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These can accurately describe the properties of dense gases, and gases with internal degrees of freedom, because they include the volume of the particles as well as contributions from intermolecular and intramolecular forces as well as quantized molecular rotations, quantum rotational-vibrational symmetry effects, and electronic excitation. [31]
The quantum gases hydrogen, helium, and neon do not conform to the corresponding-states behavior. Rao recommended that the reduced pressure and temperature for those three gases should be redefined in the following manner to improve the accuracy of predicting their compressibility factors when using the generalized graphs:
One way to write the van der Waals equation is: [8] [9] [10] = where is pressure, is temperature, and = / is molar volume. In addition is the Avogadro constant, is the volume, and is the number of molecules (the ratio / is a physical quantity with base unit mole (symbol mol) in the SI).
An important prediction of Chapman–Enskog theory is that viscosity, , is independent of density (this can be seen for each molecular model in table 1, but is actually model-independent). This counterintuitive result traces back to James Clerk Maxwell , who inferred it in 1860 on the basis of more elementary kinetic arguments. [ 11 ]
[20] [21] These forces are very important for properly modeling molecular systems, as to accurately predict the microscopic behavior of molecules in any system, and therefore, are necessary for accurately predicting the physical properties of gases (and liquids) across wide variations in physical conditions.
Principle of a group-contribution method. The Joback method is a group-contribution method.These kinds of methods use basic structural information of a chemical molecule, like a list of simple functional groups, add parameters to these functional groups, and calculate thermophysical and transport properties as a function of the sum of group parameters.
VLE prediction of cyclohexane and carbon dioxide vs. experimental measurements. As we can see, deviation between experimental data and model prediction is inevitable. A robust thermodynamic model predicts the properties (such as VLE) close to the real experimental data.
Graham's law can also be used to find the approximate molecular weight of a gas if one gas is a known species, and if there is a specific ratio between the rates of two gases (such as in the previous example). The equation can be solved for the unknown molecular weight.