chemical queries
J. A. YOUNG King. College Wilker-Barre, Pennsylvania
.
..
4
J. G. MALlK
Son Diego Stole College son D ~ ~ Colifornio ~ O .
. . . especially for introductory chemistry teachers
Question The usual conversion "formula" relating the Fahrenheit and Celsius scales of temperature is not readily understood by some students; is there another way to present this relationship to students, one which might he more lucid?
Answer
Some teachers question the utility of presenting any formula for conversion (since conversion tables are readily available) and prefer instead to occasionally refer to a Celsius temperature in an off-hand manner, as though it shouldbe commonly known by students, thus: "The temperature of the room is twenty degrees.", or, "This water is hot, its temperature is eighty." On the other hand, it is impossible to present the conversion relationshiu in a manner which houefullv makes more sense to'beginnem by starting with thk ratio of the relative size of the degrees on each of the scales, thus
By using -40 for both subscripted "a" temperatures, and rearranging, we get
These formulas are perhaps a bit more cumbersome to use, but easier to derive, or remember, since they are similar mathematically. It may also be instructive and interesting to students to substitute for the subscripted "b" symbols, or to use other temperatures in common, such as 20°C and 68'F, or 100°C and 212'F, or (another handy one to remember) 37.0°C and 98.6'F. (We are indebted to Mr. Thomas Fitzsimmons at St. Louis University, St. Louis, Mo., for calling this to our attention.)
Question Why are 4s rather than 3d electrons involved in the first and second ionizations of the first row transition elements?
Answer
The 9: 5 ratio is, of course, the ratio of the number of degrees (9) on the Fahrenheit scale compared to the number of degrees (5) on the Celsius scale. (It could also be presented as the number of degrees between the freezing and boiling points of water for each scale, expressed as the ratio 180: 100, or as the ratio between any other two sets of comparable points, say room temperature and the commonequivalent, -40°C or F, as [68 - (-40)IoF: [20 - (-40)l0C. The latter has a minor extra advantage in helping the student remember the unique quality of -40" in this context.) I n any event, this relationship of the relative degree sizes is the basis for the commonly used conversion formulas. If we choose the freezing point of water for the subscripted "a" temperatures;we have: Fb - 32 Cb-0
9 5
and this can be algebraically rearranged into the usual formulas
We solicit questions for this column and reactions to the answers given. Correspondence should be addressed to Dr. Jim G. Mdik at S m Diego State College, San Diego, California 92115. 444
/
Journal o f Chemical Educotion
by Gilbert P. Haight, Jr., University of Illinois, Urbana, Illinois I n one sense, the answer is easy, and abrupt. Because we have chosen to designate as 4s electrons those electrons which happen to be ionizable with the least energy input. I n another sense, the question has a certain illegitimacy about it, analogous to that asked of Newton: "Why do two masses exert a force of attraction on one another?" Newton replied: "I frame no hypotheses." The scientist studies how phenomena occur, and what structures are; he measures relationships. He observes connections or consistencies among different phenomena. And he develops a specialized vocabulary to describe his ideas. Often, as in this instance, it then becomes possible to ask a "why" question which superficially appears to make sense, but in reality is meaningless. Students, as we all know, sometimes tend to ask these kinds of "why" questions. However, there is a legitimate aspect to the question which is really being asked here. I n the building up (aufbau) of atoms it develops that the 19th and 20th electrons find states of lower energy as 4s instead of as 3d electrons, yet as soon as both 4s and 3d electrons are present (the 21st and 22nd electrons, for example) the 4s energy level becomes higher (lesser magnitude of negative potential energy) than the 3d level as mea-
3d and 4s levels do not have the same relative energy values as they have for nuclear charges somewhat less than +20. Or, since the 3d orbital penetrates less than the 4s, a higher nuclear charge is "required" to affect the potential energy of the 3d orbital. It happens that the different effects of nuclear charge on the 3d and 4s orbitals cause an inversion of the otherwise consistent relative energy relationships of these two orbitals for elements with atomic numbers between 16 and 21. For these elements, the 3d level is higher than the 4s; but from Sc on (atomic tpmber 21) the 3d level is lower (in negative potential energy) than the 4s, as can be seen in Figure 1. Question
Does the familiar mnemonic, "18, 28, 2p, 38, 3p, 49, 3d, 4p, 58, 4d, and so on" list the atomic orbit& in order of inoreasing energy? If not, which I slwpect is the case, what is the basis of the ordering for this mnemonic?
Answer
Figure 1. Tho roriotion of the energies of atomic orbitals with increasing atomic number in neutral otomr (energies not strictly to xole). Reproduced fmm COTTON. F. A,. AND WILKINSON. G.. "Advanced lnoroanic Chemistry." 2nd edition, l&cianca ~ublisheri(division of John ~ Y l e y8. Sons, Ins.1, 1966. p. 629, by permision of the publisher.
sured by the energy required to remove the electron from the neutral gaseous atom. Figure 1 shows the variation of orbital energies (plotted as negative potential energy; the scale is not linear) on the ordinate versus atomic number on the abscissa. Note, for example, the drop of the 4s orbital energy with increasing atomic number. The 4s orbital penetrates close to the nucleus, so the higher the nuclear charge, the greater the binding energy, the more negative the potential energy, of an electron which happens to occupy this orbital. The 3d level, on the other hand, is unaffected by nuclear charge, or almost so, until the nuclear charge is about +16, but even so, the 4s orbital energy has been steadily dropping and is now below the 3d level. Some elements in this region of the periodic table, S, C1, Ar, do not have electrons in either the 3d or 4s orbitals, in the ground state. (It is trne that an excited atom, Ar, for example, excited sufficiently to have an electron in the 4s orbital and an electron in the 3d orbital also would indeed lose that 3d electron with less energy required than would be required to lose that 4s electron.) But as indicated in Figure 1, if we consider a nuclear charge of +21, the 3d energy has decreased more than the 4s (in the interval from +16 to +21), so now less energy is required to remove a 4s electron than to remove a 3d. Further, the element now under consideration, Sc, has electrons in both the 3d and 4s orbitals in the ground state. So, the direct answer to the question is: Because for nuclear charges greater than +20, the
As suggested, the order is not descriptive of energy increase except for a few elements. To consider this further, note the figure from the preceding answer (Fig. l). Within the limitations of this printed reproduction, the relative energy relationships for each orbital designation are shown; note that these change as the atomic number of the element being considered changes. For example, consider tin, atomic number 50. I n order from most negative potential energy to least negative potential energy, we have is, 2s, 2p, 39, 3p, 3d, 4s, 4p, 4d, 5s, 5p, 6s, 6p, 4f, 5d, 7s, 7p, 6d, 5f, other less negative potential energy orbitals are not shown. I n the ground state configuration, of course, only the first few of these are occupied by the fifty electrons of a neutral tin atom. Notice that if we were to write a similar statement of the orbitals, in order, for mercury, say, atomic number 80, the list would contain the same symbols but somewhat differently arranged. I n its familiar form, then, the mnemonic is emphatically not a listing of the relative energy levels of the orbitals which is universally applicable to any arbitrary atomic number, though i t is often so used by students. It is, instead, a mnemonic for remembering ground state electron configurations in conjunction with the periodic table.' When properly used, the familiar form of the mnemonic reminds us that the ground state of elements in Groups IA and IIA is characterized by an ns' or an ns2 notation for the valence electrons, where n is the principal quantum number and is numerically equal to the period number of the element being considered. Similarly, for elements in Groups IIIA to VIIA, and the noble gases (except helium) the mnemonic reminds us that the valence electrons are characterized by npl to np6 notations, for the ground state. Then, for the transition metals (broadly defined) the mnemonic reminds us that these are characterized in their ground state by npo (no electrons in the outermost p orbitals) and by (n - l)dl to (n - l)dlonotations. Specifically, for the transition metals, the mnemonic should not be taken to signify anything about the relative energy levels of electrons i n n s compared to (n - l)d orbitals;
' EICHINGER, J. W., JR., TRIS JOURNAL,34,504 (1957). Volume 46, Number 7, July 1969
/
445
this is not its purpose. Notice, further, that the mnemonic characterizes valence electron orbitals for the A Group elements, but not for the transition metals. Further, the mnemonic does not characterize valence electrons for the actinide and lanthanide elements. Instead it clues us about the unique, determining, electron configuration of these elements in terms of (n - 2)f notations; indicating nothing about the energy levels of such orbitals, except indirectly. The content of the preceding two paragraphs is well known to teachers, hut somehow students sometimes fail to see clearly that direct reference to the periodic table is absolutely necessary if the familiar form of the mnemonic is to he correctly used; they instead conclude that the order of the symbols is consistent with relative energy relationships. Fortunately (perhaps) this is correct for many of the elements when emphasis is placed upon outer, valence electron configurations, but it leads to difficulties when it is so interpreted, literally, and applied to any element. We would like to acknowledge the assistance and helpful criticisms of Professor Gilbert P. Haight, Jr., in the preparation of this answer. Question
What is a liquid-liquid membrane electrode? Is it the same as an ionselective electrode?
Answer
by Garry A . Rechnitz, State U?f.iversityof New York, Buffalo, New York
Ion-selective electrodes are formed, in general, when a solid or glassy phase, usually in the form of a membrane, is combined with a reference element in a suitable physical arrangement. The best known example of such an electrode is the glass electrode; in its usual form it is selective for hydrogen ion. This selectivity resides in the properties of the membrane. I n general, the membrane must have appropriate properties of both ionic conductivity and chemical selectivity, to he useful. There is, however, no reason why the active phase of the memhrane cannot be a liquid; in such cases one may refer to the resulting device as a liquid-liquid memhrane electrode. Actually, there are usually three liquids involved in most membrane electrode systems of this type, as shown in Figure 2.
First, there is the "sample" liquid itself, containing the ion to be measured. The sample liquid also provides electrolytic contact between the liquid-liquid membrane electrode and the necessary external reference electrode, also immersed in the sample liquid. Second there is the active liquid phase, wit,h appropriate propert,ies (compare to the glass membrane of a glass electrode); it is usually an ion-exchange resin in liquid form. Finally, there is an internal reference solution. This solution is in contact with the active liquid phase and with a reference electrode mounted inside the body of the device. This reference solution is chosen carefully, in order to provide a stable (reference) potential. In principle, the construction of the entire electrode need not he as complex as that shown in Figure 2. I t should function quite satisfactorily if the three liquids were placed in direct contact with one another, say in layers. A phase boundary potential can arise at each of the interfaces between the layers. These phase boundary potentials, plus the potential developed between the reference solution and the reference electrode would then constitute the overall potent,iaL That potential would reflect the activity of the desired ion in the sample liquid, since the potential between the reference solution and the reference electrode is fixed by the composition of that solution and by the nature of the reference electrode. In practice, however, such an arrangement of liquid layers is not acceptable; it is difficult, to form liquidliquid interfaces and maintain them, reproducihly. So, in current practice, an additional inert memhrane is used; it partially immobilizes the interfacial portions of the ion-exchange fluid and sample solution, permitting reproducibility to be achieved. The membrane can be a disc of some inert plastic material, or a porous glass f i t . For convenience, it is usually constructed to be easily replaceable in case of contamination. I t is desirable to have the electrode clean itself, and to effect this, the internal liquids of the electrode are put under mild hydrostatic pressure; the internal fluids then tend to flow out, rather than the sample fluid flowing into the electrode. I t is now possible to prepare fairly successful electrodes sensitive for the cations Ca2+,Mgz+, Cu2+,etc., and the anions CI04-, NOa-, C1-, and others. The main difference among these successful electrodes is the chemical nature of the ion-exchange liquid. This liquid must have a preferential affinity for the ion of interest; in the case of the CaZ+electrode, the liquid is a calcium salt of a phosphoric acid ester. Since the principle involved in the construction of these electrodes is perfectly general, one may confidently expect that many new and improved electrodes will he devised in the future.% For further information see Ross. J. W. "Calcium-selective Electrode with Liauid Ion 156. 3780 ~xcbaneer." - , Science. ~, ~,~ -~ flSfi7) ~~~~~ ,
EISENMAN, G., et. &I.,"Membrane Structure and Ion PermeaINTERNAL R E F E E E K E SOLUTION
tion," Science, 155, 3765 (1967)
RECHNITZ, G. A,, "IonSelective Electrodm," Chem. Eng. News, 44(25), 146 (1967)
Figure 2. Liquid-liquid membrane electrode.
+ + + 446
/
Journal o f Chemical Education
