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. 1982 Jan-Feb;87(1):21–22. doi: 10.6028/jres.087.003

Recalculation of the Faraday Constant Due to A New Value for the Atomic Weight of Silver

V E Bower 1,*, R S Davis 1,*, T J Murphy 1,†, P J Paulsen 1,†, J W Gramlich 1,†, L J Powell 1,†,**
PMCID: PMC6706541  PMID: 34566069

Abstract

A report of the Faraday constant as determined at NBS via silver coulometry and atomic weight measurements is presented. The uncertainty of the reported result represents a five-fold improvement over measurements made at NBS 20 years ago. The result should contribute to an analysis of the self-consistency of several other fundamental constants measurements. Experimental details have been reported in other publications which are cited in the text.

Keywords: Atomic weight, atomic weight of silver, coulometer, electrochemical equivalent, Faraday constant, fundamental constants, silver, silver coulometer

The Faraday constant, F, may be derived from the following relation:

F=Ar(Ag)EAg,

where EAg is the electrochemical equivalent of pure silver and Ar(Ag) is the atomic weight of the silver used in determining EAg. In 1975, coulometrie measurements of EAg undertaken at the National Bureau of Standards [1]1 achieved sufficiently high precision to warrant a careful re-evaluation of the purity of the silver used [2] as well as a more accurate redetermination of its atomic weight [3]. This last work, which is the previous paper published in this issue of the Journal of Research, completes our efforts to measure F via the silver coulometer. Our results are:

FNBS75=96486.17(13)ANBS75⋅s⋅mol−1(1.3ppm)FBI69=96486.06(13)ABI69⋅s⋅mol−1(1.3ppm)FSI=96485.44(14)ASI⋅s⋅mol−1(1.4ppm)

where the subscripts identify the electrical units used; that is,

NBS75—electrical units as maintained at the National Bureau of Standards in March of 1975, the time of the coulometric measurements.

BI69—a convenient reference set of “as maintained” electrical units defined in ref. [4]. (BI is an abbreviation for Bureau International des Poids et Mesures (BIPM), the International Bureau of Weights and Measures in Sèvres, France.) We use ANBS75/ABI69 = 1–(1.2±0.1) × 10−6 [5].

SI—electrical units as defined in the Système International (i.e., absolute units). The transformation from NBS75 to SI amperes has been made by using what we believe to be the best available conversion factor, ANBS75/ASI = 1−(7.6±0.5) × 10−6 [5], although this is by no means a closed question [6, 7].

All uncertainties, which have been given above in parentheses, are meant to correspond to one standard deviation. In addition, the draft recommendations of the BIPM [8] regarding the calculation of uncertainty have been followed, the most noteworthy being that all uncertainties are combined by taking the square root of the sum of their squares to produce a total uncertainty. These procedures for computing uncertainty were also adhered to in reporting the most recent measurements of the electrochemical equivalent of silver [1,2] as well as in recent compilations of the fundamental constants [4,6]. In reporting the new atomic weight of silver [3], however, a more conservative approach has been taken. That is, if the BIPM recommendations were followed, the total uncertainty (at a level of one standard deviation) in the atomic weight of silver reported in ref. [3] would shrink from 0.5 ppm to 0.3 ppm [9]. It is this latter uncertainty which we have used in the results reported above. The total uncertainty at a level of one standard deviation for FNBS75, calculated, according to the BIPM recommendations, is shown in table 1. Thus the new measurement of the atomic weight of silver reported in ref. [3] has reduced the role of atomic weight in the uncertainty calculation of the Faraday experiment from dominance to insignificance.

Table 1.

Estimate of Uncertainties in FNBS75 from Known Sources

Source Uncertainty (ppm)
Electrochemical equivalent of silver 1.3*
Atomic weight of silver 0.3
Combined uncertainty 1.3
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*

Further details in Ref. [2].

Figure 1 shows the value of the Faraday calculated here as well as Faraday constants measured by other scientists. Point D is the present CODATA recommended value of Cohen and Taylor [4], which is calculated from other physical constants via least squares. It may be noted that not only has the overall uncertainty in the Faraday constant been reduced through this determination, but the new value of the Faraday is now essentially the same as that calculated from the proton gyromagnetic ratio determined by Kibble and Hunt [13]. No further work using silver coulometers is planned since it would be extremely difficult to reduce the uncertainty of the measurements below their present values.

Figure 1.

Figure 1.

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Comparison of Recent Determinations of the Faraday

Footnotes

1

Figures in brackets indicate literature references at the end of this paper.

References

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