In the Classroom
Predicting the Atomic Weights of the Trans-Lawrencium Elements: A Novel Application of Dobereiner’s Triads Sami A. Ibrahim Division of Math and Science, San Jose City College, San Jose, CA 95128;
[email protected] In 1829, Johann Wolfgang Dobreiner (1780–1849) reported that some elements may be grouped into triads, groups of three elements that show a smooth, gradual process in properties and also possess a special arithmetical relationship: the atomic weight of the second member in a given triad is almost exactly the mean of the atomic weights of the first and third member (1). Dobereiner’s early bold assertion was doomed to fail as not enough elements were then known and also because of the fact that most of the known elements could not be fitted into recognizable triads. It is interesting to note that, unlike Mendeleev, Dobereiner did not use his triads predictively. However, Dobereiner’s concept of triads provided Mendeleev with a method for correctly predicting the properties of three “missing elements”, which he named eka-boron (scandium), eka-aluminum (gallium), and eka-silicon (germanium). For more details, consult van Spronsen’s book, Periodic System of the Chemical Elements (2). An examination of the position of the first 92 elements in the modern periodic table (Figure 1) (3, 4) discloses the presence of the 10 triads, which are summarized in Table 1. The atomic weight of the second element in each triad is recalculated using the Dobereiner method and the percent error between the accepted atomic weights and those based on Dobereiner’s method are also shown. The relatively recent dis-
covery of rutherformium, dubnium, seaborgium, borhium, hassium, and meitnerium, and the recent reporting of the atomic masses of the most stable isotopes of elements number 111 and 112 (4), permit the identification of ten additional triads that include the first 10 trans-lawrencium elements as shown in Table 2. Student Challenge: Predicting Atomic Weights It is helpful when teaching the periodic table to give students problems in which they apply their knowledge of chemical periodicity for estimating unknown properties. A particularly challenging and relevant problem involves using the Dobereiner method to estimate atomic weights of the super heavy trans-lawrencium elements (113–118). A typical problem asks students to predict the properties of a yet to be synthesized super-heavy element. For example, an element may have a set of properties that resembles those of tin and lead, such as its nature and position in the periodic table and acceptable chemical formulas for the halides and oxides. Once students realize that the new element must be placed in the blank square below lead in group 14 of the periodic table, they are able to provide all remaining pertinent information. However, in order to predict the atomic weight of the element, a simple rearrangement of Dobereiner’s equation
Figure 1. This version of the periodic table is based on recommendations by the Commission on Nomenclature of Inorganic Chemistry and published in IUPAC Nomenclature of Inorganic Chemistry (4).
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In the Classroom
is needed. Thus, the idea that was first proposed by Dobereiner in 1829 may prove useful for predicting the atomic weights of elements number 113–118. The approximate atomic weights of these elements, which represent the heaviest members in their respective triads, may be estimated by subtracting the atomic weight of the first element in a given triad from twice the atomic weight of the second element. Table 3 shows six additional triads. The good agreement between the predicted and the reported atomic weights of elements 114–116 (2) attests to the usefulness of the observations that were first noted by Dobereiner. For additional information about Dobereiner’s other achievements, see Discovery of the Elements by Weeks and Leicester (5). Summary In 1829, Johann Dobereiner made the first significant attempt to show a relation between the properties of the chemical elements and their atomic weights. He reported that some similar chemical elements occurred in groups of three, which he called “triads”. An especially curious feature of these triads was that the atomic weight of the middle member of the triad was nearly equal the arithmetical mean of the atomic weights of the other two members of the triad. Dobereiner’s bold assertion was doomed to fail as not enough elements were then known. However, Mendeleev later used Dobereiner’s method as the basis for predicting the properties of three “missing elements”. The recent identification of elements 104–112 and the anticipated synthesis of the remaining super heavy “7p” elements would disclose the existence of 26 triads. Dobereiner’s groupings remain useful for providing reasonable estimates for the properties and the atomic weights of the trans-lawrencium elements. Acknowledgments The author would like to thank John Neptune, San Jose State University, for reviewing the original manuscript and for his invaluable suggestions. I would also like to express my sincere thanks to the reviewers and editorial staff of the JCE for their thoroughness, patience, and helpful suggestions. Last, but not least, I would like to thank the NSF Math and Science Teachers Preparation (MASTEP) Principal Investigators for their leadership, guidance, and generous support.
Table 1. Ten Readily Recognized Dobereiner Triads Triad 1
6.94 (Li)
2
9.01 (Be) 24.3 (Mg)
1. Poggendorff, J. C. Annalen der Physik und Chemie 1829, 15, 301–307. Reprinted in Ostwald’s Klassiker, No. 66, “J. W. Dobereiner und Max Pottenkofer, Die Anfange des naturlichen Systems der chemischen Elemente. (1829, 1850). Nebst einer geschichtlichen Uebersicht der Weiterentwichlungen der Lehre von den Triaden der Elemente. Herausgegeben von Lothar Meyer”, Leibzig, 1895; for an English translation, see Leicester, H. M.; Klickstein, H. S. A Source Book in Chemistry, McGraw-Hill: New York, 1952. 2. van Spronsen, J. W. The Periodic System of the Chemical Elements: A History of the First 100 Years; Elsevier: New York, 1969. 3. WebElements Home Page. http://www.webelements.com/ webelements/scholar (accessed Aug 2005).
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23.0 (Na)
39.1 (K)
Est. Atomic Weight
Error (%)
23.0 (Na)
40.1 (Ca) 24.6 (Mg)
0.087 1.0
3
39.1 (K)
85.5 (Rb)
132.9 (Cs) 86.0 (Rb)
0.58
4
40.1 (Ca)
87.6 (Sr)
137.3 (Ba) 88.7 (Sr)
1.3
5
27.0 (Al)
69.7 (Ga) 114.8 (In)
70.9 (Ga) 73.4 (Ge)
1.1
121.8 (Sb) 76.4 (As)
2.0
6
28.1 (Si)
72.6 (Ge) 118.7 (Sn)
7
31.0 (P)
74.9 (As)
1.7
8
32.1 (S)
79.0 (Se)
127.6 (Te)
79.9 (Se)
1.1
9
35.5 (Cl)
79.9 (Br)
126.9 (I)
81.2 (Br)
1.3
10
40.0 (Ar)
83.8 (Kr)
131.3 (Xe)
85.7 (Kr)
2.2
NOTE: The atomic weight is estimated using Dobereiner’s method.
Table 2. Triads that Include the First Ten Trans-Lawrencium Elements Triad 11
Accepted Atomic Weight 088.9 (Y)
175.0 (Lu)
12
091.2 (Zr)
178.5 (Hf)
13
092.9 (Nb) 180.9 (Ta)
262 (Lr)0
Est. Atomic Error Weight (%) 175.5 (Lu)
0.29
261 (Rf)
176.1 (Hf)
1.3
262 (Db)
177.5 (Ta) 1.9
14
095.9 (Mo) 183.8 (W) 266 (Sg)
180.9 (W) 1.6
15
098.0 (Tc)
181.0 (Re) 2.8
186.2 (Re) 264 (Bh)
16
101.1 (Ru) 190.2 (Os) 277 (Hs)
189.1 (Os) 0.59
17
102.9 (Rh) 192.2 (Ir)
268 (Mt)
185.5 (Ir)
18
106.4 (Pd) 195.1 (Pt)
281 (#110) 193.7 (Pt)
3.5 0.72
19
107.9 (Ag) 197.0 (Au) 272 (#111) 190.0 (Au) 3.6
20
112.4 (Cd) 200.6 (Hg) 285 (#112) 198.7 (Hg) 0.95
NOTE: The atomic weight is estimated using Dobereiner’s method. The relatively large errors in estimating the atomic weights of iridium and gold may be attributed to the use of the atomic masses of the most stable isotopes of Meitnerium (Mt) and element 111, respectively. However, the accuracy of the estimates of average atomic weights obtained using the triad procedure is of the same order as the average spread in isotopic weights.
Table 3. Triads Involving Trans-Lawrencium Elements Triad 21
Literature Cited
Accepted Atomic Weight
Accepted Atomic Weights
Est. Atomic Weight
Error (%)
114.8 (In) 204.4 (Tl) 284 (#113)a 294.0 (#113) 3.5
22
118.7 (Sn) 207.2 (Pb) 289 (#114)
295.7 (#114) 2.3
23
121.8 (Sb) 209.0 (Bi) 288 (#115)
296.2 (#115) 2.8
24
127.6 (Te) 210.0 (Po) 289 (#116)
292.4 (#116) 1.2
25
126.9 (I)
209.9 (At)
--- (#117)
292.9 (#117)
---
26
131.3 (Xe) 222.0 (Rn)
--- (#118)
313.0 (#118)
---
a
All atomic weights and atomic masses in this column are the 1995 recommended values of the most stable isotope (5, 6).
4. Periodic Table. http://www.chem.qmul.ac.uk/iupac/AtWt/ table.html (accessed Aug 2005). 5. Weeks, M. E.; Leicester, H. M. Discovery of the Elements, 7th ed.; Journal of Chemical Education: Easton, PA, 1968. 6. Leicester, H. M. Pure Appl. Chem. 2001, 73, 667.
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