Isochore equation

Strategy. For convenience, we will call the higher temperature T> and the lower temperature T. (1) The van t Hoff isochore, Equation (4.78), is written in terms of a ratio, so we do not need the absolute values. In other words, in this example, we can employ the solubilities s without further manipulation. We can dispense with the units of. v for the same reason. (2) We convert the two temperatures to kelvin, for the van t Hoff isochore requires thermodynamic temperatures, so T2 = 343.9 K and 7) = 312.0 K. (3) We insert values into the van t Hoff isochore (Equation (4.78)) ... 

The isochore, Equation (4.81), was derived from the integrated form of the Gibbs-Helmholtz equation. It is readily shown that the van t Hoff isochore can be rewritten in a slightly different form, as ... 

Let us return to the isochore equation (equation 8.2). To recapitulate we have shown that AH0 and AS0 may be regarded as constant over small ranges of temperature, and so the equation will simply show the variation of K with temperature. Let us therefore modify it, and write it simply as ... 

An isochoric equation of state, applicable to pure components, is proposed based upon values of pressure and temperature taken at the vapor-liquid coexistence curve. Its validity, especially in the critical region, depends upon correlation of the two leading terms the isochoric slope and the isochoric curvature. The proposed equation of state utilizes power law behavior for the difference between vapor and liquid isochoric slopes issuing from the same point on the coexistence cruve, and rectilinear behavior for the mean values. The curvature is a skewed sinusoidal curve as a function of density which approaches zero at zero density and twice the critical density and becomes zero slightly below the critical density. Values of properties for ethylene and water calculated from this equation of state compare favorably with data. 

This study is another rather successful attempt to correlate the fluid properties in the critical region. We have chosen an isochoric equation of state with constant curvature to represent these properties and we... 

Thermodynamically consistent, nonanalytical, empirical equations of state induced from experimental measurements can avoid the above difficulties. Since 1965, at least two laboratories actively were developing isochoric equations of state (Refs. 10,11). These workers had the benefit of the scaling work and included nonclassical behavior in the critical region for their equations. The equation presented in this chapter arose from utilizing the same basic strategy. 

The basic function of an isochoric equation of state is to describe isochores as they issue from the vapor pressure curve. Figure 1 illustrates... 

A relatively simple, isochoric equation of state can describe the critical region for fluids such as ethylene and water using five critical parameters, four critical exponents, and eight adjustable constants. Agreement between observed and calculated pressures is excellent and the current values are much better than those in standard reference tables. 

An isochoric equation has been developed for computing thermodynamic functions of pure fluids. It has its origin on a given liquid-vapor coexistence boundary, and it is structured to be consistent with the known behavior of specific heats, especially about the critical point. The number of adjustable, least-squares coefficients has been minimized to avoid irregularities in the calculated P(p,T) surface by using selected, temperature-dependent functions which are qualitatively consistent with isochores and specific heats over the entire surface. Several nonlinear parameters appear in these functions. Approximately fourteen additional constants appear in auxiliary equations, namely the vapor-pressure and orthobaric-densities equations, which provide the boundary for the P(p,T) equation-of-state surface. 

In a recent paper [3] we described how adsorption equilibrium constants for a range of paraffinic and olefinic species could be estimated using the following integrated form of van t Hoffs isochore equation,... 

It is often the solvent effect fliat is flie only method of radical change of relative contents of different conformer forms. Thus, with flie help of the isochore equation of chemical reaction, flie data on equilibrium constants and enthalpies of dichloroacetaldehyde conformer transformation allow us to calculate that, to reach the equilibrium constant of axial rotamer formation in cyclohexane as solvent (it is equal to 0.79) to magnitude K=0.075 (as it is reached in DMSO as solvent), it is necessary to cool the cyclohexane solution to 64K (-209"C). At the same time, it is not possible because cyclohexane freezing point is -l-6.5"C. By analogy, to reach flie dimefliylsulfoxide constant to value of cyclohexane , DMSO solution must be heated to 435K (162"C). 

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