Abbas Labbaufl The A. & M. College of Texas
College Station
The Carbon-12 Scale of Atomic Masses
A
student is not far into his first chemistry course before he encounters the concept of atomic weight. If it has not already been made clear to him, some discussion and careful definition of the terms "mass" and "weight" should be presented. Also the distinction between relative or assigned values and the absolute or inherent values of these properties should be made. All weights are relative, though precisely defined in terms of the force exerted on matter in a gravitational field in comparison to that for a standard. The amount of matter is its mass. Due to long established usage, the term"atomic weight" seems still to he preferred by most chemists a t present. Thus we speak of the atomic weight defined as the relative weight of the element-being the measured property of its atomic mass with respect to that of an intentionally agreed upon standard atomic mass. For nuclides, a term suggested by Kohman (1) and defined as "a species of atom characterized by its nucleus, in particular by the number of protons and neutrons in its nucleus," the corresponding term nuclidic mass is used. Correspondingly, the nuclidic mass has a weight relative to that for the mass of an internat,ionally agreed upon nuclide. Our use of the t,erm "weight" when referring to mass follows the precedent of the IUPAC in its presentation of the At,omic Weight Table [see THIS JOURNAL, 38, 625 (1961)l. The Commission on Atomic Weights of the Internat,ional Union of Pure and Applied Chemistry (IUPAC) had, prior to the meeting of the Union in 1959, proposed the adoption of a reference mass scale based on I2C (carbon-12 isotope = 12 exactly) to which the atomic weights of all elements would refer and which would serve as a common scale for use by both chemists and physicists. In August, 1959, the IUPAC approved the recommendation for a unified atomic weight scale providing that similar action would he taken by the physicist,^. The corresponding representative organization for physics, the International Union of Pure and Applied Physics (IUPAP), at its meeting in 1960, approved the adoption of the carbon-12 atomic weight scale, permitting the chemists to take final action a t the recent meeting of the IUPAC in 1961. This meeting was held August 2-5, 1961, in Montreal, Canada; the reference scale, based on 12C = 12 exactly, was formally adopted. The reasons
for abandoning the old reference scales and the factors that have led to the adoption of the new I2C scale, called the unified mass scale, are closely related to the progress of science and the refinement in its techniques over the past 30 years. The Concept of Atomic Weight
Only comparatively recently, in the early part of the 18th century, was the idea of the atom widely accepted. By about 1800, however, the laws of definite proportions and multiple proportions were well established. At that time the chief concern was the assigning of weights to atoms, a process which has continued for over 150 years t,o the present day. A short but interesting history of these developments from the time of Dalton to the present is given in the Information Bulletin, No. 14A, July, 1961, of the International Union of Pure and Applied Chemistry. This survey also outlines the activities of the various national organizations whose efforts finally culminated in the formation of t,he IUPAC. The chemical method of determining the atomic weight of any element is, in many cases, dependent on previous knowledge of the molecular weight of compounds in which the element is a constituent part. The determination of molecular weights is based fundamentally on Avogadro's hypothesis. The application of this hypothesis can yield only relative molecular weights and not absolute values; therefore, a defined standard is required on which one can base the atomic weights of other elements. Since hydrogen is the lightest element, it appeared best to choose this element as standard and assign the value of unity to its atomic weight. Prout's hypothesis that t,he elements were composed of a varying nnmber of hydrogen atoms favored this choice. This would have been an adequate selection if the at,omic or molecular weights alone mere to be considered. But since these values must be used in connection with combining weights, oxygen serves as a better standard for comparison because of its abundance and reactivity. Sinre oxygen is a better working standard for chemically determined ratios, a scale based on oxygen gradually came to be preferred. I t was natural to use an integral value for the atomic weight of this element. The choice of 0 = 16 had the fortunate coincidence of making nuclidic weights nearly identical with their mass numbers. The Rise and Coexistence of Two Scales
This investigation was performed under the American Petroleum Institute Research Project 44 and the Manufacturing Chemists Association Research Project. 1 Present address: Lard Mfg. Co., Erie, Pa.
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A scale based on oxygen seemed to provide a satisfactory atomic weight scale. I t remained a happy choice until it was discovered that some elements
Table 1.
Comparison of the Chemical Scale, the Physical Scale, and the Unified M a r s Scale Bared on
(1)
1957 (or 1959) International tahle (Zfi) (2)
1961 International tahle (67) (3)
awu Oxygcn-16 unit (rtmu) Csrhon-12 unit (nmu)
'H
H (natural)
..
2H
'ZC C (natural) IY, \,
0 (natural)
H1O
co*
CH, CmH.2 a
Chemical sale' (4)
12C =
12 (exactly)
Physical scale (5)
1 exactly 0.999 275 1.000 043 1.007 865 1.008 011 2.014 181 12.000 516 12.011 617d 15.995 601 16 exactly 18.016 022 44.011 618 16.043 661 282.568 809
Unified sealea (6) 0.999 957 1.000 318 1 exactly 1.007 822 1.007 967 2.014 094 12 exactly 12.011 100 15.994.912 15.999 312 18.015 247 44.009 726 1 6 0 4 2 !471 282.556 663 ~
~~~
~~~
All the values in columns (4) and (6), except those that are hased on definition, were calculated from the values b s s d on the physical
BCIL~P.
Calculated by using t,he 1957 International Table for the Atomic Weigh&. Calculated by using t,he 1961 International Table for the Atomic Weights. Nier (10) reports the value 12.0115 =t0.0004 (hasrd on the chemical scale). The mean value hased on mass determination of "C and IaC isotopes by nuclear reaction technique and mass-spectroscopic determination of their relative abundance, as reported by Scott nnrl Ware 14. ~ ~ ..~. ~ 1681. ~ ..,, ~ i~. .s 12.01 . * Cxlcnlatrd from isotopic masses and isotopir ahuntlanccs given in reference (19), appendix G.
consisted of i~ot~opicmixtures. The discovery of isotopes would not have altered the situation a t all were it. not for the fact that ordinary oxygen, the standard itself, was found2 to consist of a mixture of isotopes: 160, "0, and 180, the latter two being discovered by Giauquc and Johnston (t) in 1929. The physicists, working with mass spectrometers in their stndy of isotopes, naturally chose for their standard system the oxygen nuclide of mass 16, while t,he chemists cont,inued to use 16 for the atomic weight of the isotopic mixture. In reports on atomic weights for the years 1955 and 1956, respectively, Wichers (5) discussed the problem of the two scales. Wichers (4, 6 ) has also touched upon certain aspects of the problem elsewhere. The importance of a unified by Kieffer scale has been discussed in THIS JOURNAL (6) and more recently by Guggenheim (7). Pertinent art,icles by Kohman, Mattauch, and Wapstra (8) and also hfattauch (9) have discussed the problem in the light of the proposed 12C as a unified reference basis. The unit of the physical scale is called the "absolute mass unit" (amn) or "isotopic mass unit" and the nnit of the chemical scale is called the "atomic weight nnit" (awn). Atomic masses are given on the physical scale while atomic weights are given on the chemical srale. For isotopic elements it would be more rigorous t,o use the term "mean atomic mass or weight," but t,here is no evidence of confusion resulting from the short,er designation used by chemists. The nnit of the physical scale is of the mass of "0 atom. The unit of the chemical scale is of the weight of the mean mass of an atom of natural oxygen and is t,herefore slightly greater than the physical unit (see Table 1). The quantitative relationship between the two scales is established in the following manner:
atomic -eight, on the chemical ecalc, of any natural element X K ( 0 ' ) = atomic weight, on the chemical scale, of natural oxygen M,(X) = atomic mass, on the phyeicd lsmle, of element X M,(O*) = atomic mass, on the physical sede, of natural omen
Let M.(X)
=
By definition of the chemical scale, M,(O*) = 16 exactly. The following relation exists among the above four quantities:
M,(O*) is the average atomic mass of natural oxygen referred to '9, and may be expressed in terms of mass, M,,;, of each isotope and its abundance (atom fraction), Ai, M.(O*)
=
= ZAi X M,,!
(2)
By definition, the conversion factor is M (0')- physical mass (amu)
(:3)
?=--e M,(O*) - chemical weight (awu)
Hence from (1)
The conversion factor, r , may also be defined in terms of the ratio of the units of atomic weight (chemical scale) to the units of atomic mass (physical scale).
.
- unit of the atomic weight = unit of the atomic mass m u
r -
(5)
The numerator and the denominator are magnitudes of the units when referred to the same reference base scale. We could say that the ratio is defined as a pure number. Thus, one may write for r and r* the following identity
A detailed disoussion of the isotopes of oxygen in contsined in reference (11). Volume 39, Number 6, June 1962
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The value of r can be calculated from a knowledge of the masses and the abundanre ratios of oxygen nuclides . "0.,and 180. 7
=
mean atomic mass of natural oxygen atomic weight of natural oxygen
+
- A('60)M(UO) A("O)M("O) 16
+ A(lUO)M(lao)> 1
Using values for the isot,opic abundances from reference (11) and isotopic massesfrom reference (19),
The disparity between t.he chemical and the physical scales was further heightened when it was observed that the isotopic abundance of oxygen in nature varies from source to source (10, 11). This led to the value of T varying between 1.000268 and 1.000278. In 1940 the IUPAC Commission on Atomic Weights adopted a value of 1.000275 for r corresponding to a "typical" natural oxygen. We thus note that the physical scale differsfrom the chemical scale by 275 parts per million. The factor r has at times been referred to as the Mecke-Childs factor. For historical interest it may he pointed out that Mecke (12) and Mecke and Childs (13) gave a value of r = 1.00022, basing their calculation on their spectroscopic measurement of the abundances of '60'"0, , and The Avogadro number, which was defined as the number of oxygen atoms in 16 grams of oxygen (now defined as the number of atoms in 12 grams of carbon12), also depends on what scale is chosen. So also do other propert,ies which are functions of the mole,%for example the Faraday constant, or the gas constant, R. The value based on one scale differs from the value based on the other scale by the factor r. The following quotation from the report of the International Commission on Atomic Weights for 1931 (17) indicates the manner in which this problem was viewed a t that time: The discovery of the oxygen isotope haa created the undesirable situation that chemistry and physics are using two different scales for the determination of stomic weights. Because of this, the question of an absolute standard has already been more or less widely discussed and various proposals made, for instance, IH = 1.00Wa; 'He = 4.OW00; l6O = 16.0000, as well as the present chemical standard 0 = 16.00M). F. W. Astan, who discussed the question comprehensively before the British Association in 1931, concludes that it is advisable far chemists to retain the present chemical standard, since it amply satisfies all requirements of International Atomic Weiehta - so far as accuracv is concerned. For the more exactine requirements of physics the oxygen isotope '80 seems to him a hetter standard. The Committee agrees unanimously with Aston's opinion and sees no reason for praposing a change in the present standmd of atomic weights, 0 = 16.0000.
Proposals for Unification of the Two Scales
It is immediately clear that the key to the solution of the problem of two srales would he to agree on a single reference substance and assign a value to its
For the dehition of mole the reader is referred to a, recent article by Guggenheirn (7). See ako references (14), (15), and (16).
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mass. However, there are at least two requirements that this reference substance should meet. These are: (1) that its mass should be an invariant. and (2) , . that its mass should be intercomparable with the masses of other nuclidic species. Requirement (1) is clear in the light of what has already been discussed. Require ment (2) is closely connected with the massspectroscopic method used by the physicists in mass determinations and will be discussed later. Of course, even if the indefiniteness of the chemical scale could have been removed by another better definition, we still would have been left with two lists of atomic weights and also two sets of values for those constants that are dependent on the mole. Proposals for the giving up of one scale in favor of the other met with objections, despite the fact that the adopted scale might have improvements over the discarded one. Many of these objections were well founded. To appreciate the seriousness of the problem, let us assume that the chemical scale was to he abandoned in favor of the physical scale. On t,he basis of this scale, l6O = 16 exactly, the atomic weight of natural oxygen would he 16.00440. This would mean a change of 275 parts per million in the atomic weights and related values, an amount which cannot be regarded as negligible. The need would then arise for the immediate revision of all mass and related quantities reported in handbooks, scientific tables, and the great collection of reference works where relative masses on the discarded scale have been reported. I t is well to note that the abandoning of the chemical scale would have involved the greater burden and difficulties involved in the revision process. I t was on such grounds that the alternatives to abandoning either of the scales were being sought, both by the chemists and the physicists. At this time the necessity for giving up both the physical and the chemical scales and the need for adopting a "universal" scale were receiving more urgent, attention. Several proposals were made. Among t,hese a scale based on 'H = 1 exactly was suggested. The great disadvantage of such a scale was that on t,his basis the masses (on t,he chemical scale) of all atoms would have had to he reduced by 7870 parts per million. This, indeed, is too great a change to be ignored. Hence it was argued by some that a large change of this magnitude might provide the spur for t,he total revision of all mass and related quantities. Another proposal was put forward, urging the adoption of a scale based on l9F, with an assigned mass of 19 exactly. Fluorine consists of a single naturally occurring nuclide. Nier (10) gives the value 18.9992 for its atomic weight on the chemical scale. On the physical scale the value is 19.0044. We thus note that if this element, used as a reference mass, were t,o have a value of 19 exactly as its assigned atomic mass, all the values based on the chemical scale would have to be revised upward by 42 parts per million. On the other hand, the values based on the physical scale mould have to be decreased by 231 parts per million. It. might be added that fluorine-19 as the reference species appealed to some chemists not only because it is invariant (so far as we now know), but because it is also a naturally occurring element, and therefore, a possible direct working standard for chemical determination of atomic masses. The atomic mass of 160on the
chemical scale, as recorded in Table 2, is 15.995601. On the supposition that the physical scale he given up in favor of the chemical scale, we note that the change to the physicists in the nuclidic masses would correspond to 275 parts per million. The idea, therefore, of using 19F = 19 exactly as a scale base appeared a little more attractive to the physicists. In connection with the adoption of this scale Mattauch and Nier later pointed out that the exchange of the ' 6 0 scale to '*F would result in the lowering of precision of the masses of many other nnclides that are determined by means of mass spectrograph. They also pointed out that a scale based on lgFas the reference nuclide does not permit as many comparisons and checkings of the results as can be obtained by either nuclear reaction techniques or by mass spectroscopy. With "0, the mass number of which is twice its atomic number, such difficulties do not exist. When the Commission on Atomic Weights of the K P A C met in 1957 (at Maison de la Chimie, Paris) it was obvious that certain steps would need to be taken in order to clarify the entire situation. The ideas and suggestions that were proposed a t that time aimed to solve the chemical atomic scale problem in such a manner as to avoid, if possible, the need for the great task of revision of the already existing chemical data. The suggestions that were put forward at that time were the following: (1)
to refer the sertle of 16 (exactly) aa the atomic weight of a defined mixture of oxygen isotopes;
( 2 ) to adopt a defined ratio of the atomic weights on the chemical soale to those on the physical 8cale; and (3) to define the chemical scale such that the mass of 'Q Oll he 16/r, where 1. is the conversion ratio diecuesed above and currently taken as 1.000275.
I t should be noted that actually none of the above suggestions provided any means for the unification of the two scales. On the other hand, these suggestions and discussions served to emphasize the need for perhaps an entirely new scale instead of modifications of the existing ones. I t appears that after the meeting in 1957, A. Olander and A. 0. Nier had independently snggested the idea of using I2C = 12 exactly as a possible unified basis for atomic weights scale. ISO wa4 suggested as another possibility by Olander. This idea of taking 12 exactly grams of isotopically pure carbon-12 as one mole had great appeal to both chemists and physicists. The reasons for this will be shortly discussed. In the meantime it will be noted that the adoption of the carbon-12 scale will bring about a decrease of 43 parts per million in all atomic weights referred to the chemical scale and a decrease of 318 parts per million in those referred to the physical scale. A review and discussion of the several proposed scales and the advantages of the carbon-12 scale have been given by Mattauch (18). Like chemical reactions, nuclear reactions are usually accompanied by an exchange of energy, either absorption or release of it. In nuclear terminology the energy of reaction is called the Q-value or "the Q of the reaction" (19). There exists a method for the determination of atomic masses that is based on the measurement of the Q-values. The connection between Q-values and masses has been described by Mattauch and his associates (20), and the masses of a number of nuclides
have been computed by this procedure (81, 83). By this method, however, one can calculate the masses of only those nuclides which have exactly the same ratio of mass number to atomic number, A/Z, as the standard nuclide (this is true only if Q-values for beta disintegration are excluded). If the mass number, A, be plotted versus the atomic number, Z, it will be observed that more of the known nuclides will be on the straight line A = 2 2 than on any other. Thus, beginning with f D and up to 2;Zn there are 30 nuclides that conform to A/Z = 2. Of these, 13 are stable. If one of these, e.g , 70 or YC is taken as standard, there remain 12 others, the masses of which can be determined from massspectroscopic doublets (see below) as well as from Q-values. If ',80,with a ratio of 9/4, is taken as the standard nuclide, there will be 14 nnclides with this ratio (one for every fourth element from beryllium to barium) of which eight are stable. The list for comparison will thus have seven nuclides (one having been taken as the standard). To choose 19Fwith the ratio of A to Z equal to l9/9 as the standard nuclide would mean that every ninth element from fluorine to xenon will be included. There are six of these out of which only two are stable, thus leaving only :iAr for comparison. There is another method, the mass-spectroscopic method, that is used for the intercomparison of atomic masses (28, 23). The method is based on studymg "donblets." The term "doublet" is used to refer to a pair of mass spectral lines, produced by two species of Ions, whose ratios of charge to mass are almost, but not quite, equal. From a knowledge of the mass of one species, the doublet spacing, and the dispersion of the mass spectrometer, the mass of the other species can be calculated. Since combination of the atoms 'H and 'C can serve as reference masses a t many mass numbers, these atoms are regarded as the most useful secondary standards. The reasons which prevented the physicists from adopting fluorine as a reference scale are the following: As mentioned above, one of the most important auxiliary standards in the massspectroscopic determination of nuclidic masses is the mass of 12C. It is possible to measure the mass of 12C in relation to that of "0 by doublets containing no other nuclide. Such doublets can be produced because the ratio of the mass of 12C to that of 1 6 0 is a simple number, i.e., 3/4. I t is therefore possible to tie the mass of 12C directly to that of ' 8 0 . The same is not true for the measurement of the mass of I2C in relation to that of leF. Since the two mass numbers, 12 and 19, are incommensurable, one cannot produce a doublet containing no other nuclides. Therefore, by the mass-spectroscopic method the accuracy with which the mass of 12C can be linked to that of 19F is necessarily inferior to that of the measurement of '2C in relation to ' 6 0 . Flourine has a ratio of A/Z equal to 19/9. By choosing this element as the standard, we would sacrifice the number of nuclides that can be intercompared, since, as mentioned above, the number of stable nuclides in this category is only two. In Table 2 five reference nnclides, including those of carbon-12 and fluorine-19, are intercompared, showing what changes in parts per million their adoption as standards would bring about in the chemical scale. Volume
39,
Number
6,
June
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The figures recorded in the second column show clearly that 1 8 0 = 18 exactly is the most advantageous standard for the chemists. The nuclide of oxygen-18 was not acceptable to the physicists mainly for reasons discussed for the rejection of fluorine-19. Table 2. Changer in Atomic Weights When Various Nuclides Are Used as a Reference Standard
Change from the values based on chemical scale inarts ner million) 1ZC = 12 (exactly)
15 17 180 - 1 8 XQF= 19 ISN =
"
170 =
"
"
Of all the nuclides suggested as reference standards only 'Q and 12C meet the desired criterion of A / Z = 2. From what has been said above, it can be inferred that a weight scale based on lZC = 12 as a standard has many advantages for mass spectroscopists. Doubly, triply, and quadruply charged atomic ions of 12C have integral ratios of mass to charge and thus can be paired in dooblets having mass numbers of 6, 4, and 3, respectively. 1Iurh more important is the fact that no other nuclide (with the exception of lac) can he found whirh forms stable polyatomic molecular ions with so many atoms (up to ten and more ) in the molecule. The carhon-I2 scale mould allow many more direct doublet comparisons of masses; comparison can be made at every multiple of 12 up to and beyond A = 120. 1% has the additional advantage that it forms many more hydrides than any other nuclide (again with exception of 13C)SO that an easy reference line for doublets can he produced at almost every mass number up to and beyond A = 120. Thus for the physicists '2C = 12 exactly would form an even better standard than 160= 16 exactly. Adoption and Use of Carbon-12 Unified Scale
Having approved the adoption of the scale based on 1ZC = 12 exactly in August, 1961, the IUPAC recommends universal use of the new scale as of January 1, 1962 (f4). What does the adoption of this scale mean to the chemist? The new scale changes all chemical atomic weights by about 40 parts per million which is well within the limits of accuracy and precision of present-day chemical atomic weight determinations. However, these small changes still need to he taken into consideration whenever one is reporting critically selected physicochemical data or constants of the highest precision. I t might be stated that while carbon-12 as a reference standard does not operationally lend itself to techniques of chemical atomic weight determinations as satisfactorily as oxygen does, yet it has inherent advantages. These advantages, as has already been stated, result from the fact that the nuclidic mass of '2C can be very accurately related to the atomic weights of elements
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which in turn can be used as reference st,andards in tdic chemical atomic weight determinations. A comprehensive compilation of nuclidic masses relative to '?C and W, together with other data, is given by Everling, Konig, Mattauch, and Wapstra (26). A comparison of the atomic and molec.ular weights of some nuclides and substances in terms of t,he chemical. the physical, and the carbon-12 scales are made in Table 1 in order to show what changes in molar properties can be expected. The recognized 1957 (or 1959) and 1961 International Atomic Weights are listed in the second and third columns of Table 1. The unit on the carbon-12 scale is represented by amu.
Journal of Chemical Education
Acknowledgment
The author wishes to express his thanks for helpful comments and suggestions to Professor Tn1ma.n P. Kohman, Department of Chemistry. Carnegie Institute of Technology, Pittsburgh. Pennsrl\-nnia: and Profrs sor Bruno ~wolinski,' ~ e ~ a r t k e noft Chemistry, Agricultural and Mechanical College of Texas, College Stat,ion, Texas
7. '
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