* The deviation is expressed in absolute value.
**The average values are non-serviceable because the data of water by the S-R-K EOS and the P-R EOS are of no practical significance.
The comparison with Hou’s modified M-H EOS:Among the selected substances, the average value of the maximum deviation calculated by Hou’s modified M-H EOS is 5.80% while it is 3.50% by the novel M-H EOS. At the same time, the average deviation from the novel EOS is much less than those from Hou’s equation, as shown in Table 3 , the average value of average deviation is 2.51% by Hou’s M-H EOS while it is 1.29% by the novel M-H EOS. Therefore, the conclusion can be drawn that the novel M-H EOS can obviously reduce the deviation and improve the calculation precision in liquid-phase state. However, the degree of improvement about the strong polar substances is smaller compared with other substances. It may be attributed to the reason that intermolecular forces between strong polar moles are stronger and more complex in liquid-phase state while the single revision factor h could not appropriately revise the variation tendency.
The comparisonwith other general EOSs :The data about molar volume calculated by the S-R-K EOS and the P-R EOS are listed in Table 3 and the supporting information 41-43. It is indicated that with the increase of eccentric factor (ω ), the deviations calculated by the S-R-K EOS increase more rapidly than those by the P-R EOS in liquid-phase state, which means the S-R-K EOS is more suitable for the condition that the eccentric factor is small. The P-R EOS is an improved formula of the S-R-K EOS, it is of a broader scope of application with the increase ofωwhile it’s precision is not satisfying when ω is too small. Moreover, the S-R-K EOS and the P-R EOS are both not suitable for strong polar substances with respect to the maximum and average deviation both in excess of 20%; At the same time, the variation intervals of deviation by the two general EOS are both too large, which means the calculation results are instable for application: the maximum deviations change from 3.31% to 14.89% by the S-R-K EOS and 3.06% to 14.86% by the P-R EOS for the selected five substances except water, the average deviations change from 2.05% to 12.03% by the S-R-K EOS and 2.04% to 12.17% by the P-R EOS. The general EOSs should always be further revised for the cases in liquid-phase state if they wanted be used in the practical applications.
The novel M-H EOS has more advantages no matter the precision or the stability of calculation: The variation range of the maximum deviations about the selected five substances except water change from 2.43% to 4.00%, and the variation range of the average deviations are within the scope of 0.81% to 1.83%.
CONCLUSION
Because of the application defect for the original and Hou’s modified M-H EOS in the liquid phase, a novel M-H EOS is put forward. A new revision factor h is introduced into the EOS to reduce the deviation of molar volume calculated in liquid-phase state. According to the new detailed derivation in the appendixes, only a few number of physical properties are needed to characterize a given substance. Last, the novel M-H EOS has been applied to six representative substances to verify its generality and calculation precision in liquid-phase state. According to the analysis of the data by the above EOSs, the average value of the maximum deviations for the selected six representative substances reduces from 5.80% by Hou’s modified M-H EOS to 3.50% by the novel M-H EOS and the average value of the average deviations reduces from 2.51% to 1.29%. At the same time, this novel M-H EOS exhibit higher calculation precision compared to some other general EOSs in the liquid phase. Therefore, the conclusion can be drawn that the precision is obviously improved in liquid-phase by applying the novel M-H EOS.
Another progress is made in the solving process ofB 4. We design a new calculation program instead of the trial and error method in Hou’ modified M-H EOS. It greatly simplify the process of calculation and improve the computational efficiency. Refer to Appendix Ⅰ for details.