vatter_1996#
K. Vatter, H. J. Schmidt, E. Elias and B. Schramm, “Measurements of Interaction Second Virial Coefficients of Binary Mixtures of Inert Gases and Gases with Linear Molecules at Temperatures Ranging from 296 to 463 K”, Ber. Bunsenges. Phys. Chem. 100, 73 (1996)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Differential measurements against a reference gas (nitrogen or neon) in two matched Duran glass vessels below 0.1 MPa, where pV = nRT + npB(T), the pressure difference being nulled with a capacitance manometer by a micrometer-screw volume change (p. 74). At 296.15 K the expansion method (the authors’ refs. 12 and 13; both vessels expanded into two empty vessels of equal volume, stopcocks now opened by stepping motors) gives B_x(T0) - B_R(T0). Above it the temperature changing method (closed vessels heated) gives {B_x(T0) - B_R(T0)} - {B_x(T) - B_R(T)}: from T0 = 296.15 K to 353.15 K in a water bath, and from T0 = 353.15 K to 413.15 and 463.15 K in an oil bath (LAUDA D8/22, stirring improved). The glass’s expansion is corrected (alpha = 3.2e-6, changing B by less than 0.3 cm^3/mol). Each value was measured at different pressures, with the two gases exchanged between the vessels and, for the mixtures, at mole fractions of about 0.4, 0.5 and 0.6. Ar, CO, Ne, N2 and O2 from Messer Griesheim, stated purity better than 99.99 %, filled through liquid-nitrogen-cooled traps.
Materials in structured entries: Ar, CO, N2, Ne
Dataset quantities: cross_second_virial_coefficient, second_virial_coefficient
Contents: 9 datasets; 0 formulas.
Curation notes#
Identity VALIDATED_WITH_WARNINGS by the library (the PDF prints no DOI; a bibliographic search found this one, whose title, first author and year agree with the first page; Crossref’s title omits ‘with Linear Molecules at Temperatures Ranging from 296 to 463 K’, which the first page prints). Printed pp. 73-79 (pdf pages 1-7; the journal line on p. 73 reads ‘Ber. Bunsenges. Phys. Chem. 100, 73-79 (1996) No. 1’).
EXTRACTED: Table 1 (p. 75), ‘Second virial coefficients: data from the literature and measured data’, B in cm^3/mole at 296.15, 353.15, 413.15 and 463.15 K, its ‘This work’ rows: pure CO and the interaction second virial coefficients B_12 of Ne/O2, Ar/O2, Ne/N2, Ar/N2, Ne/CO and Ar/CO, each with its estimated error. Every cell of the extracted table, including both table notes, agrees with the table image and with a 400 dpi rendering of p. 75 (2026-10-01). The neon pairs have no 413.15 K value (blank, as printed). Each pair is filed under the first of its gases in sorted order, with the other as the partner (Ne/N2 under N2, Ne/CO under CO).
WHAT IS MEASURED AND WHAT DERIVED (pp. 74-75). The measurement is the difference of the mixture’s (or CO’s) B from the reference gas’s, and for T > T0 its change from T0; the starting values B_x(T0) at 296.15 K ‘have to be known from other sources, e.g. from measurements with the expansion method’ (p. 74). B_12 follows from B_m(T, x_1) = x_1^2 B_1 + x_2^2 B_2 + 2 x_1 x_2 B_12 with the pure-gas B’s of Table 1, so ‘the error of B_12 is at least twice as large as of B_m’ (p. 74). The mixtures’ B_m and the mole fractions of the individual runs are not printed, so no B_12 can be recomputed from the paper. The pure-gas B’s used (Table 1, ‘From the literature’, not extracted here, being other works’ values), at 296.15, 353.15, 413.15 and 463.15 K: Ne 11.3, 12.2, 12.8, 13.3 (Michels, Wassenaar and Louwerse, Physica 26, 539 (1960), their ref. 17); Ar -16.4, -6.4, 0.2, 4.4 (calculated from Aziz’s potential, J. Chem. Phys. 99, 4518 (1993), ref. 19, judged more accurate than experiment); O2 -16.4, -6.0, 1.5, 6.1 (Sommer and Schramm, Ber. Bunsenges. Phys. Chem. 92, 925 (1988), ref. 15); N2 -5.0, 4.2, 10.7, 14.5 (Pocock and Wormald, J. Chem. Soc. Faraday I 71, 705 (1975), ref. 16); CO this work’s own (table1_B_CO). The reference gas’s B (N2 or Ne) is presumably the same literature value; the paper does not say which reference was used for which mixture.
TWO VALUES ARE NOT THIS WORK’S (Table 1’s notes): CO at 296.15 K, -8.9 +- 0.5, ‘a) Taken from [21]’ (Michels, Lupton, Wassenaar and de Graaff, Physica 18, 121 (1952)); Ar/N2 at 296.15 K, -11.3 +- 0.5, ‘b) Taken from [22]’ (Ewing and Trusler, Physica A 184, 415 and 437 (1992), from the speed of sound, p. 75). They are kept as reproduced datasets. As the starting values of the temperature changing method, they presumably underlie this work’s CO and Ar/N2 values at 353.15 K (the paper does not say so explicitly). CO was remeasured because Schmiedel et al. (1980) and Michels et al. (1952) differ by more than 2 cm^3/mol and Michels’s data end at 423 K (p. 75).
UNCERTAINTY: Table 1 gives the results ‘together with their estimated errors’ (p. 74), +-0.5 to +-3.0 cm^3/mol, growing with temperature; the level is not stated. ‘Systematic errors are the main source of errors’ (adsorption, solubility in stopcock grease, temperature gradients); repeated runs under different conditions ‘all were within +-1.0 cm^3/mole’ (p. 74). On p. 76 the authors write that ‘deviations of single points from a smoothed curve give a good estimate for the error bounds of the measurements’, which suggests bounds; the datasets keep ‘not stated’ (read as one sigma, the larger reading; as bounds the standard uncertainty would be 1/sqrt(3) times smaller).
CHECKS (2026-10-01). (1) Table 2 (p. 75) repeats this work’s values beside the literature’s: CO -8.9, 0.9, 8.2, 12.7; Ar/N2 (none), -1.5, 5.7, 9.1; Ne/N2 14.0, 17.0, 20.0; Ar/CO -11.9, -2.1, 5.2, 9.3. Two differ from Table 1 (image checked in both): Ar/N2 at 353.15 K, -1.5 against -1.4, and Ne/N2 at 463.15 K, 20.0 against 20.2. Both are within the stated errors; Table 1, the results table with the errors, is the dataset. Table 2’s blank for this work’s Ar/N2 at 296.15 K agrees with Table 1’s note b. (2) The text (p. 75) says the neon pairs’ B_12 at high temperature lie outside the range of the pure components; at 463.15 K, Ne/O2 15.4 (Ne 13.3, O2 6.1), Ne/N2 20.2 (N2 14.5), Ne/CO 20.6 (CO 12.7): confirmed. (3) Table 4’s Boyle temperatures of the argon pairs, ‘determined by interpolation of measured data’ (pp. 75-76; Table 4 on p. 77), are reproduced from Table 1’s B_12: a parabola through the four points crosses zero at 403.4, 363.1 and 368.4 K for Ar/O2, Ar/N2 and Ar/CO (printed 404, 365, 368; linear interpolation between 353.15 and 413.15 K gives 405.8, 365.0, 370.4). (4) Table 3’s combination rules (p. 76), T_c12 = (T_c1 T_c2)^(1/2) and v_c12 = (v_c1^(1/3) + v_c2^(1/3))^3 / 8, reproduce all six printed T_c12 within 0.1 K and five of the six v_c12 within 0.05 cm^3/mol; for Ne/O2 they give 58.0 where 56.5 is printed (image checked), which affects only the reduced plot of Figs. 1 and 2.
NOT EXTRACTED. Table 1’s literature rows (above). Table 2’s literature values (Michels et al. 1952 and Schmiedel et al. 1980 for CO; Ewing and Trusler 1992 and Brewer for Ar/N2; Brewer for Ne/N2; Schmiedel et al. for Ar/CO; Brewer’s ref. 23 gives only an Air Force Office of Scientific Research address): other works’ values, to be curated from their own papers. Table 3, critical volumes and temperatures of the pure gases (from Harrison 1982) and the combination-rule constants of the pairs: no quantity in the vocabulary. Table 4, the Boyle temperatures (no quantity in the vocabulary) and B_12 at 2 T_Boyle (Ne pairs) or 0.5 T_Boyle (Ar pairs), interpolated through this work’s and other works’ low-temperature data, at derived temperatures partly outside the measured range: not this work’s measurements. Figs. 1-8 plot Table 1’s values (reduced, or as deviations from potential-energy-surface calculations) with other works’ points; nothing is digitised, as the values are printed. The paper has no N2-O2, helium, krypton or xenon pair; every species it names is an optmat gas.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
vatter_1996/table1_B_CO#
{
"id": "table1_B_CO",
"material": "CO",
"file": "CO/vatter_1996__table1_B_CO.csv",
"table": "tbl_9d39962ae383",
"quantity": "second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "K",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 75), This work, CO: the pure gas’s B at 353.15, 413.15 and 463.15 K by the temperature changing method; the 296.15 K value of the same row is Michels et al.’s (table1_B_CO_michels).
vatter_1996/table1_B_CO_michels#
{
"id": "table1_B_CO_michels",
"material": "CO",
"file": "CO/vatter_1996__table1_B_CO_michels.csv",
"table": "tbl_9d39962ae383",
"quantity": "second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "K",
"use": "reproduced",
"reproduced_from": [
"A. Michels, J. M. Lupton, T. Wassenaar and W. de Graaff, Physica 18, 121 (1952)"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 75), This work, CO at 296.15 K, -8.9 +- 0.5 with note a), ‘Taken from [21]’; the starting value of this work’s CO measurements.
vatter_1996/table1_B12_Ar_CO#
{
"id": "table1_B12_Ar_CO",
"material": "Ar",
"file": "Ar/vatter_1996__table1_B12_Ar_CO.csv",
"table": "tbl_9d39962ae383",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "K",
"use": "primary",
"parameters": {
"partner": "CO"
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 75), This work, Ar/CO: B_12 at 296.15 (expansion method), 353.15, 413.15 and 463.15 K (temperature changing method), with Aziz’s Ar and this work’s CO.
vatter_1996/table1_B12_Ar_N2#
{
"id": "table1_B12_Ar_N2",
"material": "Ar",
"file": "Ar/vatter_1996__table1_B12_Ar_N2.csv",
"table": "tbl_9d39962ae383",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "K",
"use": "primary",
"parameters": {
"partner": "N2"
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 75), This work, Ar/N2: B_12 at 353.15, 413.15 and 463.15 K (temperature changing method), with Aziz’s Ar and Pocock and Wormald’s N2; the 296.15 K value of the same row is Ewing and Trusler’s (table1_B12_Ar_N2_ewing). Table 2 prints the 353.15 K value as -1.5 (record notes).
vatter_1996/table1_B12_Ar_N2_ewing#
{
"id": "table1_B12_Ar_N2_ewing",
"material": "Ar",
"file": "Ar/vatter_1996__table1_B12_Ar_N2_ewing.csv",
"table": "tbl_9d39962ae383",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "K",
"use": "reproduced",
"reproduced_from": [
"M. Ewing and J. P. M. Trusler, Physica A 184, 415 and 437 (1992)"
],
"parameters": {
"partner": "N2"
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 75), This work, Ar/N2 at 296.15 K, -11.3 +- 0.5 with note b), ‘Taken from [22]’ (from speed-of-sound measurements, p. 75); Table 2 lists it under Trusler et al.
vatter_1996/table1_B12_Ar_O2#
{
"id": "table1_B12_Ar_O2",
"material": "Ar",
"file": "Ar/vatter_1996__table1_B12_Ar_O2.csv",
"table": "tbl_9d39962ae383",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "K",
"use": "primary",
"parameters": {
"partner": "O2"
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 75), This work, Ar/O2: B_12 at 296.15 (expansion method), 353.15, 413.15 and 463.15 K (temperature changing method), with Aziz’s Ar and Sommer and Schramm’s O2.
vatter_1996/table1_B12_CO_Ne#
{
"id": "table1_B12_CO_Ne",
"material": "CO",
"file": "CO/vatter_1996__table1_B12_CO_Ne.csv",
"table": "tbl_9d39962ae383",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "K",
"use": "primary",
"parameters": {
"partner": "Ne"
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 75), This work, Ne/CO: B_12 at 296.15 (expansion method), 353.15 and 463.15 K (temperature changing method), with Michels et al.’s Ne and this work’s CO; no 413.15 K value is printed.
vatter_1996/table1_B12_N2_Ne#
{
"id": "table1_B12_N2_Ne",
"material": "N2",
"file": "N2/vatter_1996__table1_B12_N2_Ne.csv",
"table": "tbl_9d39962ae383",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "K",
"use": "primary",
"parameters": {
"partner": "Ne"
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 75), This work, Ne/N2: B_12 at 296.15 (expansion method), 353.15 and 463.15 K (temperature changing method), with Michels et al.’s Ne and Pocock and Wormald’s N2; no 413.15 K value is printed. Table 2 prints the 463.15 K value as 20.0 (record notes).
vatter_1996/table1_B12_Ne_O2#
{
"id": "table1_B12_Ne_O2",
"material": "Ne",
"file": "Ne/vatter_1996__table1_B12_Ne_O2.csv",
"table": "tbl_9d39962ae383",
"quantity": "cross_second_virial_coefficient",
"unit": "cm3/mol",
"abscissa": "temperature",
"abscissa_unit": "K",
"use": "primary",
"parameters": {
"partner": "O2"
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 75), This work, Ne/O2: B_12 at 296.15 (expansion method), 353.15 and 463.15 K (temperature changing method), with Michels et al.’s Ne and Sommer and Schramm’s O2; no 413.15 K value is printed.
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.