point to just below the critical point for COz.I t is clear that the van der Waals equation is worse than either of the other equations. The corresponding ratio for HzO is shown in Figure 5, the inadequacy of the van der Wads equatiou is even more pronounced in this case. In a study of several equations of state, Shah and Thodos (35)found the van der Waals equatiou unsuitable in the liquid region. I t should not therefore be expected to predict-accur&ely the vapor pressure and coexistence curve. Figure 6 compares the vapor pressure and molar volumes generated by the spreadsheet with the experimental coeistence curve for water (36). The ~redictedvaDor volumes from both the van der Waals equation and tha't of Peng and Robinson agree well with experiment (the volumes predicted by the PengRobinson equation being indistinguishable from the experimental values on this scale). However the liquid volume predicted by the van der Waals equation is much too large while that predicted by the Peng and Robinson equation is reasonable. For both COz and Hz0 the Peng-Robinson equation is the best of the four equations of state for predicting the vapor pressure, followed by that of Berthelot. Table 1 relates the parameters a and b to the critical temperature and pressure for each of the four models. The parameter p relates b to the molar volume a t the critical ooint via the eouation b = OV.. The oarameter can be obtained by solviLg the cubic iqiation line 3 producing the numerical value in line 4.The quantities V,, T,, and PCcan be written in terms of a, b, R, and p. These expressions are sim~lifiedwhen the a ~ ~ r.o ~ r ivalue a t e of I3 is substituted (lines 5 to 7). The critical compressibility factor is given by
ih
L
A
Z , = P,VJRT,
This depends only on the value of p. It is a useful measure of how well a n equation describes nonideal behavior. For the vast majority of compounds it lies in the range (37) 0.23
