Research: Science & Education
Quantifying Electrical Character P. G. Nelson School of Chemistry, University of Hull, Hull HU6 7RX, UK In a previous article I suggested that substances be classified according to their electrical properties as shown in Figure 1 (1). There are three limiting types (metals, electrolytes, and insulators), and three intermediate types (semiconductors, semielectrolytes, and mixed conductors). I characterized these types qualitatively, and suggested a scheme for characterizing them quantitatively. This scheme was a little complicated, and could not be displayed graphically. In this article I should like to suggest a simpler scheme, which can be so displayed. Identification of Coordinates Consider, first, the axis between metals and electrolytes in Figure 1. This relates to the manner in which a substance conducts electricity. An index of this is the degree of electrolysis, t = n/nF
(1)
Here n is the amount of chemical change that takes place on the passage of a certain quantity of electricity (Q), and nF is the amount calculated from Q on the basis of Faraday’s laws. If t = 0 the conduction is metallic or semiconducting in character; if t = 1, it is electrolytic. In the first case the conduction has an electronic mechanism, in the second an ionic one.1 Physicists call t, which represents the fraction of current conveyed by an ionic mechanism, the “ionic transport number” (2). In general, t varies with the conditions of a substance, so these must be specified. This is considered further below. Consider, next, the axis between insulators and metals. This relates to the ease with which electronic conductors carry electricity. This is usually measured by the volume conductivity (σ). Since σ varies with temperature, pressure, and electric field strength, these must be specified. They need also to be chosen to make the value for one substance comparable with that for another. A reasonable choice is standard temperature (25 °C), atmospheric pressure (1 bar), and low field strength. Conductivities measured under these conditions (σ°) enable metals, semiconductors, and
insulators to be characterized as follows (1): metals σ° > 105 S m{1 semiconductors 105 S m {1 > σ° > 10{7 S m{1 insulators σ° < 10{7 S m{1 A more convenient index for use in Figure 1 is the quantity
c° = log10
σ ° + σ0 σ0
(2)
where σ0 = 10{13 S m{1. In terms of c°, the above characterizations become: metals c° > 18 semiconductors 18 > c ° > 6 insulators 6 > c° > 0 Consider, thirdly, the axis between insulators and electrolytes. This relates to the ease with which ionic conductors carry electricity. This is also measured by σ. Conditions again have to be chosen to make the value for one substance comparable with that for another. In this case account has to be taken of the fact that most electrolytes only become good conductors in the liquid state. Comparisons cannot therefore be made at the same temperature, otherwise lowmelting electrolytes are favored over high-melting ones (e.g., at 25 °C, water is a better conductor than sodium chloride [1, 2]). A reasonable choice of conditions is the liquid state at the melting point, with other conditions as before. This is a suitable point at which to make comparisons because, at it, the carriers of electricity have just enough mobility to form a liquid. Conductivities under these conditions (σ°°) enable electrolytes, semielectrolytes, and insulators to be characterized as follows (1): electrolytes σ°° > 10{2 S m{1 semielectrolytes 10{2 S m{1 > σ°° > 10{7 S m {1 insulators σ°° < 10{7 S m{1 A more convenient index is
c°° = log10
σ °° + σ0 σ0
(3)
in terms of which the characterizations are: electrolytes semielectrolytes insulators
c°° > 11 11 > c °° > 6 6 > c °° > 0
The choice of conditions for the conductivities requires t to be a mean of the values for a substance between 25 °C and the liquid at the melting point. A suitable mean is
t= 1/2 t max + t min
(4)
corresponding to the middle of the range of values. By using ¯t, c ° and c °° can be combined into a single index Figure 1. Electrical classification of substances (1).
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Journal of Chemical Education • Vol. 74 No. 9 September 1997
Research: Science & Education Application and Discussion
Figure 2. Plot of c against t¯ in the coordinate system shown. Data from Table 1 (D, diamond; G, graphite; i, intrinsic).
c = 1 – t c e° + tc i°°
(5)
where e and i refer to the electronic and the ionic component of the conductivity respectively. If t¯ and c are plotted as shown in Figure 2, a quantitative version of Figure 1 is obtained.
Values of t¯ and c for some representative substances are given in Table 1 and plotted in Figure 2. These lead to the same classifications as the scheme described in reference 1. The main difference between the two schemes is that substances for which σ ° < 10{7 S m{1, ¯t < 1, σ °° > 10{7 S m{1, and t °° = 1 are now classed as mixed conductors instead of electrolytes. This accords better with usage in physics (2). The points in Figure 2 do not generate an equilateral triangle but could be made to do so by introducing a scaling factor into eq 5. I have previously argued that an electrical classification of substances is superior to one based on bond type because the latter is an imprecise concept (1, 3). This is supported by a recent survey of published scales of ionicity, which found that these differ from one another by up to an order of magnitude (4). I accordingly believe that it would be better if students were taught to think of substances primarily in terms of electrical character rather than of bond type. By this I do not mean to imply that the two classifications are logically equivalent. As Jensen has shown (5), they are not. The bonding classification can still be taught, but at a later stage, and more critically. Acknowledgment I am very grateful to William B. Jensen for prompting me to produce a quantitative version of Figure 1. Note 1. There are two mechanisms of electrolytic conduction: (i) movement of actual ions (discrete atomic or molecular entities hav-
Substance
Table 1. Electrical Properties of Substancesa – σ e° / S m{1 σ i°° / S m {1 t
c
Diamond
0
~10{13
Silicon (intrinsic)
0
4 × 10{4
Copperb
0
6.2 × 107
20.8
Graphite i layers ⊥ layers
0 0
2.5 × 106 5 × 102
19.4 15.7
Iodine i layers ⊥ layers
0 0
1.7 × 10{6 5 × 10{10
7.2 3.7
Waterc
1
1.2 × 10{6
7.1
Sulfuric acid (100%)d
1
5.9 × 10{1
12.8
Sodium chlorideb
1
3.6 × 102
15.6
Aluminium chloride
1
~10{5
Cuprous oxide (intrinsic)
0
~10{8
Ferrous oxide
0
2 × 10 3
Titanium monoxidee
0
5 × 105
0.45
3
(5 × 102)g
14.5
Silver sulfideh
0.3
~10{4
(5 × 102)g
11
Benzene
0
7 × 10{13
Polyacetylene (polycrystalline)
0
~10{2
Cuprous
sulfidef
0.3 9.6
8 5 16.3 18.7
0.9 11
a Data
from ref. 1 except where indicated. E. A., Ed. Smithells Metals Reference Book, 6th ed.; Butterworths: London, 1983. c Dorsey, N. E. Properties of Ordinary Water-substance; Reinhold: New York, 1940. d Greenwood, N. N.; Thompson, A. J. Chem. Soc. 1959, 3474. e Data for TiO 1.00 . f Ref. 2; Pound, G. M.; Derge, G.; Osuch, G. Trans. AIME, J. Metals 1955, 203, 481; Yang, L.; Pound, G. M.; Derge, G. Trans. AIME, J. Metals 1956, 206, 783. g Estimated. h Ref. 2; Dancy, E. A.; Derge, G. J. Trans. Met. Soc. AIME 1963, 227, 1034. b Brandes,
Vol. 74 No. 9 September 1997 • Journal of Chemical Education
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Research: Science & Education ing an integral charge number, e.g., Na+, SO42{); (ii) movement of a component X of a polar entity XY by changing its attachment from one Y to another, and carrying an integral number of charges with it, e.g., H in [H 2OH] + + OH2 → H2O + [HOH 2]+ Here, i and ii are limiting types, with a continuous gradation between them. In ii, X is not an ion in the same sense as in i, and is better described as a “semi-ion” or “ionic carrier”.
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Literature Cited 1. Nelson, P. G. J. Chem. Educ. 1994, 71, 24. 2. Friauf, R. J.; Young, K. F.; Merz, W. J. In American Institute of Physics Handbook, 3rd ed.; Gray, D. E., Ed.; McGraw-Hill: New York, 1972; Sect. 9f. 3. Nelson, P. G. Educ. Chem. 1994, 31, 93. 4. Meister, J.; Schwarz, W. H. E. J. Phys. Chem. 1994, 98, 8245. 5. Jensen, W. B. Logic, History and the Teaching of Chemistry; Lectures given at the 57th Annual Summer Conference of the New England Association of Chemistry Teachers, 1995 (J. Chem. Educ. accepted for publication).
Journal of Chemical Education • Vol. 74 No. 9 September 1997
