulfate, and a copper electrode in copper sulfate, nickel would be oxidized to Ni2+ ions, copper ions would be reduced to metallic copper, and electrons would flow through the external circuit from the Ni anode to the Cu cathode. The cell would have an electrochemical potential of ******** Compared with the Daniell cell, this cell would have approximately half as intense an "electron pressure" between the two electrodes, available for doing work.

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Addition of Cell Reactions

Free energies of balanced chemical reactions always are additive. Using only the information that we have so far about Zn-Cu and Ni-Cu cells, we can predict what would happen if we built a Zn-Ni cell. The reaction of this Zn-Ni cell can be obtained by subtracting the Ni-Cu reaction from the Zn-Cu reaction. (Remember that subtracting a reaction is the same as adding the reverse reaction, with the opposite sign for the free energy.)

The negative free energy of the Zn-Ni reaction means that it is spontaneous in the direction written. The potential of the Zn-Ni cell can be calculated from D G0 =-nFE0

The positive cell potential means the same thing as the negative free energy change: The cell reaction in the direction written is spontaneous.

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Addition of Cell Reactions

From this example it appears that cell voltages are additive, as are free energies. Just as we can write for free energies of a reaction, 24.1 kcal + 26.6 kcal = 50.7 kcal, we can write for cell voltages, 0.52 volt + 0.58 volt = 1.10 volts. This case is especially simple because the number of electrons transferred is the same for all reactions, n = 2. But remember that cell potential or voltage does not represent a quantity of energy. It is a tendency to react, or an electron "pressure." The quantity of energy, which by the principles of thermodynamics always is additive when reactions are added, is the free energy, ∆ G = -nFE. Whenever there is the slightest question as to whether voltages are additive in a given situation, go back and work with free energies instead.

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Half-Reactions amd Reduction Potentials

It is both inefficient and unnecessary to tabulate the heat or free energy for every single chemical reaction that could occur. Since heats and free energies of reactions are additive, it is sufficient to tabulate only the heat and free energy of reaction of each compound as made from its elements. The heats and free energies of all reactions between these compounds then can be found by combining their heats of formation, with the contributions from the elements canceling out. In a similar way, it is not necessary to measure and tabulate the free energies and cell potentials of all conceivable oxidation-reduction cells. If there were a hundred different substances capable of oxidation and reduction, then these might be combined into as many as 100 x 99 = 9900 different electrochemical cells, each with its own free energy drop and voltage.

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Half-Reactions amd Reduction Potentials

However, one need only select one substance as a reference standard, and tabulate the free energies or voltages for reactions of all other substances with this standard. The free energy of a cell not involving the standard substance then can be found by subtracting one of these reactions from another, and subtracting free energies in the same way. The contribution of the "standard" reaction cancels out. The standard half-reaction that has been chosen is the oxidation of hydrogen gas to hydrogen ions in solution: Pairing the zinc, nickel, and copper half-reactions separately with this half-reaction leads to the following tabulation:

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Half-Reactions amd Reduction Potentials

The positive signs for free energy of the zinc and nickel reactions, and the negative signs of their cell potentials, indicate that the reactions are not spontaneous in the direction written. Zinc ions will not be reduced spontaneously by hydrogen gas. Quite the contrary, if metallic zinc is dropped into acid, in which H+ ions are plentiful, zinc will be dissolved into Zn2+ ions, and hydrogen gas will be evolved: Similarly, Ni2+ ions will not oxidize H2 to H+ spontaneously, but metallic nickel will dissolve in acid with the release of hydrogen gas, although not as readily as does zinc. Copper is not attacked by acid as zinc and nickel are, because the following reaction is spontaneous:

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Half-Reactions amd Reduction Potentials One cannot make a solid electrode out of hydrogen gas, of course, but the same effect can be achieved by bubbling a stream of hydrogen gas over an inert conductor such as a platinum electrode, as shown opposite.

The potentials as written above are reduction potentials, positive if the ion is easier to reduce than H+ ions, and negative if harder to reduce than H+. A large positive reduction potential for a half-reaction is a sign that the reduced form of the substance is strongly favored, as with copper in the above examples.

The H2 molecules can dissociate at the surface of the platinum, give up their electrons to the external circuit through the metal electrode, and go into solution as H + ions. Similar electrodes can be made with other gases. In thinking about standard cell reactions, it is customary to forget that they are paired with the hydrogen half-reaction, and to speak of them as if they were isolated reactions of one half of the cell. We can talk about half-reactions, and their free energies and half-cell potentials, as though the following had physical reality:

Click here to see a cell in action

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Half-Reactions amd Reduction Potentials

Standard reduction potentials for various half-reactions under acidic and basic conditions are given in the linked tables on the facing page. Remember that these potentials really are for cells in which the electrons required on the left side of the given half-reaction are provided by oxidizing H2 to H+ ions, but that whenever we use two of these halfreactions to calculate the potential of a real cell, the hydrogen contributions cancel. Also remember that a potential is a "pressure" on a per electron basis, no matter how many electrons appear in the halfreaction. The free energy for that half-reaction coupled in a cell with the hydrogen half-reaction can be found by multiplying the reduction potential by -23.06 kcal times the number of electrons involved in the half-reaction. Example. What are the cell voltage and free energy change in a cell with the reaction

Which way will the reaction go spontaneously? Solution Now find out how to Build cells from Half Rections

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Half-Reactions amd Reduction Potentials

Standard reduction potentials for various half-reactions under acidic and basic conditions are given in the linked tables on the facing page. Remember that these potentials really are for cells in which the electrons required on the left side of the given half-reaction are provided by oxidizing H2 to H+ ions, but that whenever we use two of these halfreactions to calculate the potential of a real cell, the hydrogen contributions cancel. Also remember that a potential is a "pressure" on a per electron basis, no matter how many electrons appear in the halfreaction. The free energy for that half-reaction coupled in a cell with the hydrogen half-reaction can be found by multiplying the reduction potential by -23.06 kcal times the number of electrons involved in the half-reaction. Example. What are the cell voltage and free energy change in a cell with the reaction

Which way will the reaction go spontaneously? Solution Now find out how to Build cells from Half Rections

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The Dry Cell

In the cells considered so far, it has been implied that the electrodes were in contact with ions in solution. The dry cell, shown on the right, is especially convenient because the solutions are replaced by a moist paste in a sealed container. The zinc casing is the anode, with the halfreaction

The cathode is a central carbon rod surrounded by a paste of manganese dioxide (MnO2), ammonium chloride (NH4Cl), and water. The paste and the zinc casing are separated only by a porous paper barrier. The cathode reaction is a complex one, but can be represented as

A dry cell delivers about 1.5 volts (0.76V + 0.75V). If the cell is used continuously, the current slowly decreases as ammonia gas builds up around the carbon rod and insulates it. If the cell is allowed to rest, this ammonia diffuses toward the anode and combines with zinc ions to form a complex ion, Zn(NH3)42+ . The cell then is able to deliver a stronger current again. This is why flashlight batteries appear to run down with steady use, but to recover after standing idle for a time.

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The Lead Storage Battery

The dry cell, useful as it is, cannot be recharged and used again. This is because the products of the electrode reactions diffuse away, and the reactions cannot be reversed simply by passing an external charging current through the cell. The lead storage battery, shown at the right, that the products of each electrode reaction When a reverse current is passed through products are reconverted to reactants, energy is ready to deliver electrical energy again.

has the great advantage adhere to the electrode. the storage battery, the is stored, and the battery

The anode is a spongy lead screen, and the cathode is a screen impregnated with lead dioxide. Both are immersed in the same sulfuric acid solution. Lead is oxidized to Pb2+ ions at the anode, and these ions immediately form insoluble lead sulfate, which sticks to the anode:

At the cathode, lead oxide with Pb in the +4 oxidation state is reduced to more Pb2+ ions, which also stick to the cathode as PbSO4:

The overall cell reaction therefore is

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The Lead Storage Battery

Six-volt and twelve-volt automobile batteries are obtained by connecting three or six of these cells in series. When the lead storage battery has run down, most of the lead and lead oxide is in the form of lead sulfate, and the battery fluid is depleted of sulfuric acid. The fluid then is less dense, which is the reason that the specific gravity (or density) of the battery fluid can be used by a service station attendant as a measure of the state of charge of the battery. If a direct current is passed through a run-down battery so electrons flow into the anode (originally Pb) and out the cathode (originally PbO2), the half-reactions are reversed. Lead sulfate is reconverted to Pb and PbO2, the battery fluid becomes a more concentrated (and denser) sulfuric acid solution, and electrochemical energy is stored in the cell, ready for later use.

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Electrolysis Cells

When the lead storage battery is being used as a power source, oxidation-reduction reactions generate electricity. When a depleted battery is being recharged, electricity from an outside source causes oxidation-reduction reactions to go against the natural free energy gradient. This same principle of using electric current to bring about energetically unfavorable chemical changes is used widely in electrolytic cells. Many metals can be obtained from their ores (usually oxides or sulfides) by reducing them with carbon, but the alkali metals, such as sodium, are too reactive for this. They must be obtained by electrolysis. In the electrolysis of molten sodium chloride, the reduction that cannot be accomplished chemically is The Cl2 gas is collected and piped away, and the sodium, which is a liquid at carried out electrochemically. Current is passed this temperature and lighter than the fused salt, floats to the surface and is through two electrodes immersed in NaCl heated recovered. above its melting point of 8010C. At one electrode, Cl- ions are oxidized to Cl2 gas, and it therefore is the anode. At the cathode, Na+ ions are reduced to sodium metal.

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Electrolysis Cells

The half-reactions are

The electrode potentials used here are only approximate because they are for dilute aqueous solutions, not for a fused salt. They do indicate that a large potential must be applied across the electrodes of the cell before electrolysis and decomposition of the salt will begin. Electrolysis is the only practical process for obtaining aluminum metal from its ores, primarily Al203. Many other metals are either obtained or purified by electrolytic cells. For example, if a current is passed through two copper electrodes immersed in a copper sulfate solution, copper will be oxidized to Cu2+ ions at the anode, and Cu2+ ions will be reduced and will plate as metallic copper on the cathode. If an ingot of impure copper is used as the anode, then pure copper will build up on the cathode, and impurities will settle to the bottom of the electrolysis tank. In a similar way, electrolysis can be used to plate metal on any object that can be made to conduct electricity and hence can be used as the cathode in an electrolysis cell.

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Electrolysis Cells

Electrolysis is the only practical process for obtaining aluminum metal from its ores, primarily Al203. Many other metals are either obtained or purified by electrolytic cells. For example, if a current is passed through two copper electrodes immersed in a copper sulfate solution, copper will be oxidized to Cu2+ ions at the anode, and Cu2+ ions will be reduced and will plate as metallic copper on the cathode. If an ingot of impure copper is used as the anode, then pure copper will build up on the cathode, and impurities will settle to the bottom of the electrolysis tank. In a similar way, electrolysis can be used to plate metal on any object that can be made to conduct electricity and hence can be used as the cathode in an electrolysis cell.

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Faraday's Law of Electrolysis

One of the most important single steps in establishing the electrical nature of the forces between atoms was the electrolysis experiments in 1833 by Michael Faraday. He carried out a series of experiments to study the chemical changes produced when electric currents were passed through solutions and mixtures of chemical substances. He observed that chemical changes occurred of the type that we have been examining in the preceding section. He made two quantitative observations, now called Faraday's laws: 1. The weight of chemical substance produced in an anode or cathode reaction in an electrolysis cell is proportional to the quantity of electricity passed through the cell. 2. The weights of two different substances produced by the same quantity of electricity are proportional to the equivalent weights of the substances in reactions between them or with other substances.

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Faraday's Law of Electrolysis

As an example, if a given amount of electricity releases 5 g of H2 gas when passed through an electrolysis cell for the decomposition of water, then twice as much electricity will produce 10 g of hydrogen gas. Furthermore, if enough electricity is passed through the cell to yield 2 g of H2 gas at the cathode, then 16 g of O2 gas will be released at the anode. These numbers are easily recognizable as representing 1 mole of H2 and 1/2 mole of O2, which are the relative proportions in which these gases combine to form H20. In Faraday's time, his experiments were a remarkable set of observations that helped to establish the principles of chemical combination. Today they are self-evident consequences of the theory that electrons form chemical bonds.

We have referred to Faraday's constant previously as representing one mole of electrons, and have used it in the form F = 23.056 kcal mol-1 eV-1 It is more convenient in electrolysis experiments to express F in coulombs, the customary unit of electrical charge.The charge on an electron is 1.6021 x 10-19 coulomb, so one mole of electrons will have a total charge of 1.6021 x 10-19 coulomb x 6.022 x 1023 mol-1 = 96,487 coulombs mol-l Passing 96,487 coulombs of electricity through a cell means sending one mole of electrons from one electrode to the other, with the corresponding chemical changes.

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Faraday's Law of Electrolysis

Example. When 96,487 coulombs of electricity are passed through an electrolysis cell containing molten NaCl, how many moles, and how many grams, of Na and Cl2 are produced? Solution Example. Exactly 200,000 coulombs of electricity are passed through an electrolysis cell containing a copper sulfate solution that is designed to purify copper electrolytically. How much copper will plate on the cathode? Solution In acid-base neutralizations , the amount of substance that would release or take up one mole of protons was referred to as one equivalent of acid or base. Hence one equivalent of acid-base neutralizing ability is supplied by one mole of HCl or NaOH, one half mole of H2SO4, or one third mole of H3PO4. In a similar manner, we can define one redox equiualent of a substance being reduced or oxidized as that amount of substance that takes up or releases one mole of electrons, or one faraday. Hence in the first example of this section, one mole of sodium metal and one half mole of Cl2 gas each represent one redox equivalent. In the second example, one mole of copper represents two redox equivalents in the reduction of Cu2+ to Cu, since two moles of electrons, or faradays, of electricity are needed.

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Faraday's Law of Electrolysis

Example. When 96,487 coulombs of electricity are passed through an electrolysis cell containing molten NaCl, how many moles, and how many grams, of Na and Cl2 are produced? Example. Exactly 200,000 coulombs of electricity are passed through an electrolysis cell containing a copper sulfate solution that is designed to purify copper electrolytically. How much copper will plate on the cathode? Solution In acid-base neutralizations , the amount of substance that would release or take up one mole of protons was referred to as one equivalent of acid or base. Hence one equivalent of acid-base neutralizing ability is supplied by one mole of HCl or NaOH, one half mole of H2SO4, or one third mole of H3PO4. In a similar manner, we can define one redox equiualent of a substance being reduced or oxidized as that amount of substance that takes up or releases one mole of electrons, or one faraday. Hence in the first example of this section, one mole of sodium metal and one half mole of Cl2 gas each represent one redox equivalent. In the second example, one mole of copper represents two redox equivalents in the reduction of Cu2+ to Cu, since two moles of electrons, or faradays, of electricity are needed

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Redox Chemistry Gone Astray - Corrosion

The corrosion of metals is an oxidation process. Iron can be oxidized either by oxygen or by acid, if enough moisture is present to allow ionic reactions to proceed at an appreciable rate:

When iron rusts, metallic iron is oxidized first to the +2 state and deposited as flakes of Fe(OH)2 and FeO, later being oxidized even further to Fe(III). Aluminum corrodes even more vigorously,

but the A1203 oxide coating, having a crystal structure similar to the metal, adheres tightly to the metal surface and prevents further corrosion. In contrast, the crystal structures of metallic iron and iron oxide are not similar, and the two do not adhere. The oxide flakes away as it forms, exposing fresh metal for attack by oxygen or acid. A good layer of paint adheres better than FeO, but still is not permanent.

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Redox Chemistry Gone Astray - Corrosion

It happens that there is an electrochemical solution to this electrochemical problem. Iron will not rust or oxidize if it is plated with a more reactive metal-one with a more negative reduction potential. Aluminum is a possible candidate. If iron and aluminum are in contact, iron will behave as the cathode and aluminum as the anode, as their reduction potentials indicate:

A coating of aluminum will prevent iron from being oxidized, and its own oxide will protect the aluminum from continual destructive corrosion. But if you are going to aluminum-plate iron, you might as well make the objects out of aluminum to begin with, and gain the advantage of lightness. Unfortunately, aluminum is expensive. A cheaper alternative is to galvanize the iron by giving it a thin coating of zinc.

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The Drive to Make Things Happen

17. The Drive To Make Things Happen

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Redox Chemistry Gone Astray - Corrosion

You can see from the half-cell potential of zinc that the principle is the same. A galvanized steel bucket is corrosion-free, not merely because zinc shields the iron as paint would, but because zinc electrochemically prevents iron from being reduced. Scratch a galvanized pail and the pail will not corrode; the zinc will be oxidized instead. In principle the iron object does not even have to be covered completely for protection to occur. The zinc itself is relatively well protected because when some of it is oxidized, it absorbs CO2 from the air and forms a tightly adhering zinc oxide-carbonate coating. A "tin can" is a different story. Tin has a higher reduction potential than iron, and a greater tendency to remain reduced as the metal. A tin can is tin-plated iron, and if the surface is scratched, the iron will oxidize preferentially instead of the tin. Nothing electrochemical is gained by plating the can with tin; it is only a super-tight protective coating like paint. When the coating is breached, corrosion is rapid

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The Drive to Make Things Happen

17. The Drive To Make Things Happen

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Free Energy, Escaping Tendency and Potential

The theme of this chapter has been the use of free energy and As long as a higher potential exists for a starting state than for a final potential as a measure of the drive toward chemical change. state, the shift from the initial state to the other is spontaneous, and the energy released can be harnessed to drive some other process. The free energy change per mole of molecules or electrons is the "pressure" on these molecules or electrons to move: from one solid, Water running downhill can turn a mill wheel or generate electricity. liquid, or gas phase to another for molecules; or from one atom, ion, or Burning gasoline can push a piston or heat a room. And electrons molecule to another for electrons. moving from zinc to silver can send a telegraph message or lay down a track of silver on a printed circuit board for a computer. An important concept adapted from gravitation is the idea that the free energy involved in a chemical change can be described as the product When a potential gradient has "run down," and no difference in of a potential for change times the amount of substance that potential exists between two states, then the system is at equilibrium. undergoes the change. No more drive toward change exists, and no more useful energy or The kinetic energy that a ball gains in rolling down a hill of height h is work can be obtained from the system. This is the situation when all E = mgh. This is the product of the mass of the ball, m, and the of the water has run to the bottom of the hill, a solution is in gravitational potential, gh. equilibrium with solid or vapor, or a battery has run down. The total free energy released by a chemical reaction is the energy change per mole times the number of moles of reaction that occur. The free energy released during the transfer of electrons in an oxidation-reduction process is the free energy change per mole of electrons times the number of moles of electrons transferred.

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