absolute deviations (AADs, see definitions in Table 1) of

the vapor pressure data are listed in Table 1.

As can be seen from Table 1, our EOS gives a good

correlation of vapor pressure and activity with an average

AAD of 1.120% and 0.106%. Mean while, it is o bviou s to

see that the predicted activities are in good agreement

with the experimental d ata over from low molality ran g es

to high molality ranges. And the agreement with experi-

mental data is very good when the maximum molality up

to 4.58 mol/kg methanol. So it reveals that our EOS is

very successful in activity calculation over molality

range about 0 - 5 mol/kg methanol in general although

the AADs about vapor pressure are little higher than the

nes obtaine d by Z uo . o

Table 1. Regressed parameters for EOS in this work and the average absolute deviations (AADs) in the vapor pressure (P)

and activity (a), from this work and other models at 1 bar and 298.15 K.

EOS parameters1 AAD%2

This work

Salt σi (Å) εassoc/k (K) Zuo, P3 Mock et al., P4 Chou, P5 P a

Molarity range

(mol/kg)

LiCl 5.326 3215.46 2.33 2.90 0.42 1.825 0.387 0 - 4.580

LiBr 5.316 3137.97 1.99 3.17 0.59 1.800 0.282 0 - 4.345

NaCl 6.126 2106.30 0.17 0.19 0.01 0.942 0.023 0.041 - 0.219

NaBr 5.651 3623.06 0.36 0.22 0.08 0.839 0.053 0.042 - 0.649

NaI 5.111 2717.21 0.84 0.84 0.26 0.907 0.063 0.024 - 0.755

KBr 6.992 4471.59 0.19 0.12 0.00 0.961 0.016 0.044 - 0.134

KI 6.008 5129.05 0.24 0.25 0.06 0.889 0.066 0.022 - 0.735

RbI 6.473 5241.23 0.20 0.24 0.01 0.945 0.045 0.02 - 0.436

CsI 7.421 5787.42 0.21 0.16 0.00 0.975 0.020 0.033 - 0.130

Average 0.99 1.63 0.26 1.120 0.106

1There are two p arameters for each salt . One is the ef fectiv e average io n diamet er, σi, and the other is the cation-methanol associating parameter, εassoc. The two

parameters are all salt dependent. 2cal exp

exp

1

100

%NP

i

f

f

AAD NP f

, where NP is the number of the experimental points and f is the property of interest (P and a).

The supers cripts cal and ex p indicate th e value is fr om the calcul ation and exp eriment, respecti vely. 3The AADs% were reported for the electrolyte EOS pro-

posed by Julia n Youxiang Zuo, Dan Zhang and Walter Furst [8] . 4The AADs% were reported for the electrolyte NRTL model proposed by Mock et al. [9]. 5The

AADs% were reported for the two-parameter ACM proposed by Tzu-Jen Chou and Akihiko Tanioka [10].

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506

02

10000

15000

20000

25000

30000

35000

40000

45000

4

298.15K

318.15K

308.15K

vapor pressure (pa)

molality (mol/kg methano l)

(a) 024

10000

15000

20000

25000

30000

35000

40000

45000

298.15K

318.15K

308.15K

vapor pressure (pa)

molality (mol/kg methanol)

(b)

Figure 1. Predicted vapor pressure of (a) LiCl and (b) LiBr nonaqueous electrolyte solutions as a function of salt molality.

The lines are calculated from equation of state with the parameters in Table 1, which were obtained by fitting the experi-

mental data at 298.15 K. The points represent the experimental data. For average absolute deviations (ADDs), see Table 2.

Table 2. The average absolute deviations (AADs) about the vapor pressure (P) for same regressed parameters of EOS in dif-

ferent temperature, from this work at 1 bar.

EOS parameters1

Salt σi (Å) εassoc/k (K) Molarity range (mol/kg) AAD%2 for P T (K)

1.825 298.15

2.802 308.15 LiCl 5.326 3215.46 0 - 4.580

4.045 318.15

1.800 298.15

2.733 308.15 LiBr 5.316 3137.97 0 - 4.345

3.630 318.15

1There are two parameter s for each salt . One is th e effecti ve averag e ion d iameter σi, and the other is the cation-methanol associating parameter: εassoc. The two

parameters are all salt dependent. 2cal exp

exp

1

100 NP

i

f

%f

NP f

AAD , where NP is the number of the experimental points and f is the property of interest (P). The

superscript cal and exp indicate the value is from the calculation and experiment, respectively.

The predictive capability of EOS in this work can be

demonstrated by extrapolating the temperature to a little

higher value. For example, Figures 1(a) and (b) show the

predictive vapor pressures by using the parameters given

in Table 1, which are correlated from experimental vapor

pressures with a temperature of 298.15 K. Strikingly,

even up to 308.15 K, our EOS can still accurately repre-

sent the non-ideality of the nonaqueous electrolyte solu-

tions and the AADs are shown in Table 2.

4. Conclusion

A fundamental two-parameter equation of state for non-

aqueous electrolyte solutions is proposed by incorpora-

tion of low density expansion of nonprimitive mean

spherical approximation and statistical associating fluid

theory. The EOS has been tested for 9 nonaqueous alkali

halide solutions at ambient condition . The parameters are

obtained by fitting the vapor pressures and activities with

the average absolute deviation (AAD, see definition in

Table 1) of 1.120% and 0.106%. With the parameters

given by 298.15 K, the EOS can also well predict the

vapor pressure data of nonaqueous electrolyte solutions

at different temperature points and over the same mo-

lality range accurately.

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