Chemical Education Today
Letters Discovery of the Elements Ranking Sweden as number one on the list of discoveries of new elements, with a score of 20 (J. Chem. Educ. 1996, 73, 937) neglects the score of 23 by Britain. All the elements attributed to Scotland and England were discovered after the union of those countries in 1707. Rule Brittania. Stephen Hawkes Department of Chemistry Oregon State University Corvallis, OR 97331-4003
✍ In a recent article (1) ranking the countries by the number of elements discovered, it is stated that only one element, and not three as usually accepted, was discovered in Spain. Apparently the author takes the geographic view that elements are discovered by the country in which they are discovered. According to this, helium was discovered by the Sun! The usual view is that elements are discovered by persons who are nationals of a given country. Going a step further, in his ranking of countries by number of Nobel Prize winners, Asimov (2) uses the criterion that in case of doubt “the key point is a man’s scientific birth and that this takes place in college”. So, he assigns Albert Einstein to Switzerland, because that is the country where he received his undergraduate training. There is no doubt in the present case: three elements were discovered by Spanish nationals born and educated in Spain. The brothers Fausto and Juan José de Elhúyar, working in Spain, discovered tungsten or wolfram in 1783. Antonio de Ulloa, an officer in the Spanish Navy, discovered platinum during a scientific expedition in what is now Colombia, and then part of the Virreinato de Nueva Granada, in 1753. And Manuel del Río, a Spanish scientist appointed as professor in the School of Mines in Mexico, then part of the Virreinato de Nueva España, discovered vanadium in 1801. Due credit is given to these Spanish scientists for the discovery of the said elements in the section “The Elements” of the CRC Handbook of Chemistry and Physics (3). Literature Cited 1. Thomsen, V. J. Chem. Educ. 1996, 73, 937. 2. Asimov, I. Asimov on Chemistry; Macdonald and Jane’s: London, 1975; p 216. 3. CRC Handbook of Chemistry and Physics, 1995–1996, 76th ed.; Lide, D. R., Ed.; CRC: Boca Raton, FL, 1995.
C. Gutiérrez Instituto de Química Física “Rocasolano”, C.S.I.C. C. Serrano, 119 28006-Madrid; Spain
Waste Treatment in the Undergraduate Laboratory: Let the Students Do It! John J. Nash, Jeanne A. R. Meyer, and Susan C. Nurrenbern (J. Chem. Educ. 1996, 73, 1183–1185) published an innovative approach to reduce the amount of waste in the general chemistry laboratory and to contribute to environmental education. They let the students work up wastes
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from their own experiments—for example, remove poisonous copper and zinc ions from complex solutions by precipitation with sodium sulfide and filtration. Before pouring the filtrates down the drain, they should not forget to add hydrogen peroxide to oxidize excess and poisonous sodium sulfide to nonpoisonous sulfate. Volker Wiskamp FBC der Fachhochschule Darmstadt Hochschulstraße 2 D-64289 Darmstadt, Germany The authors reply: Professor Wiskamp certainly raises an important point. We should be just as concerned about the removal of sulfide from the filtrate as removal of the transition metals. We have tested filtrates from this experiment with lead acetate test paper and have found that, as long as the waste treatment procedure is followed as we have described, sulfide ion is not detectable (the lower limit of the sensitivity of the lead acetate paper is 25 parts per million according to the manufacturer). John J. Nash, Susan C. Nurrenbern, and Jeanne A. R. Meyer Department of Chemistry Purdue University West Lafayette, IN 47907
Group Theory in Advanced Inorganic Chemistry Faltynek (J. Chem. Educ. 1995, 72, 20–24) discusses some very important points. We wish to draw attention to the work by Sharma (J. Chem. Educ. 1982, 59, 554– 557), which addressed the problems cited by Faltynek. It is unfortunate that the most recent work might introduce the wrong impressions that were hopefully eradicated by Sharma in 1982, and is constrained to orthogonal axes. We quote from the 1995 work (p 20, paragraph 2, line 13): “An improper rotation is a binary operation involving consecutive application of the unitary operations of rotation and reflection through a perpendicular plane (Cn mσh = σhCn m = Sn m).” This does not take into account explicitly that the operation does not mean that a symmetry element exists. We quote from the 1982 work, to make this clear (p 554, under the heading Schöenflies Notation): “In the Schöenflies notation, at the very outset, one needs to reckon with two different ways of writing the symbols, namely the boldface (or italic symbols) and the ordinary symbols. These symbols employing the same letter and number mean two entirely different ideas.” Further on page 555 under the subheading Spectroscopist’s Alternating (Rotatory-Reflection) Axes, we have “Point groups possessing just alternating axes, symbolized as Sn, involve an n-fold counterclockwise rotation of a motif to give an imaginary motif… .” The word imaginary is crucial in that students should never get any lingering thought that a rotation axis or a mirror plane exists. continued on page 1160
Journal of Chemical Education • Vol. 74 No. 10 October 1997
Chemical Education Today
Letters continued from 1152 Finally, most discussions on symmetry are based upon just the spectroscopist’s viewpoint. No attention is paid the well known Hermann–Mauguin concepts of the crystallographic point of view. I was fortunate in that I had exposure to both view points. I urge the readers to study the excellent article by the late J. D. H. Donnay (Acta Crystallogr. 1972, A28, S110 and the references cited therein.).
Literature Cited: 1. Roo, S. D.; Vermeire, L.; Görller-Walrand, C. J. Chem. Educ. 1995, 72, 419–422. 2. Clifford, A. F. Inorganic Chemistry of Qualitative Analysis; Prentice-Hall: Englewood Cliffs, NJ, 1961; pp 150–151.
Morris Bader Department of Chemistry Moravian College Bethlehem, PA 18018
Brahama D. Sharma Department of Chemistry California State University, L.A. Los Angeles, CA 90032, and Los Angeles Pierce College Woodland Hills, CA 91371
The reply: Bader makes a correct comment regarding the calculation of solubilities of carbonate salts. The usual equilibrium
Ionization Constants A small but pervasive error permeates the chemical literature concerning the first ionization constant, K1, for carbonic acid, H2CO3 . This error surfaced in this Journal in the article by De Roo et al. (1) on the exact solubilities of insoluble salts. The authors most likely used a handbook value of 4.45 × 10{7 for K1, which is incorrect. The correct value for K1 is 1.5 × 10{4. In this regard, carbonic acid is an exact analog of H2SeO3 and other similar oxyacids. Clifford (2) explains the problem as follows. The equilibrium constant K1 represents the usual process: H+ + HCO3{
H2CO3
bubble out of the solution. In De Roo’s case, on the solubility of carbonates, the error appears only in the concentration of H2CO3; it is too small to impinge on any other tabulated results.
H2CO3 + H2O
H 2CO 3
H2CO3 + H2O CO2(aq) + H2O
+
CO2(aq)
{14
2{
=
1.00 × 10 K2
=
1.00 × 10 K1
CO3
= K eq = 4.2 × 10
H2CO3 ;
{14
{ HCO3
From these two equilibria we can derive a third: CO2(aq) + H2O
{
{
{
{7
H2CO3
K hyd = 2.8 × 10{3
Since the maximum solubility of CO2 is approximately 0.034 M, the maximum concentration of H2CO3 in water is 9.5 × 10 {5 M. Any time this value is exceeded, CO2 will
K = 2.8 × 10{3
H2CO3
[Ba][CO32{] = K sp
H2CO3 OH
{
HCO3
K1 = 1.5 × 10{4
(see also ref 1 p 92). With respect to our previous text the structural equations become: For the solubility of barium carbonate
The resulting expression is the one that is incorrectly quoted for the first ionization constant of carbonic acid:
H
H3O+ + HCO3{
and
HCO3 OH
H + + HCO3{
K 1 = 4.45 × 10{7
should be replaced by
On the other hand, CO2 bubbled into water leads to the equilibrium CO 2(aq) + H2O
H3O+ + HCO3{
CO2(aq)
{3
= 2.8 × 10
(1)
with K2 = 4.7 × 10{4 (2)
with K1 = 1.5 × 10{4 (3)
with K = 2.8 × 10 {3
[Ba2+] = [CO32{] + [HCO3{] + [H 2CO 3] + [CO 2(aq)] (5)
Table 1. Solubilities of Carbonatesa Ion Cd2+ Pb2+ Ca2+ Ba2+ Mg2+ Ag+ a
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K sp 2.5E-14 3.3E-14 4.8E-9 5.1E-9 1.0E-5 8.1E-12
K 1 = 1.5 ×
10{4;
[CO3
[HCO3{]
[OH{]
[H2CO3]
[CO2(aq)]
1.6E-7
1.4E-8
1.7E-6
1.8E-6
6.5E-11
2.3E-8
5.7E-8
8.2
1.8E-7
1.7E-8
1.9E-6
1.9E-6
6.5E-11
2.3E-8
5.2E-9
8.3
1.9E-6
6.9E-5
3.8E-5
9.0E-5
9.0E-5
6.7E-11
2.4E-8
1.1E-10
10.0
1.3E-4
7.1E-5
3.9E-5
9.1E-5
9.1E-5
6.6E-11
2.4E-8
1.1E-10
10.0
1.3E-4
3.2E-3
2.8E-3
7.7E-4
7.7E-4
1.3E-9
7.8E-7
1.3E-11
10.9
3.6E-3
6.3E-5
1.2E-4
1.2E-4
6.7E-11
2.4E-8
8.6E-11
10.1
1.8E-4
(K sp
)0.5
K = 2.8 ×
10{3;
2{]
K 2 = 4.7 ×
(4)
10{11.
Journal of Chemical Education • Vol. 74 No. 10 October 1997
[H3O+]
pH
Solubility 1.8E-6
Chemical Education Today
2[Ba 2+] + [H3O+ ] = 2[CO32{] + [HCO3{] + [OH {] [H3
O+]
[OH{ ]
1.0 × 10 {14
=
Solubility =
(6) (7)
[Ba2+ ]
For the solubility of silver carbonate [Ag+]2 [CO32{] = Ksp {
{
HCO3 OH 2{
{14
=
1.00 × 10 K2
=
1.00 × 10 K1
CO3
{
H2CO3 OH {
CO2(aq)
(9)
{14
HCO3
H2CO3
(8)
(10)
Literature Cited
{3
= 2.8 × 10
(11)
[Ag+] = [CO32{] + [HCO3{] + [H2CO3] + [CO2(aq)] (12) [Ag+] + [H3 O+] = 2[CO3 2-] + [HCO3 {] + [OH{] [H3
O+]
[OH{]
= 1.00 ×
The problem now results in one more equation, leading to seven equations and seven unknowns. The solution is given in Table 1. As expected, the error only appears in the H2CO3 concentration. We still want to emphasize that the true contribution of our paper was to report on the efficient computation of solubilities using a symbolic mathematics package such as Mathematica. However, for application to the carbonates, the form of Skoog et al. (2) was a less recommendable choice, given the chemical features Bader pointed out very correctly. In the adjusted and more complex form above, Mathematica confirmed its effectiveness. On a SUN-Sparc station computation took about three seconds for the Ba2+ case and about eight seconds for the more complex Ag+ case. Thus it supports David (3), who also insisted on the importance of the tool in chemical education.
10 {14
Solubility = 1/2[Ag+]
(13) (14)
1. Harris, D. C. Quantitative Chemical Analysis, 3rd ed.; Freeman: New York, 1991. 2. Skoog, D. A.; West, D. M.; Holler, F. J. Analytical Chemistry, 6th ed.; Saunders: Fort Worth, 1992; pp 175–181. 3. David, C. W. J. Chem. Educ. 1995, 72, 995–997.
S. Roo, L. Vermeire, and C. Görller-Walrand Departement Scheikunde Katholieke Universiteit Leuven B-3001 Heverlee–Leuven, Belgium
Vol. 74 No. 10 October 1997 • Journal of Chemical Education
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