Equations of state Berthelot

The Berthelot equation of state as applied to many gases reads... 

Does the van der Waals or Berthelot equation of state satisfy the requirements of the Third Law Discuss the implications of your answer. 

Enthalpy of Formation Pohland (2) has studied the vaporization of SiBr from 260-426 K (0.8-755.5 mm Hg). This vapor pressure data (20 points) is corrected for vapor non-ideality by means of the equation AG /T -R In p - Bp/T. The Berthelot equation of state and critical constants T - 656 K and P 41.3 atm as suggested in the review article by Lapldus et al. (2) are used to calculate B. The recent study on orthobaric densities by Nisei son et al. ( ) reported T = 663 K. The use of this latter value does not signficantly affect the results. 

Because of the approximate nature of the Berthelot equation of state, it is probable that equation (20.22) is not very reliable when the pressure difference P2 — Pi is large. In connection with the study of high-pressure gas reactions, however, it is sometimes required to know the difference between the heat content of a gas at high pressure and at zero pressure. If P-V-T data are available, equation (20.21) may be used directly, but if they are lacking, or if approximate results are adequate, a generalized treatment, involving the use of reduced quantities and the compressibility factor ( 5i), is simple and convenient. 

Without going into details, it may be noted that a similar treatment based on the Berthelot equation of state gives the result... 

From the Berthelot equation of state in conjunction with (21.12) it is found that... 

FIGURE 15.6 Comparison of measured homogeneous nucleation temperature with the spinodal temperature calculated from the van der Waals and Berthelot equations of state (from Carey [4], with permission from Taylor Francis, Washington, DC, all rights reserved). 

In equation 6, Pq is the critical pressure of the solvent and pr is the reduced density (ratio of the density to the density at the critical point). Thus, for a van der Waals gas, the solubility parameter is a function only of density. An equivalent development using the Berthelot equation of state leads to a pi/T dependence of 6, but in practice T is fairly constant over the temperature range of typically used for organic synthesis. (72)... 

BpcjRTo (and hence of B itself) for all the compounds, though the slopes of the curves are generally too small. The dashed curve in Figure 9 is that given by the Berthelot equation of state... 

Repeat the previous exercise for a gas that follows the Berthelot equation of state (see exercise 1.55). 

As the first illustration, let us adopt the Berthelot equation of state for a one-component gas in the approximate form... 

By way of illustration, we first consider relations based on the Berthelot equation of state (1907) for a gas consisting of n moles ... 

Consider the Berthelot equation of state given below. Show how to calculate the constants a and b using only critical point data. 

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