R E P O R T FOR ANALYTICAL
CHEMISTS
Critique of the Harvard Method for Determining Atomic Weights b y ARTHUR F. SCOTT, Chemistry DURING THE 19TH CENTURY, when chemical analysis of a pure compound was the only practical means of establishing the atomic weight of an element, the analysis of a chloride or bromide compound, either gravimetrically as silver halide or titrimetrically with silver nitrate, came to be the foremost method. I n 1905, after a careful study of critical points in the earlier procedures, Richards and Wells undertook a new titrimetric analysis of N a C l for the purpose of determining the atomic weight of N a . T h e general procedure followed b y Richards and Wells in the preparation of pure N a C l and Ag, and their painstaking analytical technique have become known as the H a r v a r d
Department,
Reed
College,
Portland,
method. T h e development of this method opened a new and perhaps final chapter in the history of chemical atomic weight determinations. Between 1905 and 1946 the H a r v a r d method was used in 184 series of analyses of chlorides or bromides for the purpose of determining the atomic weights of 64 elements. Two papers by Honigschmid in 1946 marked t h e close of the epoch. Since t h a t date there has been only one new chemical determination (1957) by the H a r v a r d method. I t is safe t o say t h a t b y 1950 the accepted atomic weight values of a majority of the elements were based upon analyses by the H a r v a r d method. I t should be pointed out t h a t the titrimetric determination
Active participation in atomic weight determinations for the past 4 0 years well qualifies Prof. Arthur F. Scott of Reed College to prepare a critique on the Harvard Method for determining atomic weights. Dr. Scott has been professor of chemistry and chairman of the department of chemistry at Reed College, Portland, Oregon, since 1937. Dr. Scott, born in 1898, received his B.S. from Colby College in 1919 and his M.A.
Ore. of the equivalence of soluble hàlides to silver was accompanied in m a n y instances by the collection and weighing of the precipitated silver halide and t h a t the results of these gravimetric determinations were, in some instances, t a k e n into account in the calculation of atomic weights. This paper, however, is concerned only with the sources of error in the titrimetric determinations which are more commonly associated with the designation " H a r vard Method." T h e comparatively recent development of accurate physical methods for the measurement of atomic masses and isotopic abundances has afforded, for the first time, an independent check of the re-
and Ph.D. from Harvard University in 1921 and 1924, respectively. During the latter period ( 1 9 2 2 - 2 3 ) he was a travelling fellow at the University of Munich. He began his teaching career at Reed College in 1923 as an assistant professor. In 1926 he joined the staff at the Rice Institute as an assistant professor of chemistry. In 1937 he returned to Reed College and assumed the position he now holds. He was acting president at Reed from 1942 to 1945. He has been a Guest at the Massachusetts Institute of Technology ( 1 9 5 8 - 5 9 ) and at Brookhaven National Laboratory (Summer 1959) and an Honorary Research Associate at University College, London (Fall 1959). His initial interest in atomic weight determinations stems from his doctoral thesis on the determination of the atomic weight of boron. He did this work under the direction of Prof. Gregory F. Baxter. While at Munich he worked with Prof. Kasimir Fajans, Prof. Otto Honigschmid, and Edward Zintl. Prof. Scott has published about 12 papers in the field of atomic weight determinations, including some on the technique of analytical procedures. His last paper in this field, published in JACS in 1957, dealt with the atomic weights of fluorine and silver. Altogether, 13 Reed College students contributed to this project by the work of their senior thesis projects. Other areas of professional interest include physical properties of solutions of electrolytes, inorganic chemistry, and radiochemistry. Prof. Scott is a member of the ACS, American Nuclear Society, the Society of Nuclear Engineering, and the American Institute of Chemical Engineers (Nuclear Engineering Division). He received awards from the Manufacturing Chemists' Association in 1957, Research Corporation in 1958, ACS (SAMA) in 1960, and an honorary fellowship from the Petroleum Research Fund in 1958. He is a member of Phi Beta Kappa and Sigma Xi.
VOL. 33, NO. 9, AUGUST 1961 · 2 3 A
REPORT FOR ANALYTICAL CHEMISTS
suits of the chemical analytical methods. Comparisons (2, 3) of the chemical and physical atomic weight values have shown that the "chemical results have fallen somewhat short of the degree of confidence which chemists had accorded them. This conclusion has been reinforced by the recent decisions of the Commission on Atomic Weights to base certain atomic weight values on physical measurements rather than on chemical determinations. These adverse judgments of the chemical determinations reflect primarily on the Harvard method because of its dominant position among chemical methods. In view of these implied questions regarding the reliability of the Harvard method it has seemed to be of some interest to review the sources of error inherent in the analytical operations of this method and to attempt to identify points of weakness. Occasionally atomic weight investigators themselves had doubts regarding the Harvard method. Thus, in 1933, Baxter and MacNevin, in discussing some curious fluctuations in the results of determinations of atomic weight of potassium, observed: "A puzzling situation is thus created .. . which points to a serious uncertainty either in the purity of potassium salts or silver, or in the analytical operations."
It is significant to our present study that more than two thirds of all atomic weight investigations by the Harvard method were carried out in just three laboratories: There were 21 determinations reported from Richards' laboratory at Harvard; 39 from Baxter's laboratory, also at Harvard ; and 67 from Honigschmid's laboratory in Munich. Further, both Baxter and Hônigschmid had previously studied under Richards at Harvard. An atomic weight determination by the Harvard method consists basically of two parts: (1) the preparation of pure materials, the halide compound to be analyzed and silver; and (2), the analytical procedure. In the present study we shall consider only the analytical procedure which was common, with minor variations, to all determinations by the Harvard method. The general scheme of this analytical procedure is outlined below. The essential features of the analytical operations in the Harvard method are elegantly simple. A sample of the carefully purified halogen (CI or Br) compound is first weighed out and brought into solution. From the weight of the halogen sample and its stoichiometrical composition the analyst estimates the amount of silver equivalent to the halogen in the sample and then weighs it out in the
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BERZELIUS RICHARDS
0 U 1800
185C
ÎM&arfflsUl: IMMM
1900
1950
Work on atomic weight determinations reached peak in period 1890 to 1940 as reflected by number of papers published. This was the period in which Richards and his associates did most of their research using classical methods 2 4 A · ANALYTICAL CHEMISTRY
form of fused buttons and electrolytic crystals, to within a few tenths of a milligram. After solution of the silver in nitric acid, the silver nitrate solution is added quantitatively to the halide solution, silver halide being precipitated. As a rule the concentrations of Ag+ and X~ ions in the supernatant solution at this point are nearly the same. Their relative concentrations are determined by a nephelometric test as follows: Two equal portions of the supernatant solution are withdrawn; the halide ion ( X - ) in one sample is precipitated as colloidal AgX by the addition of excess Ag+, and the Ag+ in the other is similarly precipitated by excess X~. The light-scattering properties (observed as "opalescences") of these two AgX suspensions are compared by means of a nephelometer and, on the assumption that opalescence is proportional to the concentration of the ion precipitated, the analyst can estimate from the opalescence ratio the relative concentrations of Ag + and X - in the analytical solution. By means of suitably dilute standard solutions of Ag+ and X~ the solution in contact with the precipitated silver halide is brought to the end point, which is taken to be that point at which the nephelometric test suspensions show equal opalescence. The time period during which an analysis is adjusted to the endpoint is seldom less than 2 weeks and is more commonly 4 to 6 weeks. The ratio of the experimentally determined quantities in an analysis (wt. of sample taken)/(wt. of Ag required) is termed the titrimetric ratio [(S)/(Ag)]. The analytical procedure of the Harvard method carries with it only two potential sources of error. One is the possibility that, owing to occlusion or adsorption of Ag+ or X" - , the AgX precipitate does not have exactly the assumed stoichiometrical composition; and the second is the possibility that the equalopalescence end point does not correspond exactly to the true stoichiometrical point of the titration. We consider these two uncertainties first and then review certain irregularities in the behavior of the analytical systems which have been reported in atomic weight analyses.
REPORT FOR ANALYTICAL CHEMISTS Occlusion by AgX Precipitates Following Richards and Wells' original study, the occlusion phe nomenon received surprisingly little attention from atomic weight inves tigators. There is some evidence, however, to support R i c h a r d s ' early view t h a t permanent e n t r a p m e n t of Ag+ and X - by an analytical pre cipitate is avoidable if the precipi tation operation is carried out under proper conditions; a n d t h a t occlu sion of "other substances" present in an analytical solution is difficult to avoid. T h e last type of occlusion would have no effect on the results of a titrimetric analysis. T h e gen eral conclusion to be drawn from the various tests of occlusion is summed up well in the following quotation from Baxter and Butler's discussion of their experience with occlusion in their analyses of GeCL,:
Bottle
Boat S
Boat
Bottle S
After fusing in a dry atmosphere, contents of the boat are pushed into a weigh ing bottle and sealed. This procedure keeps sample free of moisture. The bottle is then removed and placed in an ordinary desiccator until weighed
There is no reason to believe that this slight contamination of silver chloride is unique in the case of germanium. It is a question whether it is possible by a single precipitation to prepare absolutely pure silver chloride owing to the phenomenon of inclusion and oc clusion. The Nephelometric End Point T h e nephelometer was devised by Richards in 1894 in connection with his early atomic weight analyses of SrBr 2 . Ten years later he and R. C. Wells described an improved design of the nephelometer and its application to the q u a n t i t a t i v e de termination of small amounts of chloride. In the following year, 1905, Richards and Wells utilized the nephelometer in their classical analyses of N a C l to establish the equal-opalescence end point, an es sential feature of the H a r v a r d method. T h e various conditions under which this end point has been used in atomic weight analyses can be classified as follows: chloride analyses a t room temperature (Rcnd point) ; chloride analyses at ice temperature (I-end point) ; and bromide analyses. There was an event in the early history of the nephelometric end point which, without doubt, influ enced the a t t i t u d e of atomic weight investigators toward the question of its validity. Very shortly after Richards and Wells' paper on
R
Β
Β
Ρ
s
S
S
Nephelometer was used to compare suspended precipitates in "unknown" tube against standard tube. The system works well with highly insoluble materials such as silver halides which produce little opalescence VOL. 33, NO. 9, AUGUST 1961 · 2 5 A
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the atomic weight of N a appeared, Wells alone published a paper on "Nephelometry." A laudable fea ture of Wells' work was the attempt to study the effect of various factors on nephelometric test suspensions by comparing the opalescences of the suspensions produced under dif ferent conditions against the opal escence of a ground glass plate as a fixed reference standard. An u n fortunate feature of Wells' paper, however, was the mistaken inter pretation of his preliminary data to mean t h a t the nephelometric end point in t h e Richards and Wells' analyses of N a C l had been in error and t h a t therefore a small correc tion in t h e derived atomic weight of N a was indicated. Richards promptly pointed out Wells' mis take a n d t h e latter retracted his criticism. I n his discussion of Wells' paper Richards stressed the fact t h a t the light-scattering prop erties of nephelometric test suspen sions are influenced by a number of factors such as temperature, t h e presence of electrolytes, and t h e concentration of solutions; and he laid down the principle t h a t the only way to eliminate disturbing ef fects from these complex variables is to subject suspensions, which are to be compared, to identical condi tions in their preparation and hand
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(1) the opalescence of a suspension is not directly proportional to the con centration of the ion precipitated; and (2), the relationship between opal escence and concentration is not the same for "excess Ag+" and "excess CI"" suspensions. On the basis of these find ings one can see that equal concentra tions of Ag* and CI" will not yield sus pensions of equal-opalescence at all con centrations of AgCl. Although the nephelometric end point is not generally sound, it a p -
T. W. Richards, G. P. Baxter, and 0. Honigschmid, and scientists associated with them, did most of the work involved in atomic weight determinations by the Harvard titrimetric method. Many of those who worked with Richards, Baxter, and Honigschmid often did independent determinations. A breakdown of this information appears below. Richards etal.
Baxter etal.
Honigschmid
Others
1893-1900
6
1901-1910
11
1911-1920
8
8
11
11
1921-1930
6
11
25
20
15
27
12
7
2
70
52
1931-1940
T
ling. This principle of identical treatment became the operating rule for all nephelometric tests in atomic weight analyses. Moreover, because of t h e confidence which Richards' dictum engendered, the validity of the equal-opalescence end point was not questioned further for the next 25 years. Tests of the nephelometric end point have been of two types: experiments with standard Ag+ and X ~ solutions; and experiments with solutions which simulate analytical systems a t the stoichiometrical point. These experiments taken to gether show decisively t h a t the basic assumptions underlying the traditional "equal-opalescence" end point are not generally valid. F o r example, the results of one series of experiments with standard solutions were summed up by the investi gators (4) as follows:
1 7
1941-to date Totals
31
41
6
REPORT FOR ANALYTICAL CHEMISTS
I FELT THIS BIG!
Atomic Weights Determined by Harvard Methods
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Ag
Ce
Ga
Μη
Ra
Ti
AI
CI
Gd
Mo
Rb
Tl
As
Co
Ge
Ν
Sb
Tm
Β
Cr
Hf
Na
Se
U
Ba
Cs
Hg
Nb
Si
V
Be
Cu
Ho
Nd
Sm
W
Sn
Y
Bi
Dy
In
Ni
Br
Er
Κ
Ρ
Sr
Yb
C
Eu
La
Pb
Ta
Zn
Ca
F
Li
Pr
Te
Zr
Cd
Fe
Lu
Pt
Th
pears to be satisfactory for chloride analyses completed at room temper ature (R-end point) but has been a potential source of error in two other cases: chloride analyses in which the analytical solution was cooled to ice temperature (I-end point), and bromide analyses. T h a t t h e results of these last two types of analyses are not seri ously in error is probably due to two different reasons. I n the case of chloride analyses at I-end point there is reason to suppose t h a t the analyses were completed in such a way t h a t the analytical solutions contained colloidal AgCl which went back into solution in the neph elometric test samples, thereby raising the concentration of AgCl in these samples to a value not too dif ferent from t h a t of analytical solutions at the R-end point. I n the case of bromide analyses the seriousness of t h e error resulting from the acceptance of equal-opalescence as the true end point is min imized by the extreme sensitivity of the end point, which arises from the very low solubility of AgBr. To complete this discussion of the nephelometric end point, it is important to mention t h a t Johnson (1) has developed an alternative procedure, known as the " s t a n d a r d solution end point" which has def inite advantages over the equalopalescence end point. Unfortu nately, Johnson is the only investi gator to have made use of this alter native procedure in atomic weight analyses.
Anomalies in the Nephelometric Titration Step In the H a r v a r d titration method the analytical system appears to be simple, consisting of A g X precip itate in equilibrium with its ions. T h a t the system is actually more complex t h a n this is indicated by two kinds of irregularities or anom alies which we review below. T h e first of these anomalies is the "drifting end point" phenomenon which can be described as follows. In the analytical procedure, shortly after the precipitation of AgX, the relative concentrations of Ag+ and X~' in the supernatant solution arc determined nephelometrically and an a t t e m p t is made to bring the solution to the equal-opalescence end point by adding the estimated amount of the deficient ion. Several days later the nephelo metric test is repeated and another addition of Ag+ or X ~ is made, if indicated. This process of nephelo metric test and addition of ion is continued until the equal-opalcscence end point is reached or crossed. In the usual, normal anal yses the response of the analytical solution to the initial addition of Ag+ or X ~ is what one would ex pect. I n some cases, however, the observed response is irregular and m a y even be in the opposite direc tion from t h a t expected. I t is this phenomenon of irregular response to additions of the deficient ion, as observed by nephelometric tests, which is known as the drifting end point.
The drifting end point phenomenon was first observed by Baxter and Moore in 1912 in their analyses of PBr 3 . Subsequently, it was mentioned in reports of 19 other atomic weight analyses, both R-end point chloride and bromide. Since other instances of drifting end point were very likely not identified specifically in published reports, the total number of cases is probably well in excess of 20. The phenomenon, therefore, cannot be dismissed as something very unusual or special. Experimental information concerning the drifting end point phenomenon is very scant; the only clear fact is that it occurs only in systems containing freshly precipitated AgX and is not observed after an analytical solution has stood for a couple of weeks. The phenomenon doubtless involves the colloidal particles initially present in the analytical system, which disappear during the aging of the precipitate. The drifting end point has been noted here because it could be a real source of error in some analyses. Thus, if an investigator, being unaware of the phenomenon, hurried to terminate his analyses, he could very well accept a false end point. The second anomaly is the fact that the S/Ag ratio appears to be influenced by the ion initially in excess following precipitation of AgX. The evidence for this anomaly is statistical in nature. In the Harvard method the investigator weighs out, as nearly as he can, the amount of silver required to precipitate the halide in the sample being analyzed, with the result that the analytical solution, immediately after precipitation of AgX, contains only a slight excess of Ag+ or X - . Because the investigator usually pays no attention to which ion will be in excess, it generally happens that, as a matter of chance, a series of analyses will contain some analyses with Ag+ in excess and some with X - in excess. Only Baxter and a few other American investigators have included in their reports information concerning the ion initially in excess. A search of the published reports has revealed a total of 61 atomic weight determinations in which a series of analyses contained
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AUGUST
1961
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A
REPORT FOR ANALYTICAL CHEMISTS
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analyses of both t y p e s : those with Ag+ ion initially in excess (Ag+-excess) ; and those with X - ion ini tially in excess (X~~-excess). Of the 61 determinations, 48 involved analyses of chloride compounds and 13 involved bromide compounds. T h e d a t a of the 61 determinations have been examined in the follow ing way. First, for a given series the analyses have been divided into two groups, (Ag+-excess) and ( X _ - e x c e s s ) , and the mean value of the S/Ag ratio has been calcu lated for each group. T h e differ ence (Δ) between these two means has been calculated Δ = mean (Ag + -excess) — mean (X~-excess)
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If the ion initially in excess had no bearing on the outcome of the analysis, one would expect: the number of positive and negative (Δ) values to be approximately equal; and the magnitude of (Δ) to be small. These two expectations are not fulfilled. I n the first place there is a strong preponderance of positive (Δ) values: 38 out of 48 in the case of chloride analyses; and 13 out of 13 in the case of bromide analyses. A statistical test of this distribution indicates t h a t the prob ability of its being a chance distri bution is extremely low. A second point is t h a t the (Δ) values are fairly uniform and not negligible. The order of magnitude of (Δ) of chloride analyses is 5 p a r t s per 10 5 a n d ; for bromide analyses, 3 parts per 10 5 . The meaning of this statistical finding in practi cal terms is the following: If an analysis happens to be of the (Ag+excess) type there is a very high probability t h a t its titrimetric ratio, S/Ag, will be significantly greater than the ratio value which would result were the analysis of the ( X ~ excess) type. This difference must arise from a difference in amount of Ag+ used in bringing an analysis to the end point: more Ag being used in (X~~-excess) t y p e analyses than in the (Ag+-excess) t y p e : This result is understandable as an adsorption effect, provided the equal-opalescence end points of the analyses we have considered in our statistical study were estab lished b y crossing the end point. This is believed to be a reasonable
assumption. I t happens t h a t the laboratories which published their experimental data in such a form t h a t types of analyses in a series can be identified were also the laboratories which followed the practice of "crossing the end point." For in this case, when the end point is crossed and the titration is ac cepted as completed, the solution of an (X~-exeess) t y p e analysis will have a very slight excess of A g + , and the (Ag+-excess) t y p e will have a slight excess of X - . T h e conditions, accordingly, are favor able t o : adsorption of Ag+ in the ( X - - e x c e s s ) t y p e of analysis; and adsorption of X - in the (Ag+-excess t y p e of analysis. T h e occur rence of either t y p e of adsorption, or of both types, in a series of analyses would lead to the positive (Δ) v a l ues found above in our test of the d a t a of the 61 determinations. In most series of analyses the
Atomic Weight Determinations Harvard All 'ritrimetric 2 Methods 1 Methods
1800-1810
2
1811-1820
7
1821-1830
34
1831-1840
40
1841-1850
90
1851-1860
58
1861-1870
53
1871-1880
29
1881-1890
111
1891-1900
170
7
1900-1910
266
25
1911-1920
201
38
1921-1930
186
62
1931-1940
147
55
8
9
1402
196
1941-present
1 Based on Clark's Comprehen sive Survey of Atomic Weight Publications. 2 Based on data supplied by the author.
number of (Ag+-excess) and ( X - excess) analyses would be nearly the same and any error due to the adsorption effect indicated above would most likely cancel out. How ever, in the exceptional case of a series of analyses in which the dis tribution of analyses between the two types is one-sided or in which the analyses are all of one type, the possibility of a small error exists. A good illustration of this is to be found in the determination of the atomic weight of Cd by Baxter, Hines, and Frevert. This deter mination comprised eight analyses of CdBr2, of which seven were of the (Ag + -cxcess) type and one of the (X"-excess) type. The S/Ag ratio of the latter was 6.1 parts in 105 lower than the mean value of the other seven analyses. Regarding this result Baxter, Hines, and Fre vert state that it differed "so markedly from the others that, al though no reason for the difference is known, it is rejected in comput ing the final average." In terms of atomic weight units the rejected analysis was 0.02 unit lower than the others. From the standpoint of the present discussion the atomic weight of Cd which Baxter et al. ac cepted is possibly too high by 0.01 unit because it is derived from only (Ag+-excess) analyses.
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ACKNOWLEDGMENT The author acknowledges with gratitude a grant from the National Science Foundation, part of which was in support of the present study.
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LITERATURE CITED (1) Johnson, C. R , J. Phys. Chem. 35, 830 (1931). (2) Nier, A. O., Science 121, 737 (1955). (3) Scott, A. F., Bettman, Max, Chem. Reus. 50, 363 (1952). (4) Scott, A. F., Hurley, F. H , Jr., / . Am. Chem. Sac. 59, 1297 (1937). Λ more detailed form of this paper has been deposited as Document Num ber 6813 with the ADI Auxiliary Pub lications Project, Photoduplication Service, Library of Congress, Washing ton 25, D. C. A copy may be secured by citing the document number and by remitting $ 10.00 for photoprints, or $3.50 for 35 m m . microfilm. Advance payment is required. Make checks o r money orders payable to: Chief, Photoduplication Service, Library of Con gress, Washington 25, D. C.
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VOL. 33, NO. 9, AUGUST 1961 · 3 1 A
