Boiling point method, theory

For the explanation of parameters A, C, and y, look into the theory of the boiling point method. The above equations consider diffusion and flow of vapor only through the exit capillary of the apparatus. The equations become very complex when the diffusion upstream through the entrance capillary is taken into account. Their application is not practical, as they contain too many unknown parameters. 

The aforementioned macroscopic physical constants of solvents have usually been determined experimentally. However, various attempts have been made to calculate bulk properties of Hquids from pure theory. By means of quantum chemical methods, it is possible to calculate some thermodynamic properties e.g. molar heat capacities and viscosities) of simple molecular Hquids without specific solvent/solvent interactions [207]. A quantitative structure-property relationship treatment of normal boiling points, using the so-called CODESS A technique i.e. comprehensive descriptors for structural and statistical analysis), leads to a four-parameter equation with physically significant molecular descriptors, allowing rather accurate predictions of the normal boiling points of structurally diverse organic liquids [208]. Based solely on the molecular structure of solvent molecules, a non-empirical solvent polarity index, called the first-order valence molecular connectivity index, has been proposed [137]. These purely calculated solvent polarity parameters correlate fairly well with some corresponding physical properties of the solvents [137]. 

Evaporating / -propanol from an n-heptane liquid is feasible, but the boiling points are very close. When we explore the design of evaporators and condensers in Chapter 4 we will learn the implications of the boiling points are very close. In theory any difference in boiling points can be exploited for a gas/liquid separation. But in practice the process may be too expensive. It is prudent to consider other methods. 

Distillation is a separation method that utilizes the different boiling points of the various components in a mixture to effect separation. Although distillation has been employed for centuries as a separation technique, the theory of the process for any but the simplest mixtures is extremely complex. However, here we are less interested in the theoretical aspects of distillation than in the factors that influence the technique as a tool for separation. 

Our method for the calculation of p(P,W) is a statistical mechanical approach known as mean-field theory (refs. 1 and 5). In this approach, the properties of the nitrogen within the graphite pore are obtained directly from the forces between the constituent molecules. The parameters of the intermolecular forces are determined by (a) ensuring that the saturation pressure and saturated liquid density of the model fluid are equal to the experimental values for nitrogen at its normal boiling point (77 K, which is the temperature at which the adsorption experiments are carried out) and (b) matching the model adsoq)tion on an isolated surface to the experimental t-curve of de Boer et al. (ref. 10). Having fixed the values for these parameters, the theory is then used to calculate model isotherms for pores of a variety of widths, which are then correlated (ref. 1) as a function of pressure and pore width to yield the individual pore isotherm p(P,W). Mean-field theory is known to become less accurate as the pore size is made very small (ref. 11) even for very small pores, however, this approach is more realistic than methods based on the Kelvin equation. 

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