As discussed in section 2.1, silica, if present, can depress the measured 205T1/203Tl isotopic ratio by as much as 0.2 percent. To ensure that silicon did not interfere in the measurement of the calibration mixes, aliquots of the mixes were treated with 2 g concentrated HF and remeasured. In all cases, the remeasured isotopic ratios were within the uncertainty of the ratios measured during the determination of the atomic weight.

3. Results and Discussion

Table 8 summarizes the results for the six synthetic mixes. The calibration factors for each analyst varied over a range of only 0.022 percent for Operator 1 and 0.026 percent for Operator 2. In addition, the calibration factors obtained for the equal atom mix were within the range of the calibration factors determined from the other mixes, indicating an insignificant degree of nonlinearity.

Table 9 contains a summary of the observed and corrected 205T1/203T1 values for the standard sample for Operators 1 and 2 as well as the absolute isotope abundance ratio for thallium and its associated uncertainty component. Table 10 gives the summary calculations of the reference sample. The atomic weight is calculated from the absolute

isotopic abundance by summing the product of the nuclidic masses obtained from Wapstra and Bos [15] and the corresponding atom fractions. The thallium reference standard used for the atomic weight measurements will become a new Standard Reference Material, SRM 997. This SRM will be certified for isotopic composition and chemical purity.

A limited survey of thallium minerals and high purity materials has failed to show any significant (±0.1%) isotopic variations. This indicates that the atomic weight determined for the thallium reference standard is, with an allowance for possible natural variations, applicable to other terrestrial thallium samples.

We are indebted to: Hsien H. Ku for statistical analysis, Paul J. Paulsen and T. C. Rains for analysis of the separated isotopes; W. A. Bowman, III for maintenance support; Karen A. Breletic and Cherrie Freedman for filament fabrication; Michele Abretski and Joy J. Shoemaker for skillful manuscript preparation.

This work is from the dissertation of Lura Powell Dunstan, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, University of Maryland.

error.

+0.000028

+0.000074

±0.0088 +0.0088

+0.0037

±0.0014

+0.0037

±0.0014

+0.0037 ±0.0037

+0.00042

+0.00017

+0.00042

4. References

[1] Shields, W. R., Garner, E. L., and Dibeler, V. H., J. Res. Nat. Bur. Stand. (U.S.) 66A (Phys. and Chem.) 1 (1962).

[2] Shields, W. R., Murphy, T. J., Garner, E. L., and Dibeler, V. H., J. Am. Chem. Soc., 84, 1519 (1962).

[3] Shields, W. R., Murphy, T. J., and Garner, E. L., J. Res. Nat. Bur. Stand. (U.S.) 68A (Phys. and Chem.) 589 (1964).

[4] Catanzaro, E. J., Murphy, T. J., Garner, E. L., and Shields, W. R., J. Res. Nat. Bur. Stand. (U.S.) 68A (Phys. and Chem.) 593 (1964). [5] Shields, W. R., Murphy, T. J., Catanzaro, E. J., and Garner, E. L., J. Res. Nat. Bur. Stand. (U.S.) 70A (Phys. and Chem.) 193 (1966). [6] Catanzaro, E. J., Murphy, T. J., Garner, E. L., and Shields, W. R., J. Res. Nat. Bur. Stand. (U.S.) 70A (Phys. and Chem.) 453 (1966). [7] Catanzaro, E. J., Murphy, T. J., Shields, W. R. and Garner, E. L., J. Res. Nat. Bur. Stand. (U.S.) 72A (Phys. and Chem.) 261 (1968). [8] Catanzaro, E. J., Champion, C. E., Garner, E. L., Marinenko, G., Sappenfield, K. M., and Shields, W. R., Nat. Bur. Stand. (U.S.) Spec. Publ. 260-17, 70 pages (Feb. 1969).

[9] Catanzaro, E. J., Murphy, T. J., Garner, E. L., and Shields, W. R., J. Res. Nat. Bur. Stand. (U.S.) 73A (Phys. and Chem.) 511 (1969). [10] Gramlich, J. W., Murphy, T. J., Garner, E. L., and Shields, W. R., J. Res. Nat. Bur. Stand. (U.S.) 77A (Phys. and Chem.) 691 (1973). [11] Barnes, I. L., Moore, L. J., Machlan, L. A., and Murphy, T. J., J. Res. Nat. Bur. Stand. (U.S.), 79A (Phys. and Chem), 727 (1975).

[12] Garner, E. L., Murphy, T. J., Gramlich, J. W., Paulsen, P. J., and Barnes, I. L., J. Res. Nat. Bur. Stand. (U.S.) 79A (Phys. and Chem.) 713 (1975).

[13] Moore, L. J., Murphy, T. J., and Barnes, I. L., (to be published). [14] Garner, E. L., Private Communication.

[20] Crookes, W., Phil. Trans., A, 163, 277 (1893).
[21] Le Pierre, M. C., Bull. Soc. Chim., 9, 166 (1893).

[22] Wells, H. L. and Penfield, S. L., Amer. J. Sci., 47, 466 (1894).
[23] Hönigschmid, O., Birchenback, L. and Kothe, E., Sitzb. Math. Physik.
Klasse Bayer Akad. Wiss. München, 1922, 179 (1924)

[24] Hönigschmid, O. and Striebel, H., Z. Anorg. Allgem. Chem., 194. 293-298 (1930).

[28] Schüler, H. and Keyston, J., Zeits. f. Physik, 1 (1931).
[29] Aston, F. W., Proc. Roy. Soc., (London), A 134, 574 (1931).
[30] Nier, A. O., Phys. Rev. 54, 5 (1938).

[31] White, J. R. and Cameron, A. E., Phys. Rev. 74, 991 (1948).
[32] Hibbs, R. F., AECU-566, Dep. (1949).

[33] Shields, W. R., ed., Nat. Bur. Stand. (U.S.), Tech. Note 426, 53 pages (Sept. 1967).

[34]

Shields, W. R., ed., Nat. Bur. Stand. (U.S.), Tech. Note 277, 99 pages (July 1966).

[35] Garner, E. L., Machlan, L. A., and Shields, W. R., Nat. Bur. Stand (U.S.), Spec. Pub. 260-17, 150 pages (April 1971).

[36] Gramlich, J. W., and Machlan, L. A., A Method for Precise Mass Spectrometric Analysis of Gallium, Proc. of the 26th Ann. Conf. of Mass Spec. and All. Topics, St. Louis, MO., 1978 (to be published). [37] Huey, J. M. and Kohman, T. P., Earth and Planet. Sci. Lett. 16, 401 (1972). Gramlich, J. W. and Shideler, R. W., A Programmable Sample Drye for Thermal Ionization Mass Spectrometry, Proc. of the 25th Ann Conf. on Mass Spec. and Allied Topics, Washington, D. C., p. 726 (1977).

[38]

[15] Wapstra and Bos, Atomic Data and Nuclear Data Tables, 19, No. 3 (1977).

[16] Baxter, G. P. and Thomas, J. S., J. Amer. Chem. Soc., 55, 2384 (1933). [17] Lamy, C. A., Zeit. Anal. Chem., 2, 211 (1863). [18] Hebberling, M., Liebigs Ann., 134, 12 (1865). [19] Werther, A. F., J. Prakt. Chem., 92, 197 (1864).

1. Introduction

The relative apparent molal enthalpy (,)' or heat content of sulfuric acid is a complicated function of the molality. The determination of this quantity requires an extrapolation of enthalpies of dilution as measured down to extremely low molalities.

There have been numerous reports and discussions of the relative apparent molal enthalpy of sulfuric acid [1-4].2 At the extreme dilutions attainable experimentally, sulfuric acid is known to have undissociated bisulfate ions [2]. This incomplete dissociation at the lowest dilutions complicates the extrapolation procedure, causes deviations from the Debye-Huckel limiting law (DHLL), and makes the final calculated values of the relative apparent molal enthalpy dependent on the method of data treatment.

Young and Blatz [2] performed an analysis of this problem in 1949. They took the degree of dissociation, and thence the enthalpy of dissociation, into consideration and

*Late professor of chemistry at the University of Chicago.

The reader is referred to the treatise of Harned and Owen [1] for the definition of the terms used in this paper and to the glossary (sect. 6) for an explanation of the symbols which we have used. 'Figures in brackets indicate references at the end of this paper.

performed a semi-theoretical calculation of the relative apparent molal enthalpy of sulfuric acid. They also found a systematic difference of 460 calories (1 cal=4.184 J) between their values and those reported in the literature [5]. This discrepancy was also confirmed later by Harned and Owen [1]. Several years later, Giauque and his co-workers at the University of California began an analysis of the thermodynamics of sulfuric acid [6]. Thus, the work of Young and Blatz [2], the research of Giauque et al., and the earlier measurements of Groenier and Young [7] indicated a need for additional experimental work on the dilution enthalpy of sulfuric acid which, in turn, led the junior author (YCW) to undertake this investigation, which also included measurements on aqueous HCl and LiCl, as a part of his Ph.D. dissertation. While some of the results obtained herein have been cited by Giauque et al. [6] and used both in the National Bureau of Standards Technical Note 270 Series [3], and in the review of Pitzer et al. [8], independent publication of the results was delayed by circumstances encountered by the senior author (TFY). Publication at this time serves both to better document the experimental results and the method of data treatment and to honor the memory of the late T. F. Young and his dedication to science.

2. Experimental Procedure

Two calorimeters of different sensitivities were employed depending on the molality. A calorimeter with lower sensitivity, as described by Young and his co-workers [9, 10], was used for most of the measurements where the molality was greater than 0.01 mol kg'. For those measurements below 0.01 mol kg', a more sensitive differential calorimeter was necessary. The latter instrument contained a thermel of 500 junctions on each side of a plastic plate which was held by petroleum "wax" in the center of a large Dewar flask having a volume of two liters. Its design was somewhat similar to that of the calorimeter used by Lange and his co-workers [11]. Details of the construction and operation have been described by Fagley [12] and Kasner [13].

All of the chemicals used in this study were purchased from Baker Chemical Company3 as "Chemically Pure Analyzed Reagents." Relatively concentrated stock solutions were prepared and were analyzed by standard methods. The two acids were analyzed by titration with sodium hydroxide which had been standardized with potassium acid phthalate using phenolphthalein as an end-point indicator. The hydrochloric acid and the lithium chloride were analyzed gravimetrically by precipitation as silver chloride. Sulfuric acid was also analyzed by measurement of its density and comparison with data given in the International Critical Tables [14]. Duplicate analyses and analyses with different methods agreed to within 0.1 percent (for all stock solutions). All stock solutions were further diluted by mass to the various molalities necessary for each experiment. Some of the solutions produced during the dilution experiments were subjected to additional tests of analytical

accuracy.

The laboratory's distilled water was further purified before use by redistillation with alkaline permanganate in a block-tin still [13]. The specific conductance of all water used was lower than 10 ohm ̄1· cm ̄'.

The temperature sensitivity of the differential calorimeter was about 2 μK, which corresponds to an uncertainty in the heat measurement of 1.5 mcal. At a molality of 0.001 mol·kg ̄', the heat liberated on dilution of sulfuric acid was about 50 meal with a corresponding uncertainty of 3 percent. For lower molalities, the heat liberated would have decreased, thus magnifying the relative error. Therefore, the heat of dilution at 0.001 mol·kg1 was about the limit that this could be measured using the then existing instrumentation.

The temperature sensitivity of the less sensitive calorimeter was about 20 μK, which corresponded to a sensitivity in the heat measurement of 15 mcal. Thus, for the enthalpy of

'Certain commercial materials are identified in this paper in order to adequately specify the experimental procedures. Such identification does not imply recommendation or endorsement by the National Bureau of Standards.

dilution of HCl at about 0.02 mol kg', where the heat. liberated was about 60 mcal, the corresponding uncertainty is about 25 percent. However, the heat liberated for the en thalpy of dilution of sulfuric acid in the same molality range was about fifty times larger and the corresponding uncer tainty was less than 1 percent.

m2,

3. Results and Calculation

L

1/2

The method of treating the data is essentially the same as described previously [10]. The molalities of the initial ant final solutions are, respectively, m, and m2. The heat ab sorbed is Q, and Q divided by the number of moles contained in the solution is the enthalpy of dilution from m1 t A/Am/2. The derivative of , with respect to m12 is S, which can be obtained from a "chord-area" plot [15, 16] The experimental data are given in tables 1, 2 and 3 and in figures 1 and 2, where, for sulfuric acid, we also show the data of Groenier [7], of Lange et al. [5], and of Giauque e al. [6]. In order to calculate , at a given molality using the relationship

For H2SO4 the situation is more complex and warrants additional discussion. From Debye-Huckel theory, S° for a 2-1 electrolyte is 2480 cal mol-3/2. kg/2 [2]. In order to join this value with the experimental data in figure la, we con sider one mole of H2SO4 to be a mixture of a moles of H.H SO, and (1-a) moles of H HSO4, where the dot between the symbols indicates the dissociation which has oc curred. The relative apparent molal enthalpy of sulfuric acid will be

.

L

a has been evaluated by Young and Blatz [2] from Raman spectral data; we have taken the enthalpy of dissociation of bisulfate ion at infinite dilution (AHDiss) as 5200 cal·mol [1]; we have estimated 1 for (H · H · SO4) from the ❤, data for Li2SO4 [1]; we have used an average, for HCl and LiC obtained in this investigation (see tables 6 and 7 and refer ence [17]) in estimating a value of ❤, for (HHSO4); and we have taken the enthalpy of mixing of the ions (AH) to be zero [10]. The results of our semi-theoretical calculations for, and S for H2SO4 are shown in table 4; the theoretical

L