2.1 BASIC ELECTROCHEMICAL THERMODYNAMICS 2.1.1 Reversibility
2.3 LIQUID JUNCTION POTENTIALS
2.3.2 Types of Liquid Junctions
The reality of junction potentials is easily understood by considering the boundary shown in Figure 23.2a. At the junction, there is a steep concentration gradient in H+ and Cl~;
hence both ions tend to diffuse from right to left. Since the hydrogen ion has a much larger mobility than Cl~, it initially penetrates the dilute phase at a higher rate. This process gives a positive charge to the dilute phase and a negative charge to the concen- trated one, with the result that a boundary potential difference develops. The correspond- ing electric field then retards the movement of H+ and speeds up the passage of Cl~ until the two cross the boundary at equal rates. Thus, there is a detectable steady-state poten- tial, which is not due to an equilibrium process (3, 24, 30, 31). From its origin, this inter- facial potential is sometimes called a diffusion potential.
Lingane (3) classified liquid junctions into three types:
1. Two solutions of the same electrolyte at different concentrations, as in Figure 2.3.2a.
2. Two solutions at the same concentration with different electrolytes having an ion in common, as in Figure 2.3.2b.
3. Two solutions not satisfying conditions 1 or 2, as in Figure 2.3.2c.
We will find this classification useful in the treatments of junction potentials that follow.
Typei 0.01 M
HCI 0.1 M
HCI
• H+
•cr
©0
Type 2 0.1 M
HCI 0.1 M
KCI
00
ТуреЗ 0.05 M
KNO;
(a) (b) (c)
Figure 2.3.2 Types of liquid junctions. Arrows show the direction of net transfer for each ion, and their lengths indicate relative mobilities. The polarity of the junction potential is indicated in each case by the circled signs. [Adapted from J. J. Lingane, "Electroanalytical Chemistry," 2nd ed., Wiley-Interscience, New York, 1958, p. 60, with permission.]
2.3 Liquid Junction Potentials < 65 Even though the boundary region cannot be at equilibrium, it has a composition that is effectively constant over long time periods, and the reversible transfer of electricity through the region can be considered.
Conductance, Transference Numbers, and Mobility
When an electric current flows in an electrochemical cell, the current is carried in solution by the movement of ions. For example, take the cell:
0Pt/H2(l atm)/H+, СГ/Н+, СГ/Н2(1 atm)/Pt'© K } («i) (*2)
where a2 > a^1 6 When the cell operates galvanically, an oxidation occurs at the left elec- trode,
H2 -> 2H+(a) + 2e(Pt) (2.3.4) and a reduction happens on the right,
2H+(j3) + 2e(Pt') -> H2 (2.3.5) Therefore, there is a tendency to build up a positive charge in the a phase and a negative charge in p. This tendency is overcome by the movement of ions: H+ to the right and Cl~
to the left. For each mole of electrons passed, 1 mole of H+ is produced in a, and 1 mole of H+ is consumed in /3. The total amount of H+ and Cl~ migrating across the boundary between a and /3 must equal 1 mole.
The fractions of the current carried by H+ and Cl~ are called their transference num- bers (or transport numbers). If we let t+ be the transference number for H+ and t- be that for Cl~, then clearly,
t+ + t- = 1 (2.3.6)
In general, for an electrolyte containing many ions, /,
(2.3.7)
Schematically, the process can be represented as shown in Figure 2.3.3. The cell initially features a higher activity of hydrochloric acid (+ as H+, — as Cl~) on the right (Figure
(«) и/н
2/! 1 / t i l l 1
_/H2/R(с)
/ ! +_ ! ! !/H2/PI
Figure 2.3.3 Schematic diagram showing the redistribution of charge during electrolysis of a system featuring a high concentration of HCl on the right and a low concentration on the left.
16A cell like (2.3.3), having electrodes of the same type on both sides, but with differing activities of one or both of the redox forms, is called a concentration cell.
66 Chapter 2. Potentials and Thermodynamics of Cells
2.3.3a); hence discharging it spontaneously produces H+ on the left and consumes it on the right. Assume that five units of H+ are reacted as shown in Figure 233b. For hy- drochloric acid, t+ ~ 0.8 and t- ~ 0.2; therefore, four units of H+ must migrate to the right and one unit of Cl~ to the left to maintain electroneutrality. This process is depicted in Figure 2.3.3c, and the final state of the solution is represented in Figure 2.3.3d.
A charge imbalance like that suggested in Figure 233b could not actually occur, be- cause a very large electric field would be established, and it would work to erase the im- balance. On a macroscopic scale, electroneutrality is always maintained throughout the solution. The migration represented in Figure 2.3.3c occurs simultaneously with the elec- tron-transfer reactions.
Transference numbers are determined by the details of ionic conduction, which are understood mainly through measurements of either the resistance to current flow in solu- tion or its reciprocal, the conductance, L (31, 32). The value of L for a segment of solution immersed in an electric field is directly proportional to the cross-sectional area perpendic- ular to the field vector and is inversely proportional to the length of the segment along the field. The proportionality constant is the conductivity, к, which is an intrinsic property of the solution:
L = KA/1 (2.3.8) The conductance, L, is given in units of Siemens (S = fl"1), and к is expressed in S cm"1
or ft"1 cm"1.
Since the passage of current through the solution is accomplished by the independent movement of different species, к is the sum of contributions from all ionic species, /. It is intuitive that each component of к is proportional to the concentration of the ion, the mag- nitude of its charge |ZJ|, and some index of its migration velocity.
That index is the mobility, щ, which is the limiting velocity of the ion in an electric field of unit strength. Mobility usually carries dimensions of cm2 V"1 s"1 (i.e., cm/s per V/cm). When a field of strength % is applied to an ion, it will accelerate under the force imposed by the field until the frictional drag exactly counterbalances the electric force.
Then, the ion continues its motion at that terminal velocity. This balance is represented in Figure 2.3.4.
The magnitude of the force exerted by the field is \z-\ e%, where e is the electronic charge. The frictional drag can be approximated from the Stokes law as 6ттг]ги, where rj is the viscosity of the medium, r is the radius of the ion, and v is the velocity. When the terminal velocity is reached, we have by equation and rearrangement,
The proportionality factor relating an individual ionic conductivity to charge, mobility, and concentration turns out to be the Faraday constant; thus
(2.3.10)
Direction of movement
Figure 2.3.4 Forces on a charged particle moving in solution under the influence of an electric field. The forces Drag force ч—У Electric force balance at the terminal velocity.
2.3 Liquid Junction Potentials 67 The transference number for species / is merely the contribution to conductivity made by that species divided by the total conductivity:
(2.3.11)
For solutions of simple, pure electrolytes (i.e., one positive and one negative ionic species), such as KC1, CaCl2, and HNO3, conductance is often quantified in terms of the equivalent conductivity, Л, which is defined by
(2.3.12) where Ce q is the concentration of positive (or negative) charges. Thus, Л expresses the conductivity per unit concentration of charge. Since C\z\ = Ce q for either ionic species in these systems, one finds from (2.3.10) and (2.3.12) that
Л = F(u+ + u-) (2.3.13) where u+ refers to the cation and u- to the anion. This relation suggests that Л could be regarded as the sum of individual equivalent ionic conductivities,
Л = Л+ + A_
hence we find
Ai = Fu{
In these simple solutions, then, the transference number tx is given by
л
or, alternatively,
(2.3.14) (2.3.15)
(2.3.16)
(2.3.17) Transference numbers can be measured by several approaches (31, 32), and numerous data for pure solutions appear in the literature. Frequently, transference numbers are mea- sured by noting concentration changes caused by electrolysis, as in the experiment shown in Figure 2.3.3 (see Problem 2.11). Table 2.3.1 displays a few values for aqueous solutions at 25°C. From results of this sort, one can evaluate the individual ionic conductivities, Aj.
Both Aj and t-x depend on the concentration of the pure electrolyte, because interactions be- tween ions tend to alter the mobilities (31-33). Lists of A values, like Table 2.3.2, usually give figures for AOi, which are obtained by extrapolation to infinite dilution. In the absence of measured transference numbers, it is convenient to use these to estimate t\ for pure solu- tions by (2.3.16), or for mixed electrolytes by the following equivalent to (2.3.11),
(2.3.18)
In addition to the liquid electrolytes that we have been considering, solid electro- lytes, such as sodium /3-alumina, the silver halides, and polymers like polyethylene
68 Chapter 2. Potentials and Thermodynamics of Cells
TABLE 2.3.1 Cation Transference Numbers for Aqueous Solutions at 25°Ca
Electrolyte HC1 NaCl KC1 NH4C1 KNO3 Na2SO4
K2SO4
0.01 0.8251 0.3918 0.4902 0.4907 0.5084 0.3848 0.4829
Concentration, Ceqb 0.05
0.8292 0.3876 0.4899 0.4905 0.5093 0.3829 0.4870
0.1 0.8314 0.3854 0.4898 0.4907 0.5103 0.3828 0.4890
0.2 0.8337 0.3821 0.4894 0.4911 0.5120 0.3828 0.4910
aFrom D. A. Maclnnes, "The Principles of Electro- chemistry," Dover, New York, 1961, p. 85 and references cited therein.
^Moles of positive (or negative) charge per liter.
oxide/LiClO4 (34, 35), are sometimes used in electrochemical cells. In these materials, ions move under the influence of an electric field, even in the absence of solvent. For ex- ample, the conductivity of a single crystal of sodium /3-alumina at room temperature is 0.035 S/cm, a value similar to that of aqueous solutions. Solid electrolytes are technologi- cally important in the fabrication of batteries and electrochemical devices. In some of these materials (e.g., a-Ag2S and AgBr), and unlike essentially all liquid electrolytes,
TABLE 2.3.2 Ionic Properties at Infinite Dilution in Aqueous Solutions at 25°C Ion
H+
K+
Na+
Li+
NH^
ka2 +
OH~
СГ Br"
I"
NO3- OAc"
СЮ4
kstit
HCO3-
|Fe(CN)^
|Fe(CN)^
A0, c m2n "1e q u i v "l f l 349.82
73.52 50.11 38.69 73.4 59.50 198
76.34 78.4 76.85 71.44 40.9 68.0 79.8 44.48 101.0 110.5
и, cm2 sec"1 V"1* 3.625 X 10"3
7.619 X 10"4
5.193 X 10"4
4.010 X 10"4
7.61 X 10~4
6.166 X 10~4
2.05 X 10"3
7.912 X 10~4 8.13 X 10"4 7.96 X 10"4 7.404 X 10"4 4.24 X 10"4 7.05 X 10"4 8.27 X 10"4
4.610 X 10"4
1.047 X 10~3
1.145 X 10"3 aFrom D. A. Maclnnes, "The Principles of Electrochemistry,"
Dover, New York, 1961, p. 342
^Calculated from AQ.
2.3 Liquid Junction Potentials 69
WWWWWWWWWWWWVWNA-J
Figure 2.3.5 Experimental system for
demonstrating reversible flow of charge through a cell with a liquid junction.
there is electronic conductivity as well as ionic conductivity. The relative contribution of electronic conduction through the solid electrolyte can be found by applying a potential to a cell that is too small to drive electrochemical reactions and noting the magnitude of the (nonfaradaic) current. Alternatively, an electrolysis can be carried out and the faradaic contribution determined separately (see Problem 2.12).