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| {{expert-subject|Mathematics|date=November 2009}}
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| [[Image:Gruppenbeitragsmethodenprinzip.png|thumb|Principle of a Group Contribution Method]]
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| In thermodynamic theory, the '''Klincewicz method'''<ref>Klincewicz K. M., Reid R. C., "Estimation of Critical Properties with Group Contribution Methods", ''AIChE Journal'', 30(1), 137-142, 1984</ref> is a predictive method based both on group contributions and on a [[correlation]] with some basic molecular properties. The method estimates the [[critical temperature]], the critical pressure, and the critical volume of pure components.
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| ==Model description==
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| As a [[group contribution method]] the Klincewicz method correlates some structural information of a chemical [[molecule]] with the critical data. The used structural information are small [[functional group]]s which are assumed to have no interactions. This assumption makes it possible to calculate the thermodynamic properties directly from the sums of the group contributions. The correlation method does not even use these functional groups, only the molecular weight and the number of atoms are used as molecular [[descriptor]]s.
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| The prediction of the critical temperature relies on the knowledge of the normal boiling point because the method only predicts the relation of the normal boiling point and the critical temperature and not directly the critical temperature. The critical volume and pressure however are directly predicted.
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| ===Model Quality===
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| The quality of the Klincewicz method is not superior to older methods, especially the method of Ambrose<ref>Ambrose D., "Correlation and Estimation of Vapour-Liquid Critical Properties. I. Critical Temperatures of Organic Compounds", ''Nat. Phys. Lab. Rep. Chem.'', Rep. No. NPL Rep. Chem. 92, 1-35, 1978</ref> gives somewhat better results as stated by the original authors and by Reid et al.<ref name="PGL">Reid R.C., Prausnitz J.M., Poling B.E., "The Properties of Gases & Liquids", Monograph, McGraw-Hill, 4 Ed., 1-742, 1987</ref> The advantage of the Klincewicz method is that it is less complex.
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| The quality and complexity of the Klincewicz method is comparable to the Lydersen method<ref>Lydersen A.L., "Estimation of Critical Properties of Organic Compounds", University of Wisconsin College Engineering, Eng. Exp. Stn. Rep. 3, Madison, Wisconsin, 1955</ref> from 1955 which has been used widely in chemical engineering.
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| The aspect where the Klincewicz method is unique and useful<ref name="PGL"/> are the alternative equations where only very basic molecular data like the molecular weight and the atom count are used. | |
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| ===Deviation diagrams===
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| The diagrams show estimated critical data of [[hydrocarbon]]s together with experimental data.<ref>[[Dortmund Data Bank]]</ref> An estimation would be perfect if all data points would lie directly on the diagonal line. Only the simple correlation of the Klincewicz method with the moelcular weight and the atom count have been used in this example.
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| <gallery>
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| Image:TCKlincewicz.png | Critical temperatures
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| Image:PCKlincewicz.png | Critical pressures
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| Image:VCKlincewicz.png | Critical volumes
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| </gallery>
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| ==Equations==
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| Klincewicz published two sets of equations.<ref>Klincewicz, K. M., “Prediction of Critical Temperatures, Pressures, and Volumes of Organic Compounds from Molecular Structure,” S.M.Thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1982</ref> The first uses contributions of 35 different groups. These group contribution based equations are giving somewhat better results than the very simple equations based only on correlations with the [[molecular weight]] and the atom count.
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| ===Group-contribution-based equations===
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| <math>T_c \, = \, 45.40 - 0.77 * MW + 1.55 * T_b+\sum_{j=1}^{35} n_j \Delta_j</math>
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| <math>(MW/P_c)^{1/2} \, = \, 0.348 + 0.0159 * MW + \sum_{j=1}^{35} n_j \Delta_j</math>
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| <math>V_c \, = \, 25.2 + 2.80 * MW + \sum_{j=1}^{35} n_j \Delta_j</math>
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| === Equations based on correlation with molecular weight and atom count only ===
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| <br>
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| <math>T_c \, = \, 50.2 - 0.16 * MW + 1.41 * T_b</math>
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| <math>(MW/P_c)^{1/2} \, = \, 0.335 + 0.009 * MW + 0.019A</math>
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| <math>V_c \, = \, 20.1 + 0.88 * MW + 13.4 * A</math>
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| with
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| {| border="0"
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| | '''MW:'''
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| | Molecular weight in <sup>g</sup>/<sub>mol</sub>
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| |-
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| | '''T<sub>b:'''</sub>
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| | Normal boiling point in K
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| |-
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| | '''A:'''
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| | Number of atoms
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| |}
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| ==Group contributions==
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| {| class="wikitable"
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| !
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| ! colspan="3" | <center>Δ<sub>j </sub>Values for</center>
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| |-
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| |bgcolor="#fff0f0" width="25%" | <center>T<sub>c</sub></center>
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| |bgcolor="#fff0f0" width="25%" | <center>P<sub>c</sub></center>
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| |bgcolor="#fff0f0" width="25%" | <center>V<sub>c</sub></center>
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| |-
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| | -CH<sub>3</sub>
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| | <div align="right">-2.433 </div>
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| | <div align="right">0.026 </div>
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| | <div align="right">16.2 </div>
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| |-
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| | -CH<sub>2</sub>-
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| | <div align="right">0.353 </div>
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| | <div align="right">-0.015 </div>
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| | <div align="right">16.1 </div>
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| |-
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| | -CH<sub>2</sub>- (Ring)
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| | <div align="right">4.253 </div>
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| | <div align="right">-0.046 </div>
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| | <div align="right">8.2 </div>
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| |-
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| | >CH-
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| | <div align="right">6.266 </div>
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| | <div align="right">-0.083 </div>
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| | <div align="right">12.1 </div>
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| |-
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| | >CH- (Ring)
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| | <div align="right">-0.335 </div>
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| | <div align="right">-0.027 </div>
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| | <div align="right">7.4 </div>
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| |-
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| | <nowiki>>C<</nowiki>
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| | <div align="right">16.416 </div>
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| | <div align="right">-0.136 </div>
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| | <div align="right">8.95 </div>
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| |-
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| | <nowiki>>C< (Ring)</nowiki>
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| | <div align="right">12.435 </div>
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| | <div align="right">-0.111 </div>
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| | <div align="right">-6.6 </div>
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| |-
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| | <nowiki>=CH</nowiki><sub>2</sub>
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| | <div align="right">-0.991 </div>
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| | <div align="right">-0.015 </div>
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| | <div align="right">13.9 </div>
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| |-
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| | <nowiki>=CH-</nowiki>
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| | <div align="right">3.786 </div>
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| | <div align="right">-0.050 </div>
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| | <div align="right">9.8 </div>
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| |-
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| | <nowiki>=CH- (Ring)</nowiki>
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| | <div align="right">3.373 </div>
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| | <div align="right">-0.066 </div>
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| | <div align="right">5.1 </div>
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| |-
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| | >C=;=C=
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| | <div align="right">7.169 </div>
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| | <div align="right">-0.067 </div>
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| | <div align="right">2.7 </div>
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| |-
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| | >C= (Ring)
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| | <div align="right">5.623 </div>
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| | <div align="right">-0.089 </div>
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| | <div align="right">0.2 </div>
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| |-
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| | <nowiki>≡CH</nowiki>
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| | <div align="right">-4.561 </div>
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| | <div align="right">-0.056 </div>
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| | <div align="right">7.5 </div>
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| |-
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| | <nowiki>≡C-</nowiki>
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| | <div align="right">7.341 </div>
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| | <div align="right">-0.112 </div>
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| | <div align="right">3.0 </div>
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| |-
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| | -OH
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| | <div align="right">-28.930 </div>
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| | <div align="right">-0.190 </div>
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| | <div align="right">-24.0 </div>
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| |-
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| | -O-
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| | <div align="right">5.389 </div>
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| | <div align="right">-0.143 </div>
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| | <div align="right">-26.1 </div>
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| |-
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| | -O- (Ring)
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| | <div align="right">7.127 </div>
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| | <div align="right">-0.116 </div>
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| | <div align="right">-36.6 </div>
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| |-
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| | >CO;-CHO
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| | <div align="right">4.332 </div>
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| | <div align="right">-0.196 </div>
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| | <div align="right">-6.7 </div>
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| |-
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| | -COOH
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| | <div align="right">-25.085 </div>
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| | <div align="right">-0.251 </div>
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| | <div align="right">-37.0 </div>
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| |-
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| | -CO-O-
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| | <div align="right">8.890 </div>
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| | <div align="right">-0.277 </div>
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| | <div align="right">-28.2 </div>
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| |-
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| | -NH<sub>2</sub>
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| | <div align="right">-4.153 </div>
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| | <div align="right">-0.127 </div>
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| | <div align="right">-0.1 </div>
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| |-
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| | >NH
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| | <div align="right">2.005 </div>
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| | <div align="right">-0.180 </div>
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| | <div align="right">53.7 </div>
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| |-
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| | >NH (Ring)
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| | <div align="right">2.773 </div>
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| | <div align="right">-0.172 </div>
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| | <div align="right">-8.0 </div>
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| |-
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| | >N-
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| | <div align="right">12.253 </div>
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| | <div align="right">-0.163 </div>
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| | <div align="right">-0.7 </div>
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| |-
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| | <nowiki>=N- (Ring)</nowiki>
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| | <div align="right">8.239 </div>
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| | <div align="right">-0.104 </div>
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| | <div align="right">-18.4 </div>
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| |-
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| | -CN
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| | <div align="right">-10.381 </div>
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| | <div align="right">-0.064 </div>
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| | <div align="right">12.0 </div>
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| |-
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| | -SH
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| | <div align="right">28.529 </div>
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| | <div align="right">-0.303 </div>
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| | <div align="right">-27.7 </div>
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| |-
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| | -S-
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| | <div align="right">23.905 </div>
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| | <div align="right">-0.311 </div>
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| | <div align="right">-27.3 </div>
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| |-
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| | -S- (Ring)
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| | <div align="right">31.537 </div>
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| | <div align="right">-0.208 </div>
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| | <div align="right">-61.9 </div>
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| |-
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| | -F
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| | <div align="right">5.191 </div>
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| | <div align="right">-0.067 </div>
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| | <div align="right">-34.1 </div>
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| |-
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| | -Cl
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| | <div align="right">18.353 </div>
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| | <div align="right">-0.244 </div>
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| | <div align="right">-47.4 </div>
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| |-
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| | -Br
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| | <div align="right">53.456 </div>
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| | <div align="right">-0.692 </div>
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| | <div align="right">-148.1 </div>
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| |-
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| | -I
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| | <div align="right">94.186 </div>
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| | <div align="right">-1.051 </div>
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| | <div align="right">-270.6 </div>
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| |-
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| | -XCX (X = halogen)
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| | <div align="right">-1.770 </div>
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| | <div align="right">0.032 </div>
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| | <div align="right">0.8 </div>
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| |-
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| | -NO<sub>2</sub>
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| | <div align="right">11.709 </div>
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| | <div align="right">-0.325 </div>
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| | <div align="right">-39.2 </div>
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| |}
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| The group XCX is used to take the pairwise interaction of halogens connected to a single carbon into account. Its contribution has to be added once for two halogens but three times for three halogens (interactions between the halogens 1 and 2, 1 and 3, and 2 and 3).
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| ==Example calculations==
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| ===Example calculation for acetone with group contributions===
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| {| class="wikitable"
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| !
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| ! colspan="2" | <center>-CH<sub>3</sub> </center>
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| ! colspan="2" | <center>>C=O (nonring)</center>
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| !
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| !
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| !
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| |- bgcolor="#fff0f0"
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| | Property
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| | No. of groups
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| | Group value
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| | No. of groups
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| | Group value
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| | <math>\sum n_j\Delta_j</math>
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| | Estimated Value
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| | Unit
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| |-
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| | T<sub>c</sub>
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| | <div align="right">2</div>
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| | <div align="right">-2.433</div>
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| | <div align="right">1</div>
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| | <div align="right">4.332</div>
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| | <div align="right">-0.534</div>
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| | <div align="right">510.4819*</div>
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| | <div align="right">K</div>
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| |-
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| | P<sub>c</sub>
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| | <div align="right">2</div>
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| | <div align="right">0.026</div>
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| | <div align="right">1</div>
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| | <div align="right">-0.196</div>
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| | <div align="right">-0.144</div>
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| | <div align="right">45.69</div>
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| | <div align="right">bar</div>
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| |-
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| | V<sub>c</sub>
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| | <div align="right">2</div>
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| | <div align="right">16.2</div>
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| | <div align="right">1</div>
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| | <div align="right">-6.7</div>
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| | <div align="right">25.7</div>
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| | <div align="right">213.524</div>
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| | <div align="right">cm<sup>3</sup>/mol</div>
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| |-
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| |}
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| <span style="font-size:87%;"> *used normal boiling point T<sub>b</sub>= 329.250 K </span>
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| ===Example calculation for acetone with molecular weight and atom count only===
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| Used molecular weight: 58.080 <sup>g</sup>/<sub>mol</sub>
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| Used atom count: 10
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| {| class="wikitable"
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| |- bgcolor="#fff0f0"
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| | Property
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| | Estimated Value
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| | Unit
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| |-
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| | T<sub>c</sub>
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| | <div align="right">505.1497</div>
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| | <div align="right">K</div>
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| |-
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| | P<sub>c</sub>
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| | <div align="right">52.9098</div>
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| | <div align="right">bar</div>
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| |-
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| | V<sub>c</sub>
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| | <div align="right">205.2</div>
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| | <div align="right">cm<sup>3</sup>/mol</div>
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| |-
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| |}
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| For comparison, experimental values for Tc, Pc and Vc are 508.1 K, 47.0 bar and 209 cm<sup>3</sup>/mol, respectively.<ref name="PGL"/> | |
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| ==References==
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| {{reflist}}
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| {{DEFAULTSORT:Klincewicz Method}}
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| [[Category:Thermodynamic models]]
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