Correlation pubs.acs.org/IECR
Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX-XXX
Correlation for the Prediction of Critical Molar Volume Alfons Mersmann† and Matthias Kind*,‡ †
Technical University Munich, Boltzmannstrasse 15, D-85748 Garching, Germany Karlsruhe Institute of Technology, Kaiserstrasse 11, D-76131 Karlsruhe, Germany
‡
ABSTRACT: A general correlation for the prediction of critical molar volume of pure substances is proposed. The equation given is based on physical considerations and is easy to evaluate. Except for inorganic compounds, phenoles, aldehydes and nitriles it demonstrates good predictive capability with relative standard deviation smaller than 10 %.
I
n a recent publication1 we gave a correlation for the prediction of the critical molar volume ṽc. This correlation
Table 1. Covalent Atomic Radii after Ref 3 atom i
atomic radius ri/pm
H C O N S Si F Cl Br J
37 77 60 71 104 117 71 99 114 133
requires the use of a tabulated empirical factor A which strayed by about 20% for the various inorganic and organic substance classes under consideration. Further work on this problem leads us to propose here the more general correlation
( ) vc̃ NA
da̅
Figure 1. Parity-diagram for the critical molar volume.
1/3
=
3.645
da̅ ≡ 2
1/2
() ra̅ rH
(1)
na
(2)
with na being the number of atoms of the molecule, and ri being the atomic radii of the ni atoms i in the molecule. The atomic
with the critical volume of a molecule of a substance ṽc /NA and the atomic radius rH = 37 pm of hydrogen as the smallest atom in the periodic system. In this eq 1 the only molecular property of the respective substance is the hypothetical mean diameter d̅a of the atoms of this substance and its mean atomic radius ra̅ = d̅a/2. Both characterizing properties are to be obtained from © XXXX American Chemical Society
∑i (ni ·ri)
Received: Revised: Accepted: Published: A
July 31, 2017 October 13, 2017 October 16, 2017 October 16, 2017 DOI: 10.1021/acs.iecr.7b03171 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Correlation
Industrial & Engineering Chemistry Research
Table 2. Classwise Mean and Standard Deviation of the Relative Error of the Critical Molar Volume vc̃ Predicted by Eq 1 Compared to the Value Given in Ref 2 class of compounds
number of compounds in class
mean of the relative error
standard deviation of the relative error
inorganic compounds organic comp. with sulfur halogenated hydrocarbons n-alkanes iso-alkanes olefins acetylene and derivatives naphthalenes aromatic compounds alcohols phenols carboxylic acids ketones ethers aldehydes esters amines nitriles nitroderivates
27 5 45 20 7 14 4 18 29 16 4 11 7 8 6 14 16 5 5
−13.9% −5.9% −6.9% −3.7% −0.1% −7.3% −9.9% 6.3% 4.2% 1.4% 24.1% −7.2% −6.1% 0.1% −2.4% −2.8% −3.5% −13.7% −9.1%
25.3% 6.4% 8.3% 3.9% 1.5% 3.8% 6.4% 2.1% 2.5% 5.1% 6.4% 4.1% 6.9% 6.2% 14.0% 3.0% 8.9% 10.0% 4.1%
radii ri are tabulated in Table 1. The fitting parameter, 3.645, was obtained by minimizing the sum of the squares of the absolute error in ṽc between prediction by eq 1 and literature data given in VDI-Heat Atlas, ref2. The physical idea behind the development of eq 1 is that the critical molar volume of a molecule of a substance could be normalized by its hypothetical mean diameter d̅a of its atoms. This normalized critical volume is found to be rather close to unity, but not to be constant. Its value is found to decrease gradually with increasing mean atomic radius by (ra̅ /rH)−1/2. The rather good predictive capability of eq 1 is demonstrated by the parity diagram given in Figure 1. There, for each substance given in ref 2 the critical molar volume calculated by eq 1 is compared to the data given in VDI-Heat Atlas, ref 2. In Table 2 is tabulated for each investigated class of compounds the mean and the standard deviation of the relative error of the critical molar volume ṽc predicted by eq 1 compared to the value given in ref 2. For most classes of compounds the mean relative error is far below 10%. This is not the case for the classes “Inorganic compounds”, “Phenols”, "Aldehydes" and “Nitriles”.
■
(3) CRC Handbook of Chemistry and Physics; CRC Press Taylor & Francis Group: Boca Raton, FL, 2007.
■
NOTE ADDED AFTER ASAP PUBLICATION After this paper was published ASAP on November 3, 2017, a correction was made to eq 1. The corrected version was reposted November 3, 2017.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Matthias Kind: 0000-0002-7203-1776 Notes
The authors declare no competing financial interest.
■
REFERENCES
(1) Mersmann, A.; Kind, M. Prediction of Mechanical and Thermal Properties of Pure Liquids, of Critical Data, and of Vapor Pressure. Ind. Eng. Chem. Res. 2017, 56 (6), 1633−1645. (2) Kleiber, M.; Joh, R. D3: Properties of Pure Fluid Substances: D3.1: Liquids and Gases. In VDI Heat Atlas, 2. ed.; VDI-GVC, Ed.; VDI-Buch; Springer-Verlag Berlin Heidelberg: Berlin, 2010; pp 301− 393. B
DOI: 10.1021/acs.iecr.7b03171 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
