Supplementary Materials
Part Ⅰ
To check the error of the experimental method (in the weighting) in the manuscript, we directly
measured the weight of three chemicals (MgCl2·6H2O(s), Mg(ClO4)2(s) and NiCl2(s)) as a
function of time (0-600s), as collected in the Table A1. The original quantity of the three
chemicals MgCl2·6H2O(s), Mg(ClO4)2(s) and NiCl2(s) was taken with ~4 g, ~3 g and ~1 g,
respectively. These quantities mainly depended on that in samples preparation of the manuscript at
that time. The preparation of per one for all samples in the manuscript can be finished within 5
minutes.
Table A1 The weight (g) of three chemicals in different time (s) (Lab environment: 25 ℃ with
less than 50% humidity).
Chemicals
NiCl2
Mg(ClO4)2
MgCl2∙6H2O
*
Time interval
s*
0
0.9074
2.9970
3.8803
30 s
0.9074
2.9970
3.8806
60 s
0.9075
2.9971
3.8807
120 s
0.9076
2.9972
3.8808
180 s
0.9076
2.9974
3.8810
240 s
0.9077
2.9975
3.8811
300 s
0.9077
2.9976
3.8812
600 s
0.9077
2.9977
3.8812
'0 s' represented that the chemicals were weighted in the glove box with humidity of < 20%.
As shown in Table A1, the water absorption for NiCl2, Mg(ClO4)2 and MgCl2∙6H2O is 0.0003,
0.0006 and 0.0009, respectively, within 5 minutes. It roughly equals to increase by 0.0018 g H2O
for per sample.
To check the water number of MgCl2·6H2O crystal, we first prepared three MgCl2 solutions
(parallel samples) with ~3.5 mol·kg–1 by the method as described in the section 2.1 of the text.
Table A2 Determination of real water number in crystal.
Sample
no.
1
2
3
Weight of
MgCl2
solution (g)
2.6909
2.6301
2.2957
Weight of
MgO solid
(g)
Conc. of
MgCl2 by
method B
0.3029
0.2965
0.2586
3.8046
3.8124
3.8083
1
Conc. of
MgCl2 by
method A
3.8158
3.8158
3.8158
Calculated water
number in the
crystal
6.0244
6.0075
6.0163
In practice, we mixed 11.5100 g MgCl2·6H2O with 8.7177 g H2O (weighted method) to obtain
20 g such MgCl2 solution (A). And then three parallel samples were prepared. Their
concentrations were measured by the thermal decomposition gravimetric method [1] (B). Finally,
the real water number of crystal was calculated, as shown in Table A2.
It can seen that real water number of the crystal is 6.0244 (largest deviation), indicating that the
MgCl2·6H2O should be rewritten as MgCl2·6.0244H2O in practice concentration calculation.
Based on the analysis above, we can roughly estimate the error of calculated concentration. The
error map was shown in Fig. A1.
Fig. A1 Absolute error vs sample number. Absolute error is the difference value between new
calculated concentration (Considering hygroscopicity above) and original concentration (No
considering hygroscopicity above)
It can be seen that the uncertainty of Ni2+ and ClO4– is less than 0.005 while that for Cl– with
larger deviation of ~0.01, leading to the calculated water activity and density of system with the
largest deviation of 0.001 and 0.006 (g/cm3), respectively. All of these deviation eventually results
into the largest deviation of 0.006 for the converted factor ( f  , Eq. 3) and generates a uncertainty
of 0.003-0.006 for absorbance, which is consistent with the reported analysis error in original text
(see 2.2.1 section).
2
Part Ⅱ
The density of mixed-electrolyte solutions, MgCl2-Mg(ClO4)2-H2O, was predicted at 298.15 K
using a new method developed by Li et al. [2, 3]. A brief summary is given here.
According to the ref. [2], the density of the electrolyte solution can be expressed as,
ion

( xiWi  xH 2 OWH 2 O )
i 1
ion
( xiVi  xH 2 OV H O )
 10 3
(A1)
Φ
2
i 1
where xi, x H 2O , Wi and WH 2O are the mole fractions and the molar mass of ion i and water,
Φ
respectively; Vi and V H
2O
refer to the effective intrinsic volume of ion i and apparent molar
volume of water, respectively. The former can be calculated by a simpler formula [4],
Vi  2.51ri3  3.15ri 2
(A2)
where ri is ionic radius of i, as listed in Table. A3. While the latter can be expressed in an
empirical piecewise polynomial,
VHΦ2O  (c1  c2  c3  2 c4  3 )(1  d1Tr  d 2 / Tr  d 3Tr )  10 6
2
(A3)
where the coefficients, c1, c2, c3, c4, d1, d2 and d3, are listed in Table A4. The symbol  stands
for the osmotic pressure, related to the osmotic coefficient  and written as,
ion

RTWH 2 O  mi
i 1
(A4)
1000V H 2 O
where V H 2O is the partial molar volume of water in electrolytes solution which is approximated
with the molar volume of pure water in the practical calculation [5]. The osmotic coefficient 
was estimated by MSE model (Eq. 6) in the text.
Table A3 Ionic radii*
*,
Ions
Mg2+
Ni2+
Cl–
ClO4–
r
0.9238
0.6909
1.81
2.341
data from ref. [2]
Table A4 Coefficients of Eq. A3*
c1
c2 × 102
c3 × 105
c4 × 107
d1
d2 × 102
d3
 /MPa
18.00
–12.860
931.8
0.0
–0.3269
10.52
0.2221
[0，1.5)
17.80
–9.761
239.0
0.0
–0.2619
7.823
0.1907
[1.5，16)
3
17.00
–4.706
52.83
–26.26
–0.1611
4.648
0.1455
[16，80)
17.00
–1.619
5.252
–1.251
–0.1895
2.295
0.1509
[80，200)
*
, data from ref. [3]
For determining the prediction deviation, we compared the calculated the density with the
experimental measured values [6] of solubility isothermal concentration solution of
MgCl2-Mg(ClO4)2-H2O system at 298.15 K. The results are collected in Table A5, displaying that
maximum error is 3.4%. And, therefore, the error is less than the maximum in the text because of
the concentration of interest system is low.
Table A5 Comparison the calculated density and experimental values of MgCl2-Mg(ClO4)2-H2O
system at 298.15 K
MgCl2 (%)
Mg(ClO4)2 (%)
Density (exp., g/mL)*
Density (calc., g∙mL–1)
AAD%**
0.0000
0.0378
0.0634
0.1170
0.1656
0.2008
0.2285
0.2284
0.2700
0.3100
0.3550
0.4990
0.4477
0.4111
0.3380
0.2770
0.2304
0.1990
0.1985
0.1300
0.0600
0.0000
1.470
1.454
1.426
1.419
1.336
1.5201
1.5033
1.4894
1.4652
1.4507
1.4368
1.4332
1.4324
1.3974
1.3600
1.3419
3.4
*,
2.4
1.7
1.0
0.44
data from ref. [6]
**, AAD%
= 100 
 cal   exp
 exp
References
1. He, P. H., Yin, X., Zhang, N., Zhu, J.: Study on thermal decomposition gravimetric method
for the determination of magnesium chloride in pure magnesium chloride solution. Metallurg.
Anal. 30, 58-61 (2010). (in Chinese)
2. Li, C.X., Park, S.B., Kim, J.S., Lee, H.: A new generalized model for predicting the density
of single- and mixed-electrolyte solutions. Fluid Phase Equilib. 145, 1–14 (1998).
3. Li, C.X., Song, H.Y.: A new approach for predicting density of electrolyte solution. Chem.
Ind. Eng. 18, 20–28 (2001).
4. Conway B.E.: Studies in physical and theoretical chemistry 12: ionic hydration in chemistry
and biophysics. Amsterdam: Elsevier, 1981.
5. Sohnel O., Novotny P.: Densities of aqueous solutions of inorganic substances. Amsterdam:
Elsevier, 1985.
6.
Lepeshkhov I.N., Leboshchina V.I.: Solubility in a quaternary mutual aqueous system of
4
chlorides and perchlorates of magnesium and ammonium at 25 ℃. Uch. Zap. Yarosl. Gos.
Ped. Inst. 59, 48–66 (1966).
5