st_arnaud_1976 ============== J\. M\. St\-Arnaud and T\. K\. Bose, "Direct determination of the second refractivity virial coefficient of CH4", J\. Chem\. Phys\. 65, 4854 \(1976\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1063/1\.432959 `__ **Source kind:** measurement **Recorded technique:** Direct \(differential\) determination of the second refractivity virial coefficient after Buckingham et al\.\: two nearly equal stainless\-steel optical cells \(path lengths 6\.3238 and 6\.3030 cm, 1\.75 cm quartz windows\) joined by a valve; the gas in one cell is expanded into the other \(density nearly halved\) and the change of the summed optical path is measured with a Hewlett\-Packard 5525A heterodyne He\-Ne laser interferometer \(6328 A\), Eq\. \(8\); seven expansions from 120\-180 atm\. A\_R and B\_P from the absolute refractive index against pressure below 12 atm \(Eq\. 9; quartz Bourdon gauge calibrated against a pressure standard\)\. Bath at 29\.72 C \(\+\-0\.01 C\)\. Matheson methane, 99\.97 % minimum \(pp\. 4854\-4855\)\. **Materials in structured entries:** CH4 **Dataset quantities:** molar\_refractivity, refractivity\_virial\_coefficient **Contents:** 7 datasets; 0 formulas. Curation notes -------------- Identity\: VALIDATED\_WITH\_WARNINGS in the library \(a caption warning only\); first page checked \(pdf page 2\: J\. Chem\. Phys\. 65, 4854 \(1976\), received 23 June 1976; pdf page 1 is the publisher's cover\)\. Page numbers are journal pages \(pdf page \+ 4852\)\. DEFINITIONS \(Eqs\. 1\-5, p\. 4854\)\: R\_m = \(n^2 \- 1\)/\(n^2 \+ 2\)/d = A\_R \+ B\_R d \+ C\_R d^2, d the molar density; \(n \- 1\)/d = A\_n \+ B\_n d \+ \.\.\.; A\_R = 2 A\_n/3, B\_R = 2 B\_n/3 \- A\_n^2/9\. A\_R is the package's molar\_refractivity and B\_R its refractivity\_virial\_coefficient\. TEMPERATURE\: 'measurements were made for methane at 29\.72 C' \(p\. 4855\), i\.e\. 302\.87 K; the table prints 302 K; the theory at 302\.7 K \(p\. 4856\)\. The B\_R dataset takes 302\.87 K\. ACCURACY\: 'Our estimated error for A\_R and B\_R is one standard deviation for a least squares fit' \(p\. 4856\); no C\_R was detected up to 180 atm; the window\-distortion correction to B\_R, \-0\.08 cm^6/mol^2, was applied; path\-length and volume changes with pressure were neglected\. A\_R IS LOW\: 6\.533 \+\- 0\.002 cm^3/mol at 6328 A is 0\.62 % below the curated CH4 dispersion at 632\.99 nm \(fit/CH4 default model, 6\.574 cm^3/mol, computed 2026\-09\-25\), 1\.0 % below Buckingham and Graham's 6\.600 at the same wavelength, and the authors note it 'agrees well with the value of A\_eps obtained from the dielectric measurements' \(p\. 4855\), a static value that should lie about 2 % lower\. Olson's 6\.614 at 5462 A is 0\.07 % below the curated value there \(6\.618\)\. The A\_R dataset is therefore excluded; B\_R, measured differentially and independent of the absolute pressure scale, is kept\. Not extracted\: B\_P = \-42\.0 \+\- 0\.4 cm^3/mol \(this work\) and \-44\.0 \+\- 3\.0 \(Olson\), density virial coefficients \(no quantity\); the Lennard\-Jones parameters of the theory row \(epsilon/k = 148\.6 K, sigma = 3\.758 A, from viscosity; footnote a\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- st\_arnaud\_1976/B\_R\_this\_work ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "B_R_this_work", "material": "CH4", "file": "CH4/st_arnaud_1976__B_R_this_work_CH4.csv", "table": "tbl_e86bfa5ea90a", "quantity": "refractivity_virial_coefficient", "unit": "cm6/mol2", "abscissa_unit": "angstrom", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "1 sigma" }, "parameters": { "temperature_k": 302.87 } } Table 1 'Our work'\: B\_R = 6\.60 \+\- 0\.38 cm^6/mol^2 at 6328 A \(He\-Ne, air wavelength\) and 29\.72 C, the mean of seven direct \(expansion\) measurements from 120\-180 atm; one standard deviation\. The paper's rounded 302 K in the table\. st\_arnaud\_1976/A\_R\_this\_work ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "A_R_this_work", "material": "CH4", "file": "CH4/st_arnaud_1976__A_R_this_work_CH4.csv", "table": "tbl_e86bfa5ea90a", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "angstrom", "wavelength_medium": "standard_air", "use": "excluded", "uncertainty": { "column": true, "level": "1 sigma" } } Table 1 'Our work'\: A\_R = 6\.533 \+\- 0\.002 cm^3/mol at 6328 A, 302 K, from the absolute refractive index below 12 atm \(Eq\. 9\)\. EXCLUDED\: 0\.62 % below the curated CH4 dispersion at 632\.99 nm and 1\.0 % below Buckingham and Graham at the same wavelength, far beyond the stated one\-sigma 0\.002 \(source notes\)\. st\_arnaud\_1976/A\_R\_buckingham\_graham\_1974 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "A_R_buckingham_graham_1974", "material": "CH4", "file": "CH4/st_arnaud_1976__A_R_buckingham_graham_1974_CH4.csv", "table": "tbl_e86bfa5ea90a", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "angstrom", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "buckingham_1974" ], "uncertainty": { "column": true, "level": "not stated" } } Table 1 'Buckingham and Graham', 299 K, 6328 A\: A\_R = 6\.600 \+\- 0\.002 cm^3/mol \(level not stated\)\. st\_arnaud\_1976/B\_R\_buckingham\_graham\_1974 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "B_R_buckingham_graham_1974", "material": "CH4", "file": "CH4/st_arnaud_1976__B_R_buckingham_graham_1974_CH4.csv", "table": "tbl_e86bfa5ea90a", "quantity": "refractivity_virial_coefficient", "unit": "cm6/mol2", "abscissa_unit": "angstrom", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "buckingham_1974" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "temperature_k": 299.0 } } Table 1 'Buckingham and Graham', 299 K, 6328 A\: B\_R = 7\.15 \+\- 0\.35 cm^6/mol^2, 'slightly higher than ours' \(p\. 4855\)\. st\_arnaud\_1976/A\_R\_olson\_1975 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "A_R_olson_1975", "material": "CH4", "file": "CH4/st_arnaud_1976__A_R_olson_1975_CH4.csv", "table": "tbl_e86bfa5ea90a", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "angstrom", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "J. D. Olson, J. Chem. Phys. 63, 474 (1975)" ], "uncertainty": { "column": true, "level": "not stated" } } Table 1 'Olson', 300 K, 5462 A\: A\_R = 6\.614 \+\- 0\.002 cm^3/mol \(Ref\. 9\)\. The original is not in the library\. st\_arnaud\_1976/B\_R\_olson\_1975 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "B_R_olson_1975", "material": "CH4", "file": "CH4/st_arnaud_1976__B_R_olson_1975_CH4.csv", "table": "tbl_e86bfa5ea90a", "quantity": "refractivity_virial_coefficient", "unit": "cm6/mol2", "abscissa_unit": "angstrom", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "J. D. Olson, J. Chem. Phys. 63, 474 (1975)" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "temperature_k": 300.0 } } Table 1 'Olson', 300 K, 5462 A\: B\_R = 5\.5 \+\- 1\.0 cm^6/mol^2, from refractive index against density \(not a direct measurement\)\. The original is not in the library\. st\_arnaud\_1976/B\_R\_kirkwood\_theory ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "B_R_kirkwood_theory", "material": "CH4", "file": "CH4/st_arnaud_1976__B_R_kirkwood_theory_CH4.csv", "table": "tbl_e86bfa5ea90a", "quantity": "refractivity_virial_coefficient", "unit": "cm6/mol2", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "use": "check", "parameters": { "temperature_k": 302.7 } } Table 1 'Kirkwood \(theory\)', 302 K\: B\_R = 6\.11 cm^6/mol^2 \(text\: 6\.1 at 302\.7 K, p\. 4856\), the classical dipole\-induced\-dipole term B\_DID = \(2/3\)\(4 pi N\_0 alpha\)^2 alpha \ with a Lennard\-Jones potential from viscosity \(footnote a\: epsilon/k = 148\.6 K, sigma = 3\.758 A\)\. No wavelength is printed \(filed at 'inf'; the alpha used is not stated\)\. The authors' calculation, a check\. 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 :doc:`review register ` for the checks and decisions.