In the Classroom
Model for Teaching about Electrical Neutrality in Electrolyte Solutions Tetsuo Morikawa* Department of Chemistry, Joetsu University of Education, Joetsu 943-8512, Japan;
[email protected] Bryce E. Williamson Department of Chemistry, University of Canterbury, Christchurch, New Zealand
In introductory courses in electrochemistry, students often develop erroneous ideas about the mechanism by which electrical current is transported through electrolyte solutions (1). If ions are evolved at one electrode and discharged at another, it is understandable that some students will imagine that the solutions in the vicinity of the electrodes will develop a net charge. Even when it is pointed out that such effects are offset by migration of counterions, the dependence of an ion’s migration rate on the ion’s charge, size, mass, and interactions with the solvent make it not intuitively obvious to the novice electrochemist that electrical neutrality will be maintained throughout the whole solution. Other misconceptions that derive from such confusion include a belief that electrons are responsible for currents through electrolyte solutions and salt bridges (2). These misunderstandings originate from a lack of appreciation of the manner in which electrical neutrality is maintained in electrolyte solutions during the passage of cations and anions. Although electronic conductance is possible in ionic solids (3), Faraday’s law of electrolysis requires that electrical current in liquid solutions be carried entirely by ions. That such transfer (100% ionic conductance) must occur under the condition of macroscopic electrical neutrality is a consequence of Gauss’s law, which shows that the electric field gradients required to achieve significant charge separations are very much greater than those employed in electrochemical cells (41). In 1853, J. W. Hittorf described a method for determining transport numbers of ions in solutions (5). This well-known procedure is described in many physical chemistry textbooks (6 ) and provides the basis for many teaching-laboratory experiments. However, its use is usually restricted to the context of electrolytic cells with emphasis on the determination of transport properties of individual ions. The aim of this note is to present a simple conceptual model, based on Hittorf ’s experiment, that can be used to rationalize the maintenance of electrical neutrality in electrolyte solutions. The same model also provides useful insight into the idea of reversibility of electrochemical cells.
give the transport numbers t(Ag+) = 0.464 and t(NO3᎑) = 0.536. This means that approximately 46% of the current passed through an AgNO3 solution is carried by Ag+ cations and about 54% by NO3᎑ anions. To understand how this relates to the maintenance of electrical neutrality, consider the electrolytic apparatus illustrated in Figure 1. Two silver electrodes are placed at the ends of a cylindrical vessel containing an aqueous solution of AgNO3, which is imagined to be partitioned into three sections; A and C are near the anode and the cathode, respectively, and B is in the center. The initial condition of this system is represented as Ag | (0+, 0᎑) (0+, 0᎑) (0+, 0᎑) | Ag Here the vertical lines indicate phase boundaries and the pairs of numerals in parentheses indicate the excess number of cations (+) and anions (᎑), with respect to the homogeneous starting condition, in each section of solution. Suppose that 100 electrons are passed from the left- to the right-hand electrode through the external circuit. On the left side, the anode yields 100 Ag+ ions into section A while on the right side 100 Ag+ ions from section C are deposited onto the cathode. The current through the solution involves transfer of both cations and anions in proportion to their transport numbers. Thus 46 Ag+ ions migrate from A to B and from B to C, and 54 NO3᎑ ions migrate from C to B and from B to A. The final state of the system is therefore expressed as Ag | (+54Ag+, +54NO3᎑) (0+, 0᎑) (᎑54Ag +, ᎑54NO3᎑) | Ag The concentration of AgNO3 remains unchanged in section B, but has increased in section A and decreased by the same amount in section C. The concentration difference between the final and initial states in sections A and C is in direct proportion to the transport number of the redox-inactive ion NO3᎑ and can therefore be used to determine t(NO3᎑) and t(Ag+) = 1 – t(NO3᎑).
100 e−
Transport of Ions in Hittorf Cells The concept of transport (or transference) number of ions is fundamental to an understanding of the maintenance of electrical neutrality in electrolyte solutions. According to an idea developed by Hittorf in the period 1853–1859, each ion has a characteristic migration rate during electrolysis (5), which determines the proportion of the total current that it carries through the solution. For example, experimental data extrapolated to infinite dilution for AgNO3 solutions at 25 °C 934
Ag anode
Ag cathode 54 NO3−
54 NO3−
+
100 Ag+
100 Ag
46 Ag
A
+
46 Ag
+
B
Figure 1. Diagram of electrolytic apparatus.
Journal of Chemical Education • Vol. 78 No. 7 July 2001 • JChemEd.chem.wisc.edu
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In the Classroom
Also evident from this model is the fact that electrical current flow in the reverse direction would bring the concentrations back to their starting values, so this Hittorf cell is thermodynamically reversible. But the main point here is that the model clearly demonstrates that electrical neutrality is maintained in all sections of the solution, without a necessity for electronic current and despite the unequal migration rates of cations and anions. Electrical Neutrality in Reversible Galvanic Cells The utility of this model is not restricted to electrolytic cells. The Harned cell (7) is an example of reversible galvanic cells commonly considered in thermodynamics courses. It comprises hydrogen and silver–silver chloride electrodes immersed in HCl solution. Pt | H2(g) | HCl(aq) | AgCl | Ag When the electrodes are connected by an external circuit, spontaneous current flow results in the production of H+ (at the anode) and Cl ᎑ (at the cathode), the transport numbers for which are t(H+) = 0.821 and t(Cl ᎑) = 0.179. After the transfer of 100 electrons, considerations analogous to those applied above to the Hittorf cell give the ionic increments in the final state represented by Pt | H2(g) | (+18H+, +18Cl᎑) (0+, 0᎑) (+82H+, +82Cl᎑) | AgCl | Ag
In this case the HCl concentrations in the vicinities of the two electrodes increase by different amounts—but again the change of concentration is in proportion to the transport number of the redox-inactive ion at that electrode, and electrical neutrality is preserved throughout each section of the solution. Furthermore, the passage of a reverse current would bring the HCl concentrations back to their original values and so this example provides a clear illustration of thermodynamic reversibility in galvanic cells. Electrical Neutrality in Salt Bridges The significance of the (0+, 0᎑) condition of the central (B) section in the examples above becomes clearly apparent when the cells are physically divided. For example, sections A and C might constitute half-cells while section B corresponds to a salt bridge or a porous barrier. There are no practical advantages to be gained by interposing such junctions in a Hittorf (or any other electrolytic) cell, but they are commonly used in galvanic cells when the reaction components must be kept separate. A simple illustration of the use and operating principles of salt bridges is provided by Owen’s concentration cell (8), in which the half-cells contain different concentrations of the same components. Such a cell is represented as Ag |x m AgNO3, (1 – x)m KNO3||m KNO3||y m AgNO3, (1 – y)m KNO3| Ag
Here KNO3 is a supporting electrolyte used to keep the ionic strength constant throughout the system, the double vertical lines represent a boundary between one half-cell and the saltbridge (agar) solution, and x m, y m, etc. are the molalities (mol/kg) of the solutions. When x and y are much smaller than one, the supporting electrolyte is the predominant solute in both half-cells. Under these conditions virtually all
of the charge passing into or out of the salt bridge is carried by ions from the supporting electrolyte. Analogous considerations demonstrate that electrical neutrality must be preserved not only within the half-cells but also throughout the salt bridge. The solution in the salt bridge is imagined to be divided into three sections, the terminal sections being in contact with half-cell solutions. The initial state is abbreviated as Ag | (0+, 0᎑) || (0+, 0᎑) (0+, 0᎑) (0+, 0᎑) || (0+, 0᎑) | Ag where the numerals in parentheses indicate the excess of cations and anions in each section. Suppose that a very small current causes two Ag+ cations to be released from the electrode into the left half-cell solution while two others are deposited from the right half-cell solution onto the electrode. Each half-cell solution is neutralized by the transfer of supporting-electrolyte ions from or to the salt bridge. For example, assuming t(K+) = t(NO3᎑) = 1⁄2 for KNO3 solution (which is approximately correct), the final state would be Ag|(+2Ag+, ᎑K+, +NO3᎑)||(0+, 0᎑)(0+, 0᎑)(0+, 0᎑)||(᎑2Ag+, +K+, ᎑NO3᎑)|Ag
The increase of AgNO3 concentration in the left half-cell and its decrease in the right half-cell are accompanied by commensurate changes in the KNO3 concentrations, and overall electrical neutrality is maintained. Moreover, ion transport between sections of the salt-bridge solution counterbalances any concentration gradients in the supporting electrolyte within the bridge, so that its contribution to the measured cell potential (the junction potential) is negligible. If a small current is reversed after a short period, both half-cell concentrations will return to their original values and the electrochemical cell will behave reversibly. However, with repeated or extended use, some redox-active Ag+ cations will eventually diffuse into the terminal sections of the salt bridge, destroying its ability to function ideally. For that reason, salt bridges must be replaced at regular intervals if the cell is to behave reversibly. Porous Barriers and Electrical Neutrality The Daniell cell is a galvanic cell containing both Zn metal in an aqueous ZnSO4 solution and Cu metal in an aqueous CuSO4 solution. The zinc plate is oxidized to Zn2+ while Cu2+ is reduced to metallic copper. If the two solutions were in direct contact, these processes would constitute thermodynamically irreversible chemical reactions. For that reason, the two half-cells must be separated—in this case, by a porous barrier with H 2SO4 as a supporting electrolyte. Ideally, the barrier should only permit the transport of redoxinactive ions, principally H+. However in practice it inevitably allows the passage of small amounts of redox-active Zn2+ and Cu2+ ions. The initial state of the electrochemical cell can be represented by Zn | (0+, 0᎑) || (0+, 0᎑) | Cu where || now denotes the porous barrier and (0+, 0᎑) in the left- and right-hand sides, respectively, refer to the aqueous ZnSO4 and CuSO4 solutions.
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Now assume that 100 electrons are transferred via an external circuit from the Zn anode to the Cu cathode. Electrical neutrality is maintained by transport of H+ ions across the barrier, the final state of the system being Zn | (+50Zn2+, ᎑100H+) || (᎑50Cu2+, +100H+) | Cu For an ideal barrier (permitting the passage of only redoxinactive ions) a reverse current would bring the concentrations back to their initial values and the Daniell cell would be reversible. However, because of the passage of some redoxactive ions, the Daniell cell is said to be only approximately reversible. For example, Zn2+ ions that cross into the Cu2+/Cu half-cell will diffuse away from the porous barrier and will not be completely returned to the Zn2+/Zn half-cell by passing a reverse current. The ZnSO4 will not revert to its original concentration and the cell is therefore not entirely reversible. Note 1. In SI units, eq 6 in ref 4 should read
Σ c i zi =
ε ∇2 φ 103 F
where ε is the permittivity (rather than the dielectric constant) of
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the solution and the factor 103 in the denominator is required for ci in mol L᎑1. For water, which has one of the largest dielectric constants of common solvents, ε ≈ 7 × 10 ᎑10 J᎑1 C 2 m᎑1. This gives
∑ c iz i ≈ 7.25 × 10᎑18(V ᎑1 m2 mol L᎑1) ∇ 2 φ Note that ∇ 2 φ represent an electric field gradient rather than the field strength or potential difference. The extremely small leading coefficient indicates that charge separation is strongly suppressed under conditions that occur in electrochemical cells.
Literature Cited 1. Ogude, A. N.; Bradley, J. D. J. Chem. Educ. 1994, 71, 29– 34. 2. Sanger, M. J.; Greenbowe, T. J. J. Chem. Educ. 1997, 74, 819–823. 3. Perrino, C. T.; Wentrcek, P. J. Chem. Educ. 1972, 49, 543–545. 4. Sastre, M.; Santaballa, J. A. J. Chem. Educ. 1989, 66, 403–404. 5. Leicester, H. M. The Historical Background of Chemistry; Dover: New York, 1956; Chapter 21, p 209. 6. Atkins, P. W. Physical Chemistry, 6th ed.; Oxford University Press: Oxford, UK, 1998; pp 744–745. 7. Harned, H. S.; Ehlers, R. W. J. Am. Chem. Soc. 1933, 55, 2179–2193. 8. Owen, B. B. J. Am. Chem. Soc. 1938, 60, 2229–2233.
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