brewer_1969#
J. Brewer and G. W. Vaughn, “Measurement and Correlation of Some Interaction Second Virial Coefficients from -125 to 50 C. I”, J. Chem. Phys. 50, 2960 (1969)
Source record · Catalogue · Review register
DOI: 10.1063/1.1671491
Source kind: measurement
Recorded technique: The excess second virial coefficient E = B12 - (B11 + B22)/2 of ten binaries of He, Ne, Ar, H2 and N2, from the pressure change on mixing two pure gases at constant temperature and volume (the differential method of Knobler et al. 1959). A brass vessel of three 300 cc compartments (equal within 0.2 %) in a stirred water or freon bath; two compartments are filled with one gas and the third with the other, at the same temperature and about 2 atm (fillings of 144-146 cm Hg, Table III); one charge of the first gas is mixed with the second by a mercury Toepler pump (15 cycles), and the pressure change is read on an Octoil-S oil manometer against the unmixed charge, with a cathetometer. Temperature by a platinum resistance thermometer, accurate to 0.02 degC, held to 0.001 degC. E is reduced by Eq. (8) (Knobler et al.), with the pure third virial coefficients of Table II and C112, C122 from their geometric means, and corrections for the manometer’s volume change and the volume outside the bath. Runs usually in triplicate, reversing the gases. B12 = E + (B11 + B22)/2 (Eq. 12) with the literature pure-gas values of Table I. -125 to 50 degC in 25 degC steps.
Materials in structured entries: Ar, H2, He, N2
Dataset quantities: cross_second_virial_coefficient, excess_second_virial_coefficient
Contents: 20 datasets; 0 formulas.
Curation notes#
Identity VALIDATED_WITH_WARNINGS by the library (the PDF’s date hint is the 2014 download cover page). Printed pp. 2960-2968 (pdf pages 2-10; pdf page 1 is the publisher’s cover).
EXTRACTED: Table IV (p. 2966, “Summarized results of excess and interaction second virial coefficients”), E and B12 in cc/mole (cm3/mol) against Temp (degC), for all ten systems: Ar-N2, Ar-H2, Ar-He, Ar-Ne, H2-N2, He-N2, N2-Ne, H2-He, H2-Ne and He-Ne, eight temperatures each. Every pair is between optmat gases and every row is extracted. The table names a system either way round (N2-Ar and Ar-N2); each pair is filed under the first species in sorted order, with the other as the partner. The temperatures are kept in degC, as printed.
CHECKED against the table image (2026-10-01): all 160 numbers and 80 labels of Table IV cell by cell, and the 45 numbers of Table I and the Table III rows. One label differs from the system it belongs to: the 25 degC row printed H2-Ne (E = 2.83, B12 = 16.01) is H2-He. Ne-H2 has its own 25 degC row (1.14, 14.23); without it H2-He would have no 25 degC row and H2-Ne two; 2.83 lies on the H2-He run of E (2.38 at 50, 3.50 at 0 degC; Ne-H2 is 1.08 and 1.23); and B12 = E + (B_H2 + B_He)/2 = 16.015 with Table I, against 15.92 for H2-Ne. The extraction script files the row under H2-He and keeps the printed label in the printed cell.
REPRODUCED (2026-10-01): B12 = E + (B11 + B22)/2 (Eq. 12) from the printed E and the printed Table I values reproduces all 80 printed B12 within 0.005 cc/mole, half a unit of the last digit (the script checks it on every run); the ties are rounded both ways, so the authors carried more digits. The E-avg column of Table III (p. 2965, three runs of nine systems at -125 degC) equals Table IV’s -125 degC E for all nine; the mean of the three printed runs reproduces E-avg to the last digit for seven, and is one unit of the last digit below it for Ar-H2 (24.003 against 24.01) and above it for Ne-H2 (2.637 against 2.63), again from unrounded runs.
UNCERTAINTY. E: “reproduced usually within 0.1 cc/mole” (abstract, p. 2960); the precision of the pressure change, usually within 0.01 cm of oil at 2 atm, “is equivalent to an error of approximately 0.1 cc/mole” in E (p. 2963), and Eq. (11) gives dE = 0.12 cc/mole at 25 degC for 1e-6 atm (p. 2963). The level is not stated, and the figure is a precision (the three runs of each system in Table III spread over 0.01-0.24 cc/mole); E’s datasets take 0.1 cc/mole, not stated. The third virial coefficients’ errors are “believed to contribute a negligible error” to E (p. 2964). B12: no uncertainty is stated. It carries E’s and that of the literature B11 and B22, which the paper does not quantify beyond saying that pure second virial coefficients are seldom accurate to 0.1 cc/mole (p. 2963); B12’s datasets state none. With better pure-gas values, B12 follows from E by Eq. (12) without a new measurement (p. 2964).
THE PURE-GAS VALUES (Table I, p. 2963, “Chosen literature values”): Otto (Handbuch der Experimentalphysik, 1929) for He, H2, N2 and Ne, Michels et al. (Physica 1949, 1958) for Ar, interpolated linearly in 1/T between Otto’s 50 degC intervals (p. 2964). They are other sources’ values and are not extracted; they are needed only to rebuild B12 from E. The extrapolations the paper mentions (Ar from -140 to -150 degC, N2 from -130 to -150 degC) touch only the -150 degC row of Table I, which Table IV does not use.
NOT EXTRACTED: Table I (literature pure B, above); Table II (p. 2964, literature third virial coefficients used in the reduction: optmat has no third-virial quantity, and they are not this work’s); Table III’s individual runs (their means are Table IV’s -125 degC E); Figs. 2 and 3 (E against T, and log E against log T: the same values as Table IV, so not digitised). The empirical correlation E = alpha T^beta (Sec. VI, Eqs. 18-20; the slopes of Fig. 3 ‘nearly constant at -1.4’) prints no alpha or beta per pair. The Kihara-potential B12 the paper compares with (Sec. V) are not tabulated. The unabridged data are in J. Brewer’s AFOSR final report (1967, the paper’s ref. 5), not in hand.
DOUBTS: the purity of the gases is not stated. B12 of H2-He alternates by 0.2 cc/mole between neighbouring temperatures (16.20, 16.43, 16.20, 16.43 from -100 to -25 degC); Table I’s pure-gas mean rises smoothly there, and the alternation is in E, whose steps are -0.62, -0.86, -0.25 cc/mole, a few times its stated precision. E of Ar-N2 is small and negative (-0.42 to -0.66) with no trend in temperature, which the paper notes (p. 2968). The Kihara comparison differs from experiment by up to 5-8 cc/mole at -125 degC for the helium and neon binaries with Ar and N2 (p. 2967); the paper attributes it mainly to the geometric-mean combining rule.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
brewer_1969/B12_Ar_H2#
{
"id": "B12_Ar_H2",
"material": "Ar",
"file": "Ar/brewer_1969__B12_Ar_H2.csv",
"table": "tbl_5752880ca58e",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "H2"
}
}
Table IV (p. 2966): the interaction second virial coefficient B12 of Ar-H2 (printed Ar-H2, and H2-Ar at 25 degC), -125 to 50 degC in steps of 25 degC: the measured E (dataset E_Ar_H2) plus the mean of the literature pure-gas B of Table I (Eq. 12). Not independent of E_Ar_H2: a fit uses one or the other. No uncertainty is stated for B12 (the record’s notes).
brewer_1969/E_Ar_H2#
{
"id": "E_Ar_H2",
"material": "Ar",
"file": "Ar/brewer_1969__E_Ar_H2.csv",
"table": "tbl_5752880ca58e",
"quantity": "excess_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "H2"
},
"uncertainty": {
"absolute": 0.1,
"level": "not stated"
}
}
Table IV (p. 2966): the measured excess second virial coefficient E = B12 - (B11 + B22)/2 of Ar-H2 (printed Ar-H2, and H2-Ar at 25 degC), -125 to 50 degC in steps of 25 degC. The -125 degC value is the mean of the three runs of Table III (p. 2965).
brewer_1969/B12_Ar_He#
{
"id": "B12_Ar_He",
"material": "Ar",
"file": "Ar/brewer_1969__B12_Ar_He.csv",
"table": "tbl_5752880ca58e",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "He"
}
}
Table IV (p. 2966): the interaction second virial coefficient B12 of Ar-He (printed He-Ar at 50 to 0 degC, Ar-He below), -125 to 50 degC in steps of 25 degC: the measured E (dataset E_Ar_He) plus the mean of the literature pure-gas B of Table I (Eq. 12). Not independent of E_Ar_He: a fit uses one or the other. No uncertainty is stated for B12 (the record’s notes).
brewer_1969/E_Ar_He#
{
"id": "E_Ar_He",
"material": "Ar",
"file": "Ar/brewer_1969__E_Ar_He.csv",
"table": "tbl_5752880ca58e",
"quantity": "excess_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "He"
},
"uncertainty": {
"absolute": 0.1,
"level": "not stated"
}
}
Table IV (p. 2966): the measured excess second virial coefficient E = B12 - (B11 + B22)/2 of Ar-He (printed He-Ar at 50 to 0 degC, Ar-He below), -125 to 50 degC in steps of 25 degC. The -125 degC value is the mean of the three runs of Table III (p. 2965).
brewer_1969/B12_Ar_N2#
{
"id": "B12_Ar_N2",
"material": "Ar",
"file": "Ar/brewer_1969__B12_Ar_N2.csv",
"table": "tbl_5752880ca58e",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "N2"
}
}
Table IV (p. 2966): the interaction second virial coefficient B12 of Ar-N2 (printed N2-Ar at 50, -100 and -125 degC, Ar-N2 otherwise), -125 to 50 degC in steps of 25 degC: the measured E (dataset E_Ar_N2) plus the mean of the literature pure-gas B of Table I (Eq. 12). Not independent of E_Ar_N2: a fit uses one or the other. No uncertainty is stated for B12 (the record’s notes).
brewer_1969/E_Ar_N2#
{
"id": "E_Ar_N2",
"material": "Ar",
"file": "Ar/brewer_1969__E_Ar_N2.csv",
"table": "tbl_5752880ca58e",
"quantity": "excess_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "N2"
},
"uncertainty": {
"absolute": 0.1,
"level": "not stated"
}
}
Table IV (p. 2966): the measured excess second virial coefficient E = B12 - (B11 + B22)/2 of Ar-N2 (printed N2-Ar at 50, -100 and -125 degC, Ar-N2 otherwise), -125 to 50 degC in steps of 25 degC. The -125 degC value is the mean of the three runs of Table III (p. 2965).
brewer_1969/B12_Ar_Ne#
{
"id": "B12_Ar_Ne",
"material": "Ar",
"file": "Ar/brewer_1969__B12_Ar_Ne.csv",
"table": "tbl_5752880ca58e",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "Ne"
}
}
Table IV (p. 2966): the interaction second virial coefficient B12 of Ar-Ne (printed Ne-Ar, and Ar-Ne at 25 and -25 degC), -125 to 50 degC in steps of 25 degC: the measured E (dataset E_Ar_Ne) plus the mean of the literature pure-gas B of Table I (Eq. 12). Not independent of E_Ar_Ne: a fit uses one or the other. No uncertainty is stated for B12 (the record’s notes).
brewer_1969/E_Ar_Ne#
{
"id": "E_Ar_Ne",
"material": "Ar",
"file": "Ar/brewer_1969__E_Ar_Ne.csv",
"table": "tbl_5752880ca58e",
"quantity": "excess_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "Ne"
},
"uncertainty": {
"absolute": 0.1,
"level": "not stated"
}
}
Table IV (p. 2966): the measured excess second virial coefficient E = B12 - (B11 + B22)/2 of Ar-Ne (printed Ne-Ar, and Ar-Ne at 25 and -25 degC), -125 to 50 degC in steps of 25 degC. The -125 degC value is the mean of the three runs of Table III (p. 2965).
brewer_1969/B12_H2_He#
{
"id": "B12_H2_He",
"material": "H2",
"file": "H2/brewer_1969__B12_H2_He.csv",
"table": "tbl_5752880ca58e",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "He"
}
}
Table IV (p. 2966): the interaction second virial coefficient B12 of H2-He (printed H2-He, and He-H2 at 50 and -25 degC; the 25 degC row is printed H2-Ne (a misprint, see the record’s notes)), -125 to 50 degC in steps of 25 degC: the measured E (dataset E_H2_He) plus the mean of the literature pure-gas B of Table I (Eq. 12). Not independent of E_H2_He: a fit uses one or the other. No uncertainty is stated for B12 (the record’s notes).
brewer_1969/E_H2_He#
{
"id": "E_H2_He",
"material": "H2",
"file": "H2/brewer_1969__E_H2_He.csv",
"table": "tbl_5752880ca58e",
"quantity": "excess_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "He"
},
"uncertainty": {
"absolute": 0.1,
"level": "not stated"
}
}
Table IV (p. 2966): the measured excess second virial coefficient E = B12 - (B11 + B22)/2 of H2-He (printed H2-He, and He-H2 at 50 and -25 degC; the 25 degC row is printed H2-Ne (a misprint, see the record’s notes)), -125 to 50 degC in steps of 25 degC. The -125 degC value is the mean of the three runs of Table III (p. 2965).
brewer_1969/B12_H2_N2#
{
"id": "B12_H2_N2",
"material": "H2",
"file": "H2/brewer_1969__B12_H2_N2.csv",
"table": "tbl_5752880ca58e",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "N2"
}
}
Table IV (p. 2966): the interaction second virial coefficient B12 of H2-N2 (printed H2-N2 at 50 and 25 degC, N2-H2 below), -125 to 50 degC in steps of 25 degC: the measured E (dataset E_H2_N2) plus the mean of the literature pure-gas B of Table I (Eq. 12). Not independent of E_H2_N2: a fit uses one or the other. No uncertainty is stated for B12 (the record’s notes).
brewer_1969/E_H2_N2#
{
"id": "E_H2_N2",
"material": "H2",
"file": "H2/brewer_1969__E_H2_N2.csv",
"table": "tbl_5752880ca58e",
"quantity": "excess_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "N2"
},
"uncertainty": {
"absolute": 0.1,
"level": "not stated"
}
}
Table IV (p. 2966): the measured excess second virial coefficient E = B12 - (B11 + B22)/2 of H2-N2 (printed H2-N2 at 50 and 25 degC, N2-H2 below), -125 to 50 degC in steps of 25 degC. The -125 degC value is the mean of the three runs of Table III (p. 2965).
brewer_1969/B12_H2_Ne#
{
"id": "B12_H2_Ne",
"material": "H2",
"file": "H2/brewer_1969__B12_H2_Ne.csv",
"table": "tbl_5752880ca58e",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "Ne"
}
}
Table IV (p. 2966): the interaction second virial coefficient B12 of H2-Ne (printed Ne-H2), -125 to 50 degC in steps of 25 degC: the measured E (dataset E_H2_Ne) plus the mean of the literature pure-gas B of Table I (Eq. 12). Not independent of E_H2_Ne: a fit uses one or the other. No uncertainty is stated for B12 (the record’s notes).
brewer_1969/E_H2_Ne#
{
"id": "E_H2_Ne",
"material": "H2",
"file": "H2/brewer_1969__E_H2_Ne.csv",
"table": "tbl_5752880ca58e",
"quantity": "excess_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "Ne"
},
"uncertainty": {
"absolute": 0.1,
"level": "not stated"
}
}
Table IV (p. 2966): the measured excess second virial coefficient E = B12 - (B11 + B22)/2 of H2-Ne (printed Ne-H2), -125 to 50 degC in steps of 25 degC. The -125 degC value is the mean of the three runs of Table III (p. 2965).
brewer_1969/B12_He_N2#
{
"id": "B12_He_N2",
"material": "He",
"file": "He/brewer_1969__B12_He_N2.csv",
"table": "tbl_5752880ca58e",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "N2"
}
}
Table IV (p. 2966): the interaction second virial coefficient B12 of He-N2 (printed He-N2 at 50 and 25 degC, N2-He below), -125 to 50 degC in steps of 25 degC: the measured E (dataset E_He_N2) plus the mean of the literature pure-gas B of Table I (Eq. 12). Not independent of E_He_N2: a fit uses one or the other. No uncertainty is stated for B12 (the record’s notes).
brewer_1969/E_He_N2#
{
"id": "E_He_N2",
"material": "He",
"file": "He/brewer_1969__E_He_N2.csv",
"table": "tbl_5752880ca58e",
"quantity": "excess_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "N2"
},
"uncertainty": {
"absolute": 0.1,
"level": "not stated"
}
}
Table IV (p. 2966): the measured excess second virial coefficient E = B12 - (B11 + B22)/2 of He-N2 (printed He-N2 at 50 and 25 degC, N2-He below), -125 to 50 degC in steps of 25 degC. The -125 degC value is the mean of the three runs of Table III (p. 2965).
brewer_1969/B12_He_Ne#
{
"id": "B12_He_Ne",
"material": "He",
"file": "He/brewer_1969__B12_He_Ne.csv",
"table": "tbl_5752880ca58e",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "Ne"
}
}
Table IV (p. 2966): the interaction second virial coefficient B12 of He-Ne (printed Ne-He), -125 to 50 degC in steps of 25 degC: the measured E (dataset E_He_Ne) plus the mean of the literature pure-gas B of Table I (Eq. 12). Not independent of E_He_Ne: a fit uses one or the other. No uncertainty is stated for B12 (the record’s notes).
brewer_1969/E_He_Ne#
{
"id": "E_He_Ne",
"material": "He",
"file": "He/brewer_1969__E_He_Ne.csv",
"table": "tbl_5752880ca58e",
"quantity": "excess_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "Ne"
},
"uncertainty": {
"absolute": 0.1,
"level": "not stated"
}
}
Table IV (p. 2966): the measured excess second virial coefficient E = B12 - (B11 + B22)/2 of He-Ne (printed Ne-He), -125 to 50 degC in steps of 25 degC. Table III gives no runs for this pair.
brewer_1969/B12_N2_Ne#
{
"id": "B12_N2_Ne",
"material": "N2",
"file": "N2/brewer_1969__B12_N2_Ne.csv",
"table": "tbl_5752880ca58e",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "Ne"
}
}
Table IV (p. 2966): the interaction second virial coefficient B12 of N2-Ne (printed Ne-N2), -125 to 50 degC in steps of 25 degC: the measured E (dataset E_N2_Ne) plus the mean of the literature pure-gas B of Table I (Eq. 12). Not independent of E_N2_Ne: a fit uses one or the other. No uncertainty is stated for B12 (the record’s notes).
brewer_1969/E_N2_Ne#
{
"id": "E_N2_Ne",
"material": "N2",
"file": "N2/brewer_1969__E_N2_Ne.csv",
"table": "tbl_5752880ca58e",
"quantity": "excess_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "C",
"use": "primary",
"parameters": {
"partner": "Ne"
},
"uncertainty": {
"absolute": 0.1,
"level": "not stated"
}
}
Table IV (p. 2966): the measured excess second virial coefficient E = B12 - (B11 + B22)/2 of N2-Ne (printed Ne-N2), -125 to 50 degC in steps of 25 degC. The -125 degC value is the mean of the three runs of Table III (p. 2965).
Formulas#
No formulas are recorded.
Corrections#
No dataset errata are recorded in this source record.
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.