R. Colton and G. J. Sketchley Parkville. Victoria, Australia and
I. M. Ritchie' The University of Western Australia
Nedlands, Western Australia
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The Measurement of the Conductance of Electrolyte Solutions A dc method
The conductance of electrolyte solutions is a topic common to all courses in physical chemistry, and one which is often treated in a fairly elementary sort of way, near the beginning. In addition, electrolytic conductance is a quantity which is easy to measure in the teaching laboratory. Despite this, many student chemists have difficulty in relating such measurements to the discussions of the classroom. The origin of their difficulties is not hard t o discern. They come to chemistry with an understanding of electrical measurements that is largely limited to direct currents and ohmic resistances. This understanding is sufficient to follow the theory of electrolyte conductance which is commonly couched in terms of an ion diffusing unidirectionally under the action of an electric field. However, since the treatment of electrolyte conductance invariably precedes the introduction of the topic of electrode kinetics, the student is left with insufficient background knowledge to grasp the need for alternating current in the measurement of conductance. The average elementary text is not particularly enlightening on this point. While all agree that the passage of a direct current through an electrolyte causes polarization of the electrodes, there does not appear to he general agreement as to what constitutes polarization. This is not surprising since the topic is one of some complexity, detailed discussions heing given by Vetter ( I ) , and Bockris and Reddy (2). Few students realize that polarization, in a practical sense, means that the electrolyte system behaves non-ohmically; i.e. the ratio of the applied potential difference t o the current passed is not a constant independent of the current's magnitude. In addition, because it is never demonstrated to them, they do not realize that an electrolyte system does behave ohmically when an alternating current is passed through it. Further conceptual difficulties arise as a result of the use of a bridge circuit. The fact that greater precision can he achieved in this way, and that compensation can he made for the electrode capacitance, itself an artefact of the use of alternating current, are points that escape all hut the best students. In any case, the greater precision is usually not necessary in a teaching laboratory. I t is the purpose of this paper to show how these difficulties can he overcome simply by suitably chosen experiments. A straightforward method of measuring the absolute value of the conductance of an electrolyte solution using direct current and applying Ohm's law is described. The technique is not new, a brief review of the work being given in the hook by Robinson and Stokes (3). However, to the best of our belief, it has not been utilized in a teaching situation before. Description of Conductance Cell The conductance cell can he readily assemhled from standard quick-fit parts by someone with little glass-blowing skill. More sophisticated versions can of course he constructed in a glass shop. The harrel of the cell, which is shown schematically in Figure 1, is made up from two B 14/23 sockets joined back to back, the total length heing about 25 cm. Double-ended sockets of this type can be ohtained commercially (e.g., Quickfit SRD1/220). Two sets of electrodes are fitted t o the cell, the outer pair heing known as the current prohes and the inner pair as the 130 / Jourmlof Chemical Education
Potential Probes
Current Electrode
1-
B 14 Cone
and socket
Figure 1. Schematic diagram (not to scale) showing the four-wabe conductance cell.
construction of the
purential pruhes. T h e current prohes are cut from thin (0.1 mm thick) platinum or some other inert metal foil into the shape of discs exactly equal in diameter to the end of a B 14/23 cone, onto which the discs are cemented, care heing taken to ensure that the outer surfaces are free of cement, and that the electrode does not impede the fit of the cone to the socket. An epoxy such as Varian "Torr-Seal" is a satisfactory cement. Prior to cementing the electrode in position, a copper lead is spot welded or soldered to the hack of the electrode. The lead is taken out through the back of the socket, which when necked down provides support for it. In principle, the metal from which the potential prohes are made is immaterial, since little or no current is drawn from these electrodes. When studying the conductance of potassium chloride, we have used hright platinum, platinized platinum, bright nickel, and a silver/silver chloride electrode with success. The potential prohes should he of thin wire, about 0.5 mm in diameter. They are located in narrow glass tubes, symmetrically positioned and about 10 cm apart, which are drawn out from the harrel of the cell. The wires are also cemented in position with about 0.5 cm of their length projecting into the cell body. A filling hole between an adjacent pair of current and potential prohes is useful but not essential. Demonslratlon of Electrode Polarization Using the current prohes of this cell, or indeed any conventional two-electrode conductance cell, it is easy to demonstrate polarization, and to show that polarization is an electrode phenomenon. The cell is filled with a solution of 0.01 mole I-' potassium iodide, and a direct current ~ a s s e d through it, the potential drop across it heing m e a s ~ r ~ with d a high-impedance device such as a vacuum tube voltmeter. In order to minimize electrolysis of the solution, the current passed should he kept as small as possible. In our experiments, it was never allowed to exceed 50 PA. I t was also necessary t o allow approximately 10 min for each reading to settle down. The current-voltage plot for the potassium iodide solution is shown in curve A of Figure 2. It can he seen that the current and voltage are not proportional. The cell resistance is non-ohmic, the conductance of the system being dependent on the amount of current nassed. The cell is said td be polarized. That polarization occurs a t the electrodes rather than in the hulk of the solution can be seen. for this system, by considering how the current is transIAuthor to whom correspondence should be sent.
VOLTAGE
IV
Fgure 2. Current-voltage plots using a two electrode ceil. Curve A Is for a '0.01 mole I-' solution of KI. Curve B is for me same solution whh a small amount of 12 added.
ported between the electrodes. In the bulk of the solution, the current will be carried hy potassium ions and iodide ions. However, it is difficult to see how electron transfer a t the cathode can take place since no easily reducihle species is present. This idea can be qualitatively confirmed by the the addition of progressively greater amounts of iodine electrolyte solution, and redetermining the current-voltage relationships. As can he seen in curve B of Figure 2, the cell resistance is reduced and ultimately becomes ohmic. By supplying iodine to the system, we have depolarized the electrodes making them reversible. The electrode reactions are I$- + 2e a 31Of course this is not the solution t o the ~ r o b l e mof measuring conductance by a dc method, since 6y adding iodine we have introduced another ionic s~ecies.namelv In- into the system. I t should also he noted that'this is-& the only tvDe of ~olarizationthat can occur, and that both elec&odes are polarized. An alternative approach to the problem is t o measure the potential drop across the electrolyte a t some point sufficiently removed from the region in which polarization is taking place. This can he achieved in a four-electrode cell, in which the functions of current supplier and potential measurer are separated. The approach is identical to that used in solid-state physics for avoiding contact resistance problems when measuring the conductance of solids. The circuit is shown schematically in Figure 3. The current electrodes become polarized as before. However, the potential probes will not become polarized provided the amount of current drawn from them is very small. This is possible if
d% Cond~ct~nce Cell
VOLTAGE - .I V Figure 4. Current-voltage plot for a 0.01 mole I-' solution of potassium chlorae at lE°C using a four-probe dc conductance cell.
a high impedance voltage measuring device such as a vacuum tube voltmeter (pH meter) is used. A potentiometer can he used if the null detector has a sufficiently high impedance. Under these circumstances, the section of electrolyte lying between the two potential probes can he expected to behave ohmically provided the potential probes are sufficiently far removed from the zone of polarization near the current probes. The fact that the electrolyte behaves ohmically (i.e. that the current is proportional to the voltage), when electrode polarization is avoided hy the use of a four-probe cell, is shown in Figure 4 for a 0.01 mole I-' solution of potassium chloride a t k c . Similar plots were obtained irrespective of whether the solutions had been degassed or not and whether the current was being increased or decreased. When a current was first passed throuah the cell the potential difference measured between the potential probes drifted for 5-10 min. After this initial period, the readings over the whole current range could be made rapidly. If Ohm's law were applicable, then one would expect the notential of the solution to varv linearlv alone the conductance cell. Near the electrodes, such a rilationihip might he exoected to break down as a result of ~olarization.In order to determine how far the potential probes should be located from the current probes, a modified version of the fourelectrode cell was constructed with a large number of potential probes inserted into the barrel of the cell at intervals along its length. The variation of the potential along the cell is shown in Fieure 5. I t is clear from this lot that polarization, shown b i t h e region in which the potential is not a linear function of distance. extends about 5 cm into the electrolyte from each current electrode. Accordingly, the potential probes should be sited a t least 5 cm away from the current probes. Determination of Solution Conductance The slope of the voltage-current plot is clearly proportional to the resistance ( R ) of the solution between the two notential nrobes. In fact. the constant of ~ r o ~ o r t i o n a l i t v can be detkrmined directly from the dimensions of the ceil since the current flow is isotrodc. The conductivit~( n ) is given by the expression x =
Figure 3.Circuit diagram for measuring the conductance of an electroiyte solution using a lour-probe dc methad. A is a moving-coil ammeter having a full-scale deflection of 0-50 &A. V is a high-impedance voltage measuring device and R is a variable resistor.
LIRA
(1)
where 1 is the spacing between the two potential probes, and A is the cross-sectional area of the tube. The probe spacing can be measured with a vernier slide calliper to within 0.1%. The best way to determine A is t o weigh the Volume 53, Number 2,February 1976 / 131
DISTANCE I C M
Figure 5. Potentialdistance plots for various currems showing non-ahmic behaviw in the vicinity of the current carrying elechades. The eladrolyte is m d e I-' KC1 at 18%.
volume of water that fills up a known length of cell, such as that between the two potential probes; the determinations are accurate to ahout 0.2%. The barrel of the conductance cell is often somewhat ellivtical in shave. . . hut the variation in cross-sectional area canbe neglected over a length of 10 cm. The resistance can be estimated from the dove of the voltage-current plots. T h e standard deviation i f R obtained in this wav is usuallv smaller than 1%. In order to ascertain the suitability of this apparatus for use in a student laboratory, the molar conductivities (A) of solutions of potassium chloride and acetic acid of various concentrations (c) were determined a t 25'C. Temperature control was achieved by immersing the cell in a water bath. Figure 6 shows the molar conductivity of degassed potassium chloride plotted as a function of the square root of concentration. It can be seen that the agreement with the literature values (4) is good. For acetic acid, the Ostwald Dilution equation (5) which relates the degree of dissociation (a) to the dissociation constant (K,), is applicable a 2 e / ( l- a ) = Ka (2) In eqn. (21, we have neglected activity coefficients and therefore the equation is only valid a t low concentrations. Replacing a by AlAo, where Ao is the molar conductivity at infinite dilution, and rearranging, we obtain AC/K.AO~= ( I l A )
- (l/Ao)
(3)
A plot of Ac against 1/A should therefore he linear, with slope 1/K,Ao2 and intercept l/Ao. This is shown in Figure 7. A least-squares analysis gives A,, = 40 mS m2 mole-' and K, = 1.6 X 10-5 mole I-', although the standard deviation in the intercept was large, being 60%. Given the literature value (4) of An = 39.06 mS m2 mole-', the slope of the graph yields a K . of 1.72 X mole I-' with a standard The value quoted for the dissociadeviation of 0.03 X tion constant of acetic acid (6) a t 25°C is 1.75 X 10-"ole 1-1. .
~
Discussion
I t has been known for some time (7) that the four-probe dc method for measuring the conductance of electrolyte solutions can give very accurate results, a point we have confirmed above using relativelv unsovhisticated eouivment. In addition, we beteve that this approach is prefe>a61e in a teaching laboratory since the students are made more aware of the problems associated with polarization, and can more easily relate the dc measurements to their existing knowledge of electrical circuits. There is a further not inconsiderable advantage in cost. A commercial bridge circuit costs several hundreds of dollars. The conductance cell and 132 / Journal of Chemical Education
Figure 6. The molar conductivity of potassium chloride at 25OC as a function of the square r w t of the concentration. The sold black line has been lotted using the values of Shedlovsky (4).
10% m2 M' 1 A Figure 7. A plot of A c against 11.4 for acetic acid solutions at 2 5 T . The solid line has been computed by a least-squarer analysis.
a suitable ammeter can he acquired for approximately $10-15. We have not included the cost of a potential measuring device because these are standard equipment in most laboratories. Certain disadvantages of the dc method should he noted. One is that the range of the conductances that can he measured is restricted by the potential measuring device. If the electrolyte is very dilute, the potential drop across i t can be very large, and so measurements can only be made a t low currents. For example, with the cell described here, the potential drop across a 0.0005 mole l-' solution of acetic acid was 3.5 V for a 19 pA current. Another disadvantage is that it takes somewhat longer to determine the resistance of a given solution. Several pairs of voltage-current readings are desirable. Literature Cited (11 Vetter. K. J., "Electrochcmieal Kineti-." Academic Prers Inc., N e w York. 1967. p. ln4. 12) Bockris, J. O'M.. and Reddy, A. K. N.. "Modern Elaetroehemistry." Vol. 2. Plenum Pies N e w York. I97O.p. 991. (31 Robinson, R. A., and Sfokos, a. H.."Electefmly~Solutions." 2nd. Ed.,Buttowarths, London. 1959. o.98 141 ~hedluvrky.~.,i ~ i e rCham . So
