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 `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1002/bbpc\.19840881013 `__ **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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 :doc:`review register ` for the checks and decisions.