kerl_1984#
K. Kerl and H. Häusler, “Mean polarizabilities and second virial coefficients of the gases Ar, CH4, C2H6, C3H8 and C(CH3)4”, Ber. Bunsenges. Phys. Chem. 88, 992 (1984)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Absolute refractivity at the green Hg line (546.226 nm, vacuum) with an evacuated Michelson interferometer (Kerl and Jescheck’s apparatus), 260-366 K and 0-3 bar: the gas is pumped out of the cell in about 10 steps (pressure to 5 Pa, temperature to 1 mK) while the fringe number is counted, and n - 1 is fitted to a quadratic in rho_0 = p/RT (Eqs. 2.1-2.3, p. 993). Two sample cells: the earlier one and an improved one of length 126.49(2) cm at 20 C (starred isotherms). Gas purity better than 99.99 % (CH4, Ar).
Materials in structured entries: Ar, CH4
Dataset quantities: molar_refractivity
Contents: 12 datasets; 2 formulas.
Curation notes#
Page numbers are the journal’s (992-997; pdf page 1 = p. 992, which begins with the end of the previous article’s reference list, and the last pdf page carries the start of the next article, Vogel on viscosities).
Reduction (Eqs. 2.2-2.5, p. 993): n - 1 = a_1 rho_0 + a_2 rho_0^2 with the ideal-gas density rho_0 = p/RT; A_R = (4/3) pi N_A alpha_0 = 2 a_1/3 is the molar refractivity of the free molecule (zero density), so no state applies. B(T) (Table 1’s last column, Eq. 2.8) assumes b_R = a_1/6 (Eq. 2.7): an equation-of-state quantity, not extracted.
Wavelength: the text (pp. 993 and 995) and Table 1’s caption give lambda_0 = 546.226 nm; the abstract (p. 992) prints 546.266 nm. 546.226 nm is right: it is the one used in the evaluation, and it is the vacuum wavelength of the green Hg line (546.077 nm in standard air by Edlén 1966, the line’s familiar label 546.07-546.1 nm), while 546.266 nm matches no Hg line; a transposition in the abstract. No dataset uses the abstract.
Uncertainty (pp. 994-995): ‘The figures in parenthesis behind the data in Table 1 are standard deviations’ (1 sigma, of the fit). Stated systematic parts: the cell length (Delta l = 0.02 cm) gives Delta A_R/A_R = +-1.6e-4; a missetting of the monochromator by 0.1 nm on the 6 nm-wide Hg line gives +-1.8e-4 (p. 995); a missetting of about 2 nm ‘may be the reason for the low value A_R(299 K) = 4.2091’ of Ar (bracketed, excluded). Typical fit deviation Delta(n - 1)/(n - 1) = +-1e-4 (p. 993).
Temperature (Section 3.3, p. 995): A_R rises slightly with T for the molecules, and the authors propose A_R = c_0 + c_1 T (Eq. 3.5, Table 3; formulas A_R_T_Ar, A_R_T_CH4), ‘Additional experiments with an improved technique shall give more accurate results’. The same group later found no temperature dependence for the noble gases (hohm_1990, which contradicts this paper’s and Hohm and Kerl 1986’s earlier 1 %-per-100 K increase) and supersedes these values: all datasets are use = ‘check’.
Checks (2026-09-26): Table 2’s means are the arithmetic means of the unbracketed Table 1 values (Ar 4.23073, CH4 6.64046) with the sample standard deviation of the values (0.0063, 0.0396); a least-squares line through the same values gives c_0 = 4.1588 and 2.22e-4 (Ar, r = 0.67, s = 0.0057) and 6.2270 and 12.64e-4 (CH4, r = 0.91, s = 0.019), Table 3’s figures. Against optmat’s fits at 546.226 nm (fit/Ar 4.2151, fit/CH4 6.6185 cm^3/mol) the means are +0.37 % (Ar) and +0.34 % (CH4), far beyond the stated standard deviations; hohm_1994b’s Ar at 543.516 nm (4.2163 cm^3/mol) is 0.35 % lower too.
Not extracted: C2H6, C3H8 and C(CH3)4 (not curated species); p_max, K, |s|, a_1, a_2 and B of Table 1; Table 2’s critical constants (from the Encyclopédie des Gaz) and Boyle temperatures; Table 4 (fits of B(T)/V_c and B(T)/A_R against (T_c/T)^2, an equation-of-state correlation); Eqs. (4.2)-(4.3) (A_R against V_c for 11 gases).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
kerl_1984/A_R_299_12K_Ar#
{
"id": "A_R_299_12K_Ar",
"material": "Ar",
"file": "Ar/kerl_1984__A_R_299_12K_Ar.csv",
"table": "tbl_6ccbf5b10dc1",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 299.12
}
}
Table 1 (p. 994), Ar isotherm at 299.12(1) K, p_max 2.819 bar, K = 12, the old sample cell.
kerl_1984/A_R_299_15K_Ar#
{
"id": "A_R_299_15K_Ar",
"material": "Ar",
"file": "Ar/kerl_1984__A_R_299_15K_Ar.csv",
"table": "tbl_6ccbf5b10dc1",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "excluded",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 299.15
}
}
Table 1, Ar at 299.15(1) K: printed in brackets (‘uncertain ... by no means [used] in all further calculations’, p. 994); the authors suspect a monochromator missetting of about 2 nm (p. 995).
kerl_1984/A_R_323_47K_Ar#
{
"id": "A_R_323_47K_Ar",
"material": "Ar",
"file": "Ar/kerl_1984__A_R_323_47K_Ar.csv",
"table": "tbl_6ccbf5b10dc1",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 323.47
}
}
Table 1, Ar at 323.47(1) K, the old sample cell.
kerl_1984/A_R_325_53K_Ar#
{
"id": "A_R_325_53K_Ar",
"material": "Ar",
"file": "Ar/kerl_1984__A_R_325_53K_Ar.csv",
"table": "tbl_6ccbf5b10dc1",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 325.53
}
}
Table 1, Ar at 325.53(1) K (its a_2 and B in brackets; A_R not), the old sample cell.
kerl_1984/A_R_345_19K_Ar#
{
"id": "A_R_345_19K_Ar",
"material": "Ar",
"file": "Ar/kerl_1984__A_R_345_19K_Ar.csv",
"table": "tbl_6ccbf5b10dc1",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 345.19
}
}
Table 1, Ar at 345.19(1) K (its a_2 and B in brackets; A_R not), the old sample cell.
kerl_1984/A_R_299_44K_CH4#
{
"id": "A_R_299_44K_CH4",
"material": "CH4",
"file": "CH4/kerl_1984__A_R_299_44K_CH4.csv",
"table": "tbl_6ccbf5b10dc1",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 299.44
}
}
Table 1, CH4 at 299.44(1) K, starred: the improved sample cell of length 126.49(2) cm at 20 C.
kerl_1984/A_R_301_47K_CH4#
{
"id": "A_R_301_47K_CH4",
"material": "CH4",
"file": "CH4/kerl_1984__A_R_301_47K_CH4.csv",
"table": "tbl_6ccbf5b10dc1",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 301.47
}
}
Table 1, CH4 at 301.47(1) K, the old sample cell.
kerl_1984/A_R_323_01K_CH4#
{
"id": "A_R_323_01K_CH4",
"material": "CH4",
"file": "CH4/kerl_1984__A_R_323_01K_CH4.csv",
"table": "tbl_6ccbf5b10dc1",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 323.01
}
}
Table 1, CH4 at 323.01(1) K, the old sample cell.
kerl_1984/A_R_345_22K_CH4#
{
"id": "A_R_345_22K_CH4",
"material": "CH4",
"file": "CH4/kerl_1984__A_R_345_22K_CH4.csv",
"table": "tbl_6ccbf5b10dc1",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 345.22
}
}
Table 1, CH4 at 345.22(1) K, the old sample cell.
kerl_1984/A_R_365_63K_CH4#
{
"id": "A_R_365_63K_CH4",
"material": "CH4",
"file": "CH4/kerl_1984__A_R_365_63K_CH4.csv",
"table": "tbl_6ccbf5b10dc1",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 365.63
}
}
Table 1, CH4 at 365.63(2) K, the old sample cell.
kerl_1984/A_R_mean_Ar#
{
"id": "A_R_mean_Ar",
"material": "Ar",
"file": "Ar/kerl_1984__A_R_mean_Ar.csv",
"table": "tbl_44fdf7d2e6c3",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
}
}
Table 2 (p. 994), A_R-bar: ‘the arithmetic mean of the A_R-values of Table 1’ (the four unbracketed Ar values, 299-345 K); the parenthesised figure is the sample standard deviation of those values (checked), not the uncertainty of the mean. No single temperature.
kerl_1984/A_R_mean_CH4#
{
"id": "A_R_mean_CH4",
"material": "CH4",
"file": "CH4/kerl_1984__A_R_mean_CH4.csv",
"table": "tbl_44fdf7d2e6c3",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "check",
"uncertainty": {
"column": true,
"level": "1 sigma"
}
}
Table 2 (p. 994), A_R-bar of the five CH4 values (299-366 K), which rise with temperature (Table 3); the parenthesised figure is their sample standard deviation (checked). No single temperature.
Formulas#
kerl_1984/A_R_T_Ar#
{
"id": "A_R_T_Ar",
"material": "Ar",
"equation": "Eq. (3.5) with Table 3, p. 995",
"printed": "A_R/cm^3 mol^-1 = c_0 + c_1 T; Ar: K = 4, |s| = 0.0057, r = 0.67, c_0 = 4.159(57), 10^4 c_1/K^-1 = 2.2(1.8), 10^4 (c_1/c_0)/K^-1 = 0.53",
"variable": "T: temperature in K; A_R: molar refractivity at 546.226 nm (vacuum), cm^3/mol",
"range": "299-345 K (the four unbracketed Table 1 isotherms)",
"coefficients": {
"c0": "4.159",
"c0_sigma": "0.057",
"c1": "2.2e-4",
"c1_sigma": "1.8e-4"
},
"check": "A least-squares line through Table 1's four unbracketed Ar values gives c_0 = 4.1588, c_1 = 2.22e-4, r = 0.67, s = 0.0057: Table 3 to its printed digits. Checked 2026-09-26."
}
The slope is not significant (1.2 sigma) and hohm_1990 found none for argon at 300-1100 K; a check only.
kerl_1984/A_R_T_CH4#
{
"id": "A_R_T_CH4",
"material": "CH4",
"equation": "Eq. (3.5) with Table 3, p. 995",
"printed": "A_R/cm^3 mol^-1 = c_0 + c_1 T; CH4: K = 5, |s| = 0.019, r = 0.91, c_0 = 6.23(11), 10^4 c_1/K^-1 = 12.6(3.3), 10^4 (c_1/c_0)/K^-1 = 2.03",
"variable": "T: temperature in K; A_R: molar refractivity at 546.226 nm (vacuum), cm^3/mol",
"range": "299-366 K (Table 1's five CH4 isotherms)",
"coefficients": {
"c0": "6.23",
"c0_sigma": "0.11",
"c1": "12.6e-4",
"c1_sigma": "3.3e-4"
},
"check": "A least-squares line through Table 1's five CH4 values gives c_0 = 6.2270, c_1 = 12.64e-4, r = 0.91, s = 0.0188: Table 3 to its printed digits. Checked 2026-09-26."
}
c_1/c_0 = 2.0e-4 per K (20 % per 1000 K), about 17 times the rise of hohm_1990’s CH4 alpha(T) (1.2 % per 1000 K) and of kerl_1992’s Eq. (10): not borne out by the group’s later work. The first CH4 point (299.44 K, the new cell) is 0.67 % below the second (301.47 K, the old cell); without it the slope is still about 9e-4 cm^3/mol per K.
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.