Richard 5. Johnson and David E. Crawford University
of Alabama
i n B~rmingham Birmingham, 35233
Laboratory Experiment Concerning the Gibbs-Helmholtz Relationship
The Gibbs-Helmholtz relationship can be readily illustrated by the use of a suitable electrochemical cell. Various thermodynamic systems have been suggested and details about these are available.' The lead-acid storage cell is well-suited to this application because the students are familiar with the system, chemical reactions are straightforward, and excellent calorimetric values for the enthalpy change are available.2 The cell described here has a highly stable voltage and the cell itself is small enough so that temperature equilibrium can be rapidly attained when immersed in a water bath. Cell Construction
A sketch of the cell is shown in the figure. The
General view of the cell.
The overoll height is about 12 centimeters
component configuration and actual dimensions can be varied, but this particular cell has a 180-ml electrolytic beaker as a container. The strap-type clamp bolted to the steel rod with an offset greatly facilitates holding the cell in a thermostated bath. The laminated insulating plastic plate holder is cut from l/s-in. thick clear polystyrene sheet stock. All of the members are of the same width, except the two outer ones. These are wider, but cut to conform to the contour of 'HILL,D. L., MOSS,S. J., AND STRONG,R. L., J. CHEM.EDITC., 42. 541 (1965). ; V I N * L G.'w., ''Storage Batteries," (4th ed.), John Wiley & Sonn, Inc., New York, 1955, p. 187.
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the beaker. This addition polymer resin is unaffected by the sulfuric acid electrolyte, has almost zero water absorption, and is readily obtainable from electronics supply houses. The draw bolts of threaded 3/16-in. diameter stainless steel rods with washers and nuts of the same material complete the electrode holder. The clamping action of this holder is obvious from the sketch. The two anodes, placed at each side of the cathode for good current distribution a t the latter electrode during the charge cycle, are cut from thick rolled, technical grade, sheet lead. Each electrode is 1 X 6 in. The lead can be cleaned by immersion in 1 : 1 nitric acid. The cathode is part of a positive plate from a discarded automobile battery. The plate is easily cut with a hand hack-saw and then filed. The dimensions are roughly 1 X 4 in. This plate should be cut and finished so that the lead-antimony grid is of a whole number of spces, both vertically and horizontally. Along the wused edge of the original cathode grid a rod, about '/s-in. in diameter, of lead alloy can be sawed off. This is then welded to a notch in the original tab of the plate in order to have an extended cathode terminal. A small gas-air torch is useful for the lead welding operation. After cleaning the parts with a file the melting should be done in the reducing cone of the flame in order to avoid nonmetallic inclusions in the joint. Flux is not necessary and no solder or other dissimilar metal should be added to the autogenous weld, so that a source of corrosion in the finished plate will be eliminated. The plates reach to within about 1/2-in. of the bottom of the cell vessel, and because of the space between them no separators are necessary. The plates are far enough apart so that stirring rods, pipets, and a thermometer can be easily inserted. A solution of 20% by volume of reagent grade sulfuric acid serves as the electrolyte. This yields a solution of nearly 30y0 by weight of acid, and it has a specific gravity at room temperature of about 1.20. The electrolyte level should be high enough so that the active material on the cathode remains totally immersed. Cell Operation
One positive plate from an ordinary 12-V automotive storage battery will have about 10-12 amperehours of capacity, when discharged a t the 20-hr rate. Based on the fraction of the plate used and a charging time of 8 hr, one can compute a reasonable charging current for this cell. The use of a pasted plate, wherein the active PbOz is contained in a ladder-type cast grid of noncorroding lead-antimony alloy, is far superior to a Plante (electroformed) cathode. I t is almost impos-
sible to make stable PbOz on a smooth cathode by a simple electroforming ~ p e r a t i o n . ~Admittedly, while on charge a film of dark brown oxide is formed on the plate, when the charging current is interrupted the particles of PbOz discharge a t the lead plate interface through local action and within a few minutes the cathode is completely discharged. Visibly, to the unaided eye, the cathode is unaltered. The pasted plate largely circumvents this rapid local action phenomenon. With this particular electrolyte concentration, a lead-acid cell has about 0.3 mV per degree for the d&/dT value, which is near the maximum for voltage change with temperature. Moreover, this acid concentration favors a minimal amount of self-discharge of the cell. Although this cell has a long shelf-life, the cell should always be fully charged before the experiment is started. This cell has a voltage that corresponds to the literature value.4 Experimental Determinations
From the generally accepted double-sulfate theory for the operation of this system and simple redox equations it is obvious that a t constant temperature both the open circuit voltage and enthalpy change on discharge are a function only of the activity of the aqueous sulfuric acid solution. The students determine the specific gravity of the electrolyte near room t.emperature by the use of a 5- or 10-ml pycnometer bottle. Within the temperature and concentration ranges encountered the change in specific gravity with temperature is given by
VINAL,G. W., p. 49, (see footnote 2). KNOWLTON, A. E. (Edilw),"Standard Handbook for Electrical Engineers," (Yth ed.), McGrmv-Hill, New York, 1957, sect. 21-58. 6 VINAI, G. W., p. 125 (see footnote 2). %ee footnote 2. 4
The students can convert their value to a temperature corresponding to the one tabulated in a handbook and thus arrive a t the percent composition by weight of the binary electrolyte. From this they can calculate the mole ratio of water to sulfuric acid. With a potentiometer and suitable water baths the students can make cell voltage measurements over the range of 0-45°C. The latter temperature represents a practical upper limit with this type of cell, for a t higher temperatures the voltage will change from the self-discharge effect, and non-repeatable voltages will then be obtained. From a graph of voltage as a function of temperature, which is linear in this region, the temperature coefficient, d&/dT, is determined as well as the averaged cell voltage a t 2 5 T . By use of the Gibhs-Helmholtz relationship the enthalpy change, AH, can be calculated. The calculated AH is then compared with the National Bureau of Standards calorimetrically determined value^.^ Electrolyte Composition, moles IInO/mole HISOl 25 20 15 12 10 8
Enthalpy Change, koal at 25°C. 88.01 88.88 90.57 92.59 94.33 96.88
Conclusions
I n use over the past several years, this experiment has proved to be helpful in stressing the relationship between the two thermodynamic functions, Gibbs free energy and enthalpy. Even with ordinary laboratory thermometers and potentiometers that give values to the nearest millivolt the students consistently obtain an enthalpy change that is within one or two percent of the accepted value. Moreover, the experimental voltage data and tabulated enthalpy values can be treated analytically and graphically to illustrate several types of curve fitting and interpolation.
Volume 46, Number 1 , January 1969
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