INTRODUCTION

In recent years, the "greenhouse effect" has garnered increased attention in the news media, academia, the government, and the general public. The term alludes to the elevation of the earth’s temperature in response to increased carbon dioxide levels. This heightened level of concern for the environment may provide the impetus for funding of energy alternatives to fossil fuel combustion, which has been indicted as the major cause of the rising CO₂ levels.

However, even if the naysayers are correct (i.e., those who interpret recent high temperatures as part of the natural fluctuation of the earth’s mean temperature), such basic research is necessary. The world’s supply of oil and natural gas are not infinite and procuring what remains of these resources is increasingly a challenge with offshore drilling and the like becoming commonplace.

In the future some research will surely focus on a class of reactions known as "redox" reactions. These simultaneous oxidation and reduction reactions are the force behind batteries and a host of other processes including the plating of chrome on car bumpers, the transmission of nerve impulses, and corrosion. This experiment will examine these reactions on a basic level and illustrate their connection to thermodynamic principles.

References

Fine, L.W., Beall, H, and Stuehr, J. Chemistry for Engineers and Scientists. (Preliminary paperback version of the Second Edition). Philadelphia: Saunders College Publishing, 1999. 633-658.

THEORETICAL BACKGROUND

Fundamentals of Oxidation Reduction Chemistry

Chemical reactions are generally considered to belong to one of four categories: dissolution, precipitation, acid-base, and oxidation-reduction. In this experiment, we will consider the last kind, which can be represented as the composite of two reactions, each involving one of the reactants. For example, consider the following reaction:

A + B Aⁿ⁺ + B^n-

where A and B are neutral atoms that become ionized with a charge of n+ and n-,
respectively. We may also view this equation as the sum of two processes called half-reactions:

A Aⁿ⁺ + ne^-

B + ne^-B^n-

On a mundane level, separating the half-reactions facilitates the balancing of atoms and charge in the total equation. On a more fundamental level, the half-reactions clearly represent the oxidation state (or number) changes that the two reactant atoms undergo. One atom increases in oxidation number or experiences an oxidation; in the above example, the oxidation state of A changes from 0 (the oxidation number of a neutral atom) to +n. The other atom decreases in oxidation number or experiences a reduction; in the above, the oxidation state of B changes from 0 to -n.

What exactly does the term "oxidation state" mean? It’s a representation of approximately how many electrons an atom is lacking or has in excess compared to its neutral state. For instance, chlorine often bears an oxidation number of -1. The negative one means that, instead of having the seventeen electrons that it has in its neutral state, it has one extra negative charge or eighteen electrons. Most atoms only have a single ionized state: negative for nonmetals (the right side of the periodic table) and positive for metals (the left side of the table). Only transition metals (the middle of the table) show a great deal of variability in their oxidation number, although like ordinary metals, the number is always positive.

The oxidation state of an atom is important as it determines the compounds it can form. For example, Cu⁺ forms CuCN, a white crystal that melts in the presence of nitrogen at 473 C. On the other hand, Cu²⁺ forms Cu(CN)₂, a yellow-green powder that decomposes before melting. These two compounds, which are alike but for the oxidation state of the metal, also have different magnetic properties: Cu(CN)₂ is drawn into a magnetic field while CuCN is repelled.

Spontaneity and the Electrochemical Series

A spontaneous reaction is defined as one that will occur on its own given sufficient time. A nonspontaneous one will never happen unless energy is put into the reaction system. Many of the conveniences of everyday life are made possible by both spontaneous and nonspontaneous oxidation-reduction reactions. For example, batteries are driven by spontaneous redox reactions, while electrolysis and electroplating rely on nonspontaneous oxidation-reduction reactions effected by adding electrical energy to a reaction system.

How can one determine whether an oxidation-reduction reaction will be spontaneous or not? The answer is to divide the overall reaction into its component half-reactions and then consult a "table of standard reduction potentials" found in reference books like the CRC Handbook of Chemistry and Physics. Such a table will list most common half-reactions along with their corresponding potentials or voltages. By convention, these tables sometimes contain half-reactions written as either oxidations or reductions and so will only have one of the two half-reactions needed. However, if, for example, the consulted reference table is one of reductions, the oxidation potential (i.e., the potential of the opposite reaction) is simply the negative of the reduction potential.

As an example, let's consider the following half-cell reactions and potentials.

Sn(s) Sn²⁺(aq) + 2e^- xxxxxxxxxxxxxxxxxxxxE = .1375 V

Al³⁺ (aq) + 3e^- Al(s) xxxxxxxxxxxxxxxxxxxxE = -1.662 V

(The "standard" symbol, ƒ , just indicates that this is the potential for the reaction run at 25ƒ C, gas pressures of 1 atm, and solution concentrations of 1 M).

This equation needs to be balanced.

3Sn(s) 3Sn²⁺(aq) + 6e^-xxxxxxxxxxxxxxxxxxx xE = .1375 V

2Al³⁺ (aq) + 6e^- 2Al(s) xxxxxxxxxxxxxxxxxxxxE = -1.662 V

3Sn(s) + 2Al³⁺(aq) 3Sn²⁺ (aq) + 2Al(s) xxxxxxE _total = -1.5245 V

The sum of the half-cell potentials is the overall potential, and spontaneous reactions have overall cell potentials greater than zero. Since Eƒ _total is negative, the reaction is nonspontaneous. However the reverse reaction is spontaneous.

3Sn²⁺(aq) + 6e^- 3Sn(s) xxxxxxxxxxxxxxxxxxxE = -.1375 V

2Al(s) 2Al³⁺ (aq) + 6e^- xxxxxxxxxxxxxxxxxxxE = 1.662 V

3Sn²⁺ (aq) + 2Al(s) 3Sn(s) + 2Al³⁺(aq) xxxxxE _total = 1.5245 V

In comparing tin and aluminum, in light of this equation, we would say aluminum is a "more reactive" metal than tin, because the above reaction is spontaneous while the reverse reaction with tin metal as a reactant is nonspontaneous. A ranking of the relative reactivity of metals is called an activity series. The most reactive metal has the highest potential for its oxidation, while the least reactive has the lowest potential. Metals at the top of the activity series are said to be effective reducing agents (i.e., they are easily oxidized) while metals at the bottom are effective oxidizing agents (i.e., they are easily reduced).

The Battery: An Application of Oxidation-Reduction Chemistry

In order to understand the usefulness of this group of reactions, we need to consider the first law of thermodynamics. It tells us that energy cannot be created or destroyed; energy can only change form. Electrochemistry is the study of the transformation of chemical energy into electrical energy or electrical energy into chemical energy.

A battery, also known as a galvanic or voltaic cell, is a well-known example of a device that works by changing chemical energy into electrical energy. As shown in Figure 1, a battery consists of two physically separate half-reactions connected by a conductor (i.e., a wire). The wire allows electrons to flow from the anode (the site of oxidation in the half-cell) to the cathode (the site of reduction in the half-cell). As electrons pass through the wire from the anodic compartment to the cathodic compartment, the electrical energy being generated can be converted to other forms of energy like mechanical energy if a motor is inserted in the circuit. Unfortunately, it is inevitable that some of the energy will be dissipated as heat.

Figure 1: A Simple Galvanic Cell

The battery described above lacks a complete pathway through which electrons can flow. It is an open circuit and so will not work. It needs a salt bridge (a medium that allows free passage of ions) filled with an electrolyte (a solution that conducts electricity). Negative ions from the electrolyte, perhaps an aqueous solution of KNO₃, and from the reaction itself flow through the salt bridge toward the anodic compartment. At the same time, positive ions flow toward the cathodic compartment. This redistribution of ions prevents charge accumulation in the half-cells, and if this movement of charge did not occur, an electric field would develop in opposition to the field generated by the battery. This ultimately would cause the battery to fail.

Let's consider more carefully each of the components of the battery. We see that each half-cell contains one of the reactants (Al in the anodic compartment and Sn²⁺ in the cathodic department) and an electrode or conducting surface (Al in the anodic compartment and Sn in the cathodic compartment). Each half-cell also includes an electrolyte (Al₂(SO₄)₃ in the anodic compartment and SnSO₄ in the cathodic compartment), in addition to the electrolyte (Na₂SO₄) in the salt bridge.^. Electrons released by the aluminum electrode (the anode) travel through the wire to the tin electrode (the cathode) onto which solid tin "plates out" from the SnSO₄ salt. Simultaneously, charge redistribution occurs through the salt bridge: negative sulfate ions flow toward the anodic compartment where positive charge is developing and positive aluminum and sodium ions travel toward the cathodic compartment where positive tin ions are being consumed. This ion movement completes the electrical circuit and prevents the charge accumulation discussed above.

Although the theory behind all batteries is the same, the specific chemicals involved are not unimportant details. First, why were Al₂SO₄18H₂0, SnSO₄, and Na₂SO₄ chosen here? They are all water-soluble. Also, generally, when designing a battery like this one, an attempt is made to keep consistency in the spectator ions to reduce the interaction of unlike ions and the number of variables involved in predicting cell output and the like. Therefore, the sulfates of tin, aluminum, and sodium are used. Second, how are the electrodes chosen? Aluminum is a natural choice for the anode as it is a reactant and a conductor. The cathode could be (and is) tin, because it will not react with the tin salts in the compartment and will begin to form on the cathode as the reaction begins. It could also be another substance inert in this chemical environment, but conducting, like graphite.

The Thermodynamics of Batteries

In the sections above, we have referred a few times to spontaneity, a thermodynamic concept. Whether a reaction is spontaneous or not is predicted by the value of D G, the change in Gibbs free energy. The Gibbs free energy is defined as,

G = H - TS xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx(1a)

or

G = H - TS xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx(1b)

where H represents enthalpy, T represents temperature, and S represents entropy. (Note that 1b is identical to 1a except that the latter equation uses the standard state values of the thermodynamic functions.) Since we will work only with the change, D , in these functions, it is more meaningful to rewrite these equations as

D G = D H - TD S xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx(2a)

or

D G = D H - TD S xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx(2b)

where temperature is kept constant. A reaction with a predicted negative D G, or loss in the Gibbs free energy of the system, will occur spontaneously; one with a positive D G will not.

How is this important thermodynamic indicator related to the measurable electrical properties of a cell? The following equation provides the necessary link:

D G=-nFE xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx(3a)

or

D G =-nFE xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx(3b)

where n is the number of electrons transferred from one species to another in a reaction (six in our aluminum-tin battery as indicated by the coefficient in front of the electrons in the two half-reactions), F is the Faraday constant (96,485 Coloumbs per mole of electrons), and E is the cell voltage (in Volts, V). This can be taken a bit further by combining equations 2a and 3a or 2b and 3b to obtain the following:

-nFE = D H - TD S xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx(4a)

or

-nFE = D H - TD S xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx(4b)

Then this can be rearranged.

or

Of course, equation 5b is particularly useful, because D H and D S can be determined if the variation of cell voltage with temperature is known. Additionally, these values can be checked in a reference book that has tables of D H and D S, such as the CRC.

We should consider one more equation in discussing the thermodynamics of a galvanic cell. This formula, known as the Nernst equation, summarizes the effect of both temperature and concentration variation on voltage:

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx(6)

where Q is the reaction quotient, defined in the same manner as the equilibrium constant, K, but for concentrations and pressures other than those at equilibrium. For example, the reaction quotient for aluminum-tin battery described above would be

where substances in the solid phase are excluded from both K and Q by convention.

Note the similarity of equation (6) to a familiar thermodynamic expression:

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx(7)

Equation (6) can be derived from equation (7) by using equation (3a) and (3b).

DESCRIPTION OF THE EXPERIMENT AND ITS COLLABORATIVE LEARNING ASPECTS

In the first part of the experiment, the activity series of metals will be determined by combining metals with different metal ions and noting any possible reaction. Such a reaction is called a displacement, because one metal ion replaces another in a salt solution. An example would be magnesium displacing tin in a reaction of SnCl₄ with Mg and forming MgCl₂.

Ideally, since some redox reactions are slow to start and difficult to see, two trials should be performed for each metal/metal ion combination. This would be somewhat time- consuming for groups with only three students. Therefore, in developing a plan of action, it might be wise to only retest combinations of metals and metal ions that produce no noticeable reaction initially.

In the second part of the experiment, the variation of cell voltage with temperature will be studied and the value of three thermodynamic quantities of interest will be determined: D Hƒ , D Sƒ , and D G. The significance of the signs of these functions will be considered. At least two trials are necessary, so each group should divide the work accordingly.

In the third part, knowing that galvanic cells take advantage of spontaneous reactions, the activity series determined in Part One will be used to construct simple batteries. The efficiency of different electrodes as conductors and the usefulness of these "homemade" batteries will be briefly considered. After your battery is operating and you understand the mechanism of the cell, teach your fellow group mates about it.

Finally, in the fourth part, you will learn how to use a potentiostat to determine concentrations and diffusion coefficients by voltammetry.

WASTE

Dispose of all liquid waste in the "liquid waste beaker". All solid waste must be placed into the plastic beaker labeled "solid waste". Gloves can be discarded in the regular trash.

INSTRUMENTATION

BK‚ Tool Kit Multimeter and Pine Instrument AFCBPI Biopotentiostat

 

PROCEDURE

Part One: Partial Derivation of the Electrochemical Series

Part Two: Variation of Cell Voltage with Temperature

Part Three