*
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.