G. P. Haight, Jr. University o f Illinois Urbano, Illinois
I I I
The Use of Tables of Data in Teaching The students discover laws about ionization potentials
Several years ago a senior student (now Dr.), Paul Resnick, in a course in inorganic chemistry came to the author's office and announced his belief that the published value for the fifth ionization potential' for selenium was wrong. He had become curious concerning the difference in ionization energies2 between the last p and first s electrons removed from an atom and had constructed Table 1 which is reproduced exactly as he first presented it, showing an ohvious break in the pattern a t selenium. This inspired curiosity of one student naturally led to making a regular assignment to students of inorganic chemistry. They are asked to see what they can discover in a table of ionization potentials beyond the usual periodic fluctuations in the first ionization potential of the elements which are presented graphically in most general chemistry texts. The observation concerning the fifth ionization potential of selenium is quoted and students are asked to examine it critically. Usually, individually or collectively, a class will discover what we now refer to as the law of second differences, namely: In a series of isoelectronic atoms and ions arranged in order of increasing nuclear charge the second differences between ionization potentials are constant as shown in Table 2. Such a relationship has been known and is in the literature3 but has been left out of modern textbooks of physical and inorganic chemistry. One student observed a consequence of the second difference law without actually discovering the law. He took differences between ionization potentials for atoms in the same column in periods 2 and 3 and found that the second differences of the differences for species of the same outer shell configuration were the same (Table 3).
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A physics major, with chemical interests, asked the question in class discussion if some theoretical justification for the law of second differences could he obtained from atomic theory. The students in his class responded by showing that the law of second differencesis a consequence of the Bohr theory of the hydrogen atom as follows: The energy of an electron in a Bohr orbit is given by:
where the symbols have their usual meaning. Since 7
n2h' 4r%.Zea
= --
'Complete tables of ionization potentids may be found in handbooks of chemistry and physics and advanced inorgmic chemistry tests, e.g.: a. "Lange's Handbook of Chemistry," (10th Ed.), McGraw-Hill Book Company, New York, 1961. b. "Chemical Rubber Company Handbook," (46th Ed.), Cleveland, Ohio, 1965. c. SIENKO, hl. J., PLANE,R. A,, AND HESTER,R. E., "Inorganic Chemistry," W. A. Benjamin, Inc., New York, 1965. d. MOELLER,T., "Inorganic Chemistry," John W k y and Sons. Inc., New York, 1962. a I t is probably more accurate to discuss ionization energies than potentials but the quantity being discussed is labeled ioniaation potential in d l tables known to the author and abbreviated I.P. in nearly all texts. a TreatiseonPhysical Chemistry," ($rdEd.),Volume 1,(Editors: T-~YLOR, H. S., IND GLASSTONE, S.), D. Van Nostrand & Go., h e . , New York, 1942, contains a thorough discussion of ionisstion potentials of isoelectronic species. Here are presented plots i j ,,x- 6 versus Z showing slopes of 1, I/?, and '/a for n = of d .~ 1, 2, and :irespectively. It is alw shown that this 15 merely a apwialaarc uf the 3loseley 1.m ahlrh led to thcmnr?pt oiatomic number ~
Table 2. Ionization Potentialr: Changes for Ira-electronic Atoms and Ions
Table 4. Observed Second Differences in lonization Potentials for Various lsoelectronic Sequences
Species
N
-
Ground State for Isoelectronic Sequences like those in Table 1
Second Difference (v) Predicted Founde
1I
He +
Li, Bef, BE+,etc. Be, B+, C2+, etc. B, C+, NP+,etc. C, st, 02+, etc. S , O+, Fezf, etc. 0, Ft, etc. F, S e t , etc. S e , SaC, etc.
L12+ Be3+
B4+
CS s,-s+ +
O'+
He Li+ Be2+ B3+
c4+ S' +
oo+ p+ Thelaw @E/dZz = 2i.2/nPisseento bequite goodforn = 1,2, andj3. Paucity of data and uncertainty concerning its accuracy is reflected in values riven far n = 4 and n = 5. Virtuallv no data on f electrons g a s found in standard handbooks. \There tables hive been revised in recent years agreement with the law has been improved. Data used is fmm reference (c) given in footnote 1.
Table 3. Comparison of Differences of Ionization Potentials in Periods 2 and 3
I.P. for Period 3 element minus I.P. for Period 2 element
A
AA
Difference
Difference
Table 5.
Predictem
Be+-3lg+
anr
B?+-A1+
I.
9.48
c"7yi3+
19.35
N't*"
32.85
0s+-s6 +
50.05
FB+-Cl'+
Svecies
9.87
13.50 17.20 20.82 70.87 All values m electron volts a
back, one obtains an ionization potential of 0.74 v. The electron affinity of H is usually given as 0.76 v. The prediction of electron affinities for other atoms and ions is not entirely accurate, but the order of magnitude is reasonable as shown in Table 5. Students working on the ionization potential assignment trace the origins of data that appear wrong, learning a healthy skepticism for published data. They also review some older literature such as that in the "Treatise" by Taylor and Glasstonea and its references. Best of all, they think and argue critically about data in the manner of scientists with data of their own to explain. They wonder and argue about why the law of second differences works so well if the 470
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Calculated second differences emplol-ed.
Bohr model is so poor, especially for n = 2. They are stimulated to look freshly into atomic theory and to see if the wave mechanical atom offers as good or better model for correlating ionization potential data as the Bohr model. The point of this paper is not to present new information concerning relationships among ionization potentials hut to show what students are capable of discovering for themselves if their curiosity is aroused. I t would be interesting to see, for instance, how many freshmen might be able to find a relationship between vapor pressure and temperature. A table for water vapor pressure versus temperature is available in nearly all general texts and labor at or:^ manuals.
