# Volumetric Properties in the NaAsO2 + H2O System at Temperature from 283.15 to 363.15 K and Atmospheric Pressure

Authors: Hongfang Hou; Wanjing Cui; Jiaojiao Chen; Lingzong Meng; Yafei Guo; Tianlong Deng
Journal: Journal of Chemistry
 (2020)

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## Abstract

Densities of sodium arsenite (NaAsO2) aqueous solution with the molality varied from 0.19570 to 1.94236 mol·kg−1 at temperature intervals of 5 K from 283.15 to 363.15 K and 101 ± 5 kPa were measured by a precise Anton Paar Digital vibrating-tube densimeter. Apparent molar volumes (VΦ) and thermal expansion coefficient (α) were obtained on the basis of experimental data. The 3D diagram of apparent molar volume against temperature and molality and the diagram of thermal expansion coefficient against molality were generated. According to the Pitzer ion-interaction equation of the apparent molar volume model, the Pitzer single-salt parameters (βM,X0υ, βM,X1υ, βM,X2υ, and CM,Xυ, MX = NaAsO2) and their temperature-dependent correlation F(i, p, T) = a1 + a2ln (T/298.15) + a3(T − 298.15) + a4/(620 − T) + a5/(T − 227) (where T is temperature in Kelvin and ai are the correlation coefficients) for NaAsO2 were obtained for the first time. The predictive apparent molar volumes agree well with the experimental values, and those results indicated that the single-salt parameters and the temperature-dependent formula are reliable.


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## Body

## 1. Introduction

Arsenic (As) is a ubiquitously toxic, carcinogenic, and possibly teratogenic element [1, 2], and the toxicity of arsenite (AsIII) is 60 times higher than that of arsenate (AsV) in the environment [3]. Many studies show that arsenic as a carcinogenic agent poses a high risk to human health if it is released into the environment, typically arsenicosis, a serious disease mainly caused by As-contaminated drinking groundwater [4–8]. Apparent molar volume reveals the volume change in solution caused by changes of temperature, concentration, and pressure and further provides some basic understanding of the structure and ion interaction in aqueous solution [9]. Accurate acknowledge of the thermodynamic properties of arsenic plays a vital role in solving environmental geochemistry of arsenic pollution [10].As to arsenate compounds, the thermodynamic properties (ΔGf0, ΔHf0, S0, Cp0, V0, and ω) of arsenate and arsenite aqueous systems were evaluated and the coefficients of the Helgeson–Kirkham–Flowers equations were revised [11]. Perfetti et al. measured the densities of arsenious and arsenic acid aqueous solution and obtained the standard partial molar volumes V0 of the neutral aqueous AsIII and AsV (oxy) hydroxide species [10]. Nordstrom et al. reviewed and updated thermodynamic data of arsenic minerals and aqueous species, focusing on internal consistency and the quality of the original measurements [12, 13]. Till now, the apparent molar volume properties on NaAsO2 aqueous solution are not reported in the literature.In this paper, the densities of the binary system NaAsO2 + H2O from 0.19570 to 1.94236 mol·kg−1 at temperature from 283.15 to 363.15 K were measured. Apparent molar volumes and thermal expansion coefficients were obtained, and the Pitzer single-salt parameters and their temperature-dependent equation of NaAsO2 were fitted on the basis of the Pitzer ion-interaction model for the first time.


## 2. Experimental

### 2.1. Reagents

NaAsO2 was obtained, with an analytical grade of 0.99 in mass fraction. The chemical was recrystallized after filtration, washing, and drying at 35°C before use in the glove box filled with nitrogen (UNIlab Plus, MBraun, Germany). The purity of the recrystallized NaAsO2 was 0.9950 in mass fraction, which was analyzed by inductively coupled plasma-mass (iCAP Q ICP-MS Thermo Scientific, Massachusetts, USA) with an uncertainty of ±0.0063 in mass fraction, shown in Table 1. The characterization of the recrystallized NaAsO2 by TG−DSC (Labsys, Setaram, France) is shown in Figure 1, and the weight loss of the sample was 0.0205 in mass fraction between 298 and 473 K, which was basically due to no loss of water within the range of the measured temperature. Double deionized water (DDW) was produced by an ultrapure water machine (Ulupure Technologies Co. Ltd., China) with conductivity less than 1 × 10−4 S·m−1 and pH = 6.60 at 25°C, and it was used during the whole experiment.Table 1
Source and purity of the chemical used in this work.
Reagents
CAS reg. no
Initial mass fraction purity
Purification method
Final mass fraction purity
Analysis method
NaAsO2a
7784-46-5
0.99
Recrystallization
0.995
ICP-MS for AsO2−b
aXiya Reagent Co., Ltd. bStandard uncertainty u is u(m) = 0.0063 in mass fraction.Figure 1
The TG–DSC curve of the recrystallized NaAsO2.


### 2.2. Apparatus and Method

The stock solution was prepared with NaAsO2 and fresh DDW in a glovebox filled with nitrogen by weight using a precision electronic balance (Mettler Toledo, Swiss) with an uncertainty of 0.2 mg. All other aqueous solutions were prepared by mass dilution from the stock solution with an uncertainty of 0.2 mmol·kg−1 and stored in glass bottles at 4°C in the refrigerator.Densities of sodium arsenite aqueous solution were measured by a precise Anton Paar Digital vibrating-tube densimeter (DMA4500, Anton Paar Co. Ltd., Austria), which was controlled within ±0.01 K by the automatically thermostat with an uncertainty of 1.4 mg·cm−3. Before the measurement, the apparatus was calibrated using dry air and fresh DDW at 293.15 K and 101 ± 5 kPa. Density of pure water was measured with 10 K intervals from 279.15 to 369.15 K, and the results agree well with the literature [14], and the deviations between the experimental and reference data were within 0.003%, as shown in Table 2. Densities of the NaAsO2 aqueous solutions were measured with molality from 0.19570 to 1.94236 mol·kg−1 at temperature intervals of 5 K from 283.15 to 363.15 K and atmospheric pressure.Table 2
Comparison of densities of pure water at different temperatures between the experimental and the literature data.a
T (K)
ρ
exp (g·cm−3)
ρ
lit (g·cm−3)b
∆(ρ)%c
279.15
0.99997
0.99994
0.0030
289.15
0.99896
0.99894
0.0020
299.15
0.99680
0.99678
0.0020
309.15
0.99369
0.99369
0.0000
319.15
0.98979
0.98979
0.0000
329.15
0.98520
0.98521
0.0010
339.15
0.97999
0.98001
0.0020
349.15
0.97422
0.97424
0.0021
359.15
0.96796
0.96796
0.0000
369.15
0.96119
0.96118
0.0010
aStandard uncertainties u are u(T) = 0.01 K and u(p) = 5 kPa, and u(ρ) for ρ is 1.4 mg·cm−3. bLiterature [14]. c∆(ρ)% = 100 × ∣ρexp/ρlit−1∣.


## 2.1. Reagents

NaAsO2 was obtained, with an analytical grade of 0.99 in mass fraction. The chemical was recrystallized after filtration, washing, and drying at 35°C before use in the glove box filled with nitrogen (UNIlab Plus, MBraun, Germany). The purity of the recrystallized NaAsO2 was 0.9950 in mass fraction, which was analyzed by inductively coupled plasma-mass (iCAP Q ICP-MS Thermo Scientific, Massachusetts, USA) with an uncertainty of ±0.0063 in mass fraction, shown in Table 1. The characterization of the recrystallized NaAsO2 by TG−DSC (Labsys, Setaram, France) is shown in Figure 1, and the weight loss of the sample was 0.0205 in mass fraction between 298 and 473 K, which was basically due to no loss of water within the range of the measured temperature. Double deionized water (DDW) was produced by an ultrapure water machine (Ulupure Technologies Co. Ltd., China) with conductivity less than 1 × 10−4 S·m−1 and pH = 6.60 at 25°C, and it was used during the whole experiment.Table 1
Source and purity of the chemical used in this work.
Reagents
CAS reg. no
Initial mass fraction purity
Purification method
Final mass fraction purity
Analysis method
NaAsO2a
7784-46-5
0.99
Recrystallization
0.995
ICP-MS for AsO2−b
aXiya Reagent Co., Ltd. bStandard uncertainty u is u(m) = 0.0063 in mass fraction.Figure 1
The TG–DSC curve of the recrystallized NaAsO2.


## 2.2. Apparatus and Method

The stock solution was prepared with NaAsO2 and fresh DDW in a glovebox filled with nitrogen by weight using a precision electronic balance (Mettler Toledo, Swiss) with an uncertainty of 0.2 mg. All other aqueous solutions were prepared by mass dilution from the stock solution with an uncertainty of 0.2 mmol·kg−1 and stored in glass bottles at 4°C in the refrigerator.Densities of sodium arsenite aqueous solution were measured by a precise Anton Paar Digital vibrating-tube densimeter (DMA4500, Anton Paar Co. Ltd., Austria), which was controlled within ±0.01 K by the automatically thermostat with an uncertainty of 1.4 mg·cm−3. Before the measurement, the apparatus was calibrated using dry air and fresh DDW at 293.15 K and 101 ± 5 kPa. Density of pure water was measured with 10 K intervals from 279.15 to 369.15 K, and the results agree well with the literature [14], and the deviations between the experimental and reference data were within 0.003%, as shown in Table 2. Densities of the NaAsO2 aqueous solutions were measured with molality from 0.19570 to 1.94236 mol·kg−1 at temperature intervals of 5 K from 283.15 to 363.15 K and atmospheric pressure.Table 2
Comparison of densities of pure water at different temperatures between the experimental and the literature data.a
T (K)
ρ
exp (g·cm−3)
ρ
lit (g·cm−3)b
∆(ρ)%c
279.15
0.99997
0.99994
0.0030
289.15
0.99896
0.99894
0.0020
299.15
0.99680
0.99678
0.0020
309.15
0.99369
0.99369
0.0000
319.15
0.98979
0.98979
0.0000
329.15
0.98520
0.98521
0.0010
339.15
0.97999
0.98001
0.0020
349.15
0.97422
0.97424
0.0021
359.15
0.96796
0.96796
0.0000
369.15
0.96119
0.96118
0.0010
aStandard uncertainties u are u(T) = 0.01 K and u(p) = 5 kPa, and u(ρ) for ρ is 1.4 mg·cm−3. bLiterature [14]. c∆(ρ)% = 100 × ∣ρexp/ρlit−1∣.


## 3. Results and Discussion

### 3.1. Densities of NaAsO2 Aqueous Solution

The densities of NaAsO2 aqueous solution were measured at different temperatures and molalities, and the results are listed in Table 3. It was clearly seen that the densities of NaAsO2 aqueous solution are decreased with increasing of temperature at constant molality. Nevertheless, at the same temperature, the density values of NaAsO2 aqueous solution are increased indistinctively with the increasing of NaAsO2 molality.Table 3
Apparent molar volumes and densities of the NaAsO2 + H2O system at various temperatures and molalities at 101 ± 5 kPa.a
m(NaAsO2)
ρ
V
Φ
ρ
V
Φ
ρ
V
Φ
Mol·kg−1
g·cm−3
cm3·mol−1
g·cm−3
cm3·mol−1
g·cm−3
cm3·mol−1
T = 283.15 K
T = 288.15 K
T = 293.15 K
1.94236
1.54174
−96.8179
1.53826
−96.1708
1.53474
−95.6638
1.74671
1.47538
−96.6072
1.47215
−95.8962
1.46886
−95.3316
1.55298
1.41632
−97.7718
1.41333
−96.9925
1.41027
−96.3714
1.35720
1.35951
−99.5389
1.35679
−98.6871
1.35397
−98.0068
0.97105
1.25604
−106.8454
1.25389
−105.8578
1.25159
−105.0693
0.77617
1.20993
−116.6088
1.20801
−115.4939
1.20593
−114.6058
0.58372
1.16344
−129.5826
1.16181
−128.3595
1.15999
−127.3822
0.39237
1.12068
−159.3925
1.11935
−158.0320
1.11780
−156.9634
0.19570
1.07768
−249.5148
1.07670
−248.0568
1.07546
−246.9547
0.00000
0.99966
—
0.99908
—
0.99820
—
T = 298.15 K
T = 303.15 K
T = 308.15 K
1.94236
1.53116
−95.2661
1.52752
−94.9783
1.52383
−94.7832
1.74671
1.46549
−94.8841
1.46207
−94.5577
1.45857
−94.3245
1.55298
1.40712
−95.8741
1.40390
−95.5091
1.40060
−95.2448
1.35720
1.35105
−97.4614
1.34805
−97.0548
1.34494
−96.7549
0.97105
1.24917
−104.4410
1.24663
−103.9809
1.24397
−103.6459
0.77617
1.20370
−113.8897
1.20132
−113.3462
1.19881
−112.9440
0.58372
1.15800
−126.5968
1.15584
−126.0085
1.15354
−125.5718
0.39237
1.11605
−156.0997
1.11412
−155.4848
1.11201
−155.0170
0.19570
1.07399
−246.0876
1.07230
−245.5014
1.07041
−245.0817
0.00000
0.99707
—
0.99569
—
0.99410
—
T = 313.15 K
T = 318.15 K
T = 323.15 K
1.94236
1.52007
−94.6709
1.51626
−94.6424
1.51237
−94.6850
1.74671
1.45501
−94.1840
1.45137
−94.1289
1.44767
−94.1534
1.55298
1.39722
−95.0767
1.39376
−94.9992
1.39022
−95.0067
1.35720
1.34175
−96.5581
1.33847
−96.4597
1.33510
−96.4499
0.97105
1.24119
−103.4289
1.23831
−103.3333
1.23533
−103.3445
0.77617
1.19616
−112.6608
1.19340
−112.5145
1.19050
−112.4632
0.58372
1.15108
−125.2659
1.14848
−125.1021
1.14575
−125.0503
0.39237
1.10973
−154.6928
1.10731
−154.5528
1.10473
−154.5289
0.19570
1.06834
−244.8692
1.06609
−244.8135
1.06368
−244.9561
0.00000
0.99231
—
0.99033
—
0.98817
—
T = 328.15 K
T = 333.15 K
T = 338.15 K
1.94236
1.50842
−94.7894
1.50439
−94.9561
1.50025
−95.1719
1.74671
1.44388
−94.2384
1.44001
−94.3908
1.43604
−94.5963
1.55298
1.38660
−95.0791
1.38289
−95.2211
1.37907
−95.4202
1.35720
1.33163
−96.5086
1.32807
−96.6411
1.32440
−96.8342
0.97105
1.23224
−103.4322
1.22904
−103.6081
1.22574
−103.8600
0.77617
1.18749
−112.4984
1.18436
−112.6244
1.18111
−112.8292
0.58372
1.14289
−125.0870
1.13990
−125.2217
1.13678
−125.4425
0.39237
1.10201
−154.5877
1.09916
−154.7787
1.09617
−155.0549
0.19570
1.06111
−245.1416
1.05840
−245.5166
1.05554
−245.9837
0.00000
0.98586
—
0.98339
—
0.98077
—
T = 343.15 K
T = 348.15 K
T = 353.15 K
1.94236
1.49599
−95.4295
1.49156
−95.7097
1.48689
−95.9977
1.74671
1.43194
−94.8431
1.42768
−95.1155
1.42320
−95.3957
1.55298
1.37512
−95.6640
1.37102
−95.9411
1.36671
−96.2108
1.35720
1.32060
−97.0712
1.31666
−97.3367
1.31251
−97.6106
0.97105
1.22229
−104.1578
1.21869
−104.4757
1.21489
−104.7911
0.77617
1.17773
−113.0901
1.17420
−113.3740
1.17050
−113.6742
0.58372
1.13353
−125.7234
1.13013
−126.0281
1.12657
−126.3459
0.39237
1.09304
−155.3910
1.08978
−155.7837
1.08635
−156.1701
0.19570
1.05254
−246.5379
1.04940
−247.1269
1.04610
−247.7096
0.00000
0.97801
—
0.97512
—
0.97209
—
T = 358.15 K
T = 363.15 K
1.94236
1.48185
−96.2392
1.47621
−96.3650
1.74671
1.41837
−95.6235
1.41299
−95.7264
1.55298
1.36208
−96.4328
1.35689
−96.4935
1.35720
1.30806
−97.8220
1.30308
−97.8506
0.97105
1.21081
−105.0049
1.20629
−104.9954
0.77617
1.16656
−113.8768
1.16227
−113.8641
0.58372
1.12278
−126.5346
1.11867
−126.4490
0.39237
1.08271
−156.3771
1.07877
−156.1936
0.19570
1.04262
−248.0259
1.03890
−247.7787
0.00000
0.96895
—
0.96570
—
aStandard uncertainties u are u(T) = 0.01 K and u(p) = 5 kPa. u(m) for NaAsO2 aqueous solution is 0.2 mmol·kg−1, u(ρ) for ρ is 1.4 mg·cm−3, and u(VΦ) for VΦ is 0.0030 cm3·mol−1.


### 3.2. Thermal Expansion Coefficient of NaAsO2 Aqueous Solution

Thermal expansion coefficient of NaAsO2 aqueous solution, α, was defined as follows [15]:(1)α=1V∂V∂Tp,m=−1ρ∂ρ∂Tp,m.An empirical equation can be obtained at constant molality and pressure as follows:(2)ρ=A0+A1T−273.15+A2T−273.152,where ρ is the density of NaAsO2 aqueous solution, T is the absolute temperature in Kelvin, and Ai are the empirical constants. The values of ρ obtained at different temperatures have been fitted by the least square method and are shown in Table 4, with the correlation coefficients (R2) and standard deviations of 0.9997 and 0.00007, respectively.Table 4
The empirical constants (Ai) and standard deviations (SD) of NaAsO2 aqueous solution at different temperatures and ρ at constant molality and pressure.
m (mol·kg−1)
A
0
104 A1
106 A2
R
2
SD
1.94236
1.5476
−5.9767
−2.0638
0.9997
0.00002
1.74671
1.4808
−5.5469
−2.1204
0.9998
0.00003
1.55298
1.4214
−5.1049
−2.2069
0.9998
0.00005
1.35720
1.3642
−4.6333
−2.3221
0.9998
0.00002
0.97105
1.2598
−3.5908
−2.5584
0.9999
0.00004
0.77617
1.2134
−3.2059
−2.7181
1.0000
0.00007
0.58372
1.1665
−2.6774
−2.9045
1.0000
0.00002
0.39237
1.1233
−2.1469
−3.0987
1.0000
0.00003
0.19570
1.0798
−1.5388
−3.3456
0.9999
0.00005At constant molality and pressure, equation (3) was used to acquire partial derivatives of temperature ∂ρ/∂Tp:(3)∂ρ∂Tp=A1+2A2T–273.15.Substituting equation (3) into equation (1), the thermal expansion coefficients of NaAsO2 aqueous solution were calculated with various molalities at different temperatures. According to the calculated data, the relation of the thermal expansion coefficient and the molality at temperature intervals of 5 K from 283.15 to 363.15 K is plotted in Figure 2. It can be seen that the thermal expansion coefficient for NaAsO2 aqueous solution increased with the increasing of temperature at the constant molality. Also, with the increasing of molality, the thermal expansion coefficient increased obviously at T = 283.15 to 333.15 K, almost unchanged at T = 338.15 to 348.15 K, and decreased lightly at T = 353.15 to 363.15 K.Figure 2
Thermal expansion coefficient (α) of NaAsO2 (aq) against the molality (m) at different temperatures.


### 3.3. Apparent Molar Volume and Pitzer Parameter of NaAsO2

The apparent molar volumes of NaAsO2 aqueous solution were calculated using measured densities of pure water and the sample solutions by the following equation:(4)Vϕ=1000ρw−ρsmi⋅ρw⋅ρ+Miρ,where mi is the molality (mol·kg−1) of the solute in the aqueous solution, Mi is the molar mass (kg·mol−1) of the solute, and ρw and ρ are the densities (g·cm−3) of pure water and sample solution, respectively. The calculated apparent molar volumes of NaAsO2 with an uncertainty of 0.0030 cm3·mol−1 are listed in Table 3, and the 3D surfaces (mi, T, VΦ) of apparent molar volume of NaAsO2 versus temperature and molality are plotted in Figure 3. The results indicate that apparent molar volume of NaAsO2 universally increased with increasing temperature at low molality, and it foremost increased and then decreased with the increasing temperature at high molality.Figure 3
Apparent molar volumes of NaAsO2 aqueous solution against temperature and molality at atmospheric pressure.Pitzer’s electrolyte solution theory is based on the model of ion interaction and statistical mechanics. It can accurately express the thermodynamic properties of electrolyte aqueous solution. The apparent molar volumes of NaAsO2 were calculated using the following Pitzer equation to construct the Pitzer model [16, 17]:(5)VΦ+υwnr=Vmrnr+υZMZXAV2bln1+bI1+bIr+2υMυXRTmBMXυm−mrBMXυmr+υMzMCM,Xυm2−mr2.The relationship betweenBM,Xυ(m) and ionic strength I of aqueous solution was employed as follows: (6)BM,Xυ=βM,X0υ+βM,X1υgαB1I+βM,X2υgαB2I,(7)gt=21–1+texp−tt2,where m (mol·kg−1) is the molality of NaAsO2 aqueous solution, υw is the volume of 1 kg pure water, V(mr) is the volume of a certain solution of reference molality mr = 1.5 mol·kg−1 containing 1 kg of water, nr = 1.5 mol is the moles number of this certain solution, Av is the Debye–Hückel limiting-law slope for the apparent molar volume, zM and zX are the charges of the cation and anion for NaAsO2 (zM = 1, zX = 1), υM and υX are the stoichiometric numbers of M and X ions formed by stoichiometric dissociation of one molecule of MX, and υ = υM + υX, as for NaAsO2 (υM = 1, υX = 1, υ = 2), αB1  = 1.4 kg1/2 mol1/2, αB2  = 9.3 kg1/2 mol1/2, b = 1.2 kg1/2 mol−1/2, and I (mol·kg−1) is the ionic strength of the aqueous solution calculated as (1/2)Σmizi2, R (cm3·MPa·K−1·mol−1) is the gas constant, and T is the temperature. The temperature-dependent and pressure-dependent volumetric ion-interaction parameters are BM,Xυ(m) and CM,Xυ(m).The Pitzer ion-interaction parameters of the volumetric properties are expressed as functionsF(i, p, T):(8)βM,X0υ=F0,p,T,(9)βM,X1υ=F1,p,T,(10)βM,X2υ=F2,p,T,(11)CM,Xv=F3,p,T,with F(i, p, T) represented as(12)Fi,P,T=a1+a2lnT298.15+a3T−298.15+a4620−T+a5T−227,where T is the temperature in Kelvin, p is the pressure in MPa, and ai are the polynomial coefficients. All the thermodynamic and dielectric properties involved were calculated by the IAPWS-95 equation from Ref. [18].On the basis of equations (5) to (7), the single-salt parameters βM,X0v, βM,X1v, βM,X2v, and CM,Xv for NaAsO2 at each temperature were fitted and are listed in Table 5. The temperature relation coefficients ai in equations (8) to (12) were fitted and are listed in Table 6, and the fitted results of each single-salt parameter βM,X0v, βM,X1v, βM,X2v, and CM,Xv of NaAsO2 were in good agreement with the experimental values, which indicated that the Pitzer model we constructed is suitable to describe the volumetric properties of the binary system NaAsO2 + H2O. On the basis of temperature-dependent coefficients and calculated Pitzer single-salt parameters, the apparent molar volume for NaAsO2 aqueous solution at each temperature from 283.15 to 363.15 K could be predicted, not only for the experimental temperature, which are meaningful for the actual application.Table 5
The pitzer single-salt parameters of NaAsO2 at different temperatures.
T (K)
β
0
v
β
1
v
β
2
v
C
0
v
283.15
−0.0252
0.1036
9.6726
0.0026
288.15
−0.0245
0.1008
9.5275
0.0025
293.15
−0.0239
0.0982
9.3899
0.0025
298.15
−0.0233
0.0956
9.2592
0.0024
303.15
−0.0229
0.0938
9.1245
0.0023
308.15
−0.0223
0.0916
9.0005
0.0023
313.15
−0.0217
0.0895
8.8891
0.0022
318.15
−0.0213
0.0878
8.7694
0.0021
323.15
−0.0209
0.0860
8.6669
0.0021
328.15
−0.0204
0.0841
8.5631
0.0020
333.15
−0.0200
0.0826
8.4661
0.0020
338.15
−0.0195
0.0809
8.3752
0.0019
343.15
−0.0191
0.0792
8.2921
0.0019
348.15
−0.0189
0.0781
8.2003
0.0019
353.15
−0.0186
0.0769
8.1137
0.0019
358.15
−0.0182
0.0755
8.0237
0.0018
363.15
−0.0174
0.0729
7.9326
0.0017Table 6
The temperature-dependent equation coefficients of Pitzer parameters of NaAsO2.
Polynomial coefficient
Pitzer parameters
β
0
v
β
1
v
β
2
v
C
0
v
α
1
−1.6307 × 10−1
4.8917 × 10−1
3.2765 × 101
3.6363 × 10−2
α
2
5.4520 × 10−1
−1.5004 × 100
−1.0041 × 102
−1.3276 × 10−1
α
3
−2.0407 × 10−3
5.6413 × 10−3
3.6187 × 101
5.0425 × 10−4
α
4
4.2987 × 101
−1.2384 × 102
−7.1663 × 103
−1.0344 × 101
α
5
4.3834 × 10−1
−6.0862 × 10−1
−8.8443 × 101
−1.3035 × 10−1


## 3.1. Densities of NaAsO2 Aqueous Solution

The densities of NaAsO2 aqueous solution were measured at different temperatures and molalities, and the results are listed in Table 3. It was clearly seen that the densities of NaAsO2 aqueous solution are decreased with increasing of temperature at constant molality. Nevertheless, at the same temperature, the density values of NaAsO2 aqueous solution are increased indistinctively with the increasing of NaAsO2 molality.Table 3
Apparent molar volumes and densities of the NaAsO2 + H2O system at various temperatures and molalities at 101 ± 5 kPa.a
m(NaAsO2)
ρ
V
Φ
ρ
V
Φ
ρ
V
Φ
Mol·kg−1
g·cm−3
cm3·mol−1
g·cm−3
cm3·mol−1
g·cm−3
cm3·mol−1
T = 283.15 K
T = 288.15 K
T = 293.15 K
1.94236
1.54174
−96.8179
1.53826
−96.1708
1.53474
−95.6638
1.74671
1.47538
−96.6072
1.47215
−95.8962
1.46886
−95.3316
1.55298
1.41632
−97.7718
1.41333
−96.9925
1.41027
−96.3714
1.35720
1.35951
−99.5389
1.35679
−98.6871
1.35397
−98.0068
0.97105
1.25604
−106.8454
1.25389
−105.8578
1.25159
−105.0693
0.77617
1.20993
−116.6088
1.20801
−115.4939
1.20593
−114.6058
0.58372
1.16344
−129.5826
1.16181
−128.3595
1.15999
−127.3822
0.39237
1.12068
−159.3925
1.11935
−158.0320
1.11780
−156.9634
0.19570
1.07768
−249.5148
1.07670
−248.0568
1.07546
−246.9547
0.00000
0.99966
—
0.99908
—
0.99820
—
T = 298.15 K
T = 303.15 K
T = 308.15 K
1.94236
1.53116
−95.2661
1.52752
−94.9783
1.52383
−94.7832
1.74671
1.46549
−94.8841
1.46207
−94.5577
1.45857
−94.3245
1.55298
1.40712
−95.8741
1.40390
−95.5091
1.40060
−95.2448
1.35720
1.35105
−97.4614
1.34805
−97.0548
1.34494
−96.7549
0.97105
1.24917
−104.4410
1.24663
−103.9809
1.24397
−103.6459
0.77617
1.20370
−113.8897
1.20132
−113.3462
1.19881
−112.9440
0.58372
1.15800
−126.5968
1.15584
−126.0085
1.15354
−125.5718
0.39237
1.11605
−156.0997
1.11412
−155.4848
1.11201
−155.0170
0.19570
1.07399
−246.0876
1.07230
−245.5014
1.07041
−245.0817
0.00000
0.99707
—
0.99569
—
0.99410
—
T = 313.15 K
T = 318.15 K
T = 323.15 K
1.94236
1.52007
−94.6709
1.51626
−94.6424
1.51237
−94.6850
1.74671
1.45501
−94.1840
1.45137
−94.1289
1.44767
−94.1534
1.55298
1.39722
−95.0767
1.39376
−94.9992
1.39022
−95.0067
1.35720
1.34175
−96.5581
1.33847
−96.4597
1.33510
−96.4499
0.97105
1.24119
−103.4289
1.23831
−103.3333
1.23533
−103.3445
0.77617
1.19616
−112.6608
1.19340
−112.5145
1.19050
−112.4632
0.58372
1.15108
−125.2659
1.14848
−125.1021
1.14575
−125.0503
0.39237
1.10973
−154.6928
1.10731
−154.5528
1.10473
−154.5289
0.19570
1.06834
−244.8692
1.06609
−244.8135
1.06368
−244.9561
0.00000
0.99231
—
0.99033
—
0.98817
—
T = 328.15 K
T = 333.15 K
T = 338.15 K
1.94236
1.50842
−94.7894
1.50439
−94.9561
1.50025
−95.1719
1.74671
1.44388
−94.2384
1.44001
−94.3908
1.43604
−94.5963
1.55298
1.38660
−95.0791
1.38289
−95.2211
1.37907
−95.4202
1.35720
1.33163
−96.5086
1.32807
−96.6411
1.32440
−96.8342
0.97105
1.23224
−103.4322
1.22904
−103.6081
1.22574
−103.8600
0.77617
1.18749
−112.4984
1.18436
−112.6244
1.18111
−112.8292
0.58372
1.14289
−125.0870
1.13990
−125.2217
1.13678
−125.4425
0.39237
1.10201
−154.5877
1.09916
−154.7787
1.09617
−155.0549
0.19570
1.06111
−245.1416
1.05840
−245.5166
1.05554
−245.9837
0.00000
0.98586
—
0.98339
—
0.98077
—
T = 343.15 K
T = 348.15 K
T = 353.15 K
1.94236
1.49599
−95.4295
1.49156
−95.7097
1.48689
−95.9977
1.74671
1.43194
−94.8431
1.42768
−95.1155
1.42320
−95.3957
1.55298
1.37512
−95.6640
1.37102
−95.9411
1.36671
−96.2108
1.35720
1.32060
−97.0712
1.31666
−97.3367
1.31251
−97.6106
0.97105
1.22229
−104.1578
1.21869
−104.4757
1.21489
−104.7911
0.77617
1.17773
−113.0901
1.17420
−113.3740
1.17050
−113.6742
0.58372
1.13353
−125.7234
1.13013
−126.0281
1.12657
−126.3459
0.39237
1.09304
−155.3910
1.08978
−155.7837
1.08635
−156.1701
0.19570
1.05254
−246.5379
1.04940
−247.1269
1.04610
−247.7096
0.00000
0.97801
—
0.97512
—
0.97209
—
T = 358.15 K
T = 363.15 K
1.94236
1.48185
−96.2392
1.47621
−96.3650
1.74671
1.41837
−95.6235
1.41299
−95.7264
1.55298
1.36208
−96.4328
1.35689
−96.4935
1.35720
1.30806
−97.8220
1.30308
−97.8506
0.97105
1.21081
−105.0049
1.20629
−104.9954
0.77617
1.16656
−113.8768
1.16227
−113.8641
0.58372
1.12278
−126.5346
1.11867
−126.4490
0.39237
1.08271
−156.3771
1.07877
−156.1936
0.19570
1.04262
−248.0259
1.03890
−247.7787
0.00000
0.96895
—
0.96570
—
aStandard uncertainties u are u(T) = 0.01 K and u(p) = 5 kPa. u(m) for NaAsO2 aqueous solution is 0.2 mmol·kg−1, u(ρ) for ρ is 1.4 mg·cm−3, and u(VΦ) for VΦ is 0.0030 cm3·mol−1.


## 3.2. Thermal Expansion Coefficient of NaAsO2 Aqueous Solution

Thermal expansion coefficient of NaAsO2 aqueous solution, α, was defined as follows [15]:(1)α=1V∂V∂Tp,m=−1ρ∂ρ∂Tp,m.An empirical equation can be obtained at constant molality and pressure as follows:(2)ρ=A0+A1T−273.15+A2T−273.152,where ρ is the density of NaAsO2 aqueous solution, T is the absolute temperature in Kelvin, and Ai are the empirical constants. The values of ρ obtained at different temperatures have been fitted by the least square method and are shown in Table 4, with the correlation coefficients (R2) and standard deviations of 0.9997 and 0.00007, respectively.Table 4
The empirical constants (Ai) and standard deviations (SD) of NaAsO2 aqueous solution at different temperatures and ρ at constant molality and pressure.
m (mol·kg−1)
A
0
104 A1
106 A2
R
2
SD
1.94236
1.5476
−5.9767
−2.0638
0.9997
0.00002
1.74671
1.4808
−5.5469
−2.1204
0.9998
0.00003
1.55298
1.4214
−5.1049
−2.2069
0.9998
0.00005
1.35720
1.3642
−4.6333
−2.3221
0.9998
0.00002
0.97105
1.2598
−3.5908
−2.5584
0.9999
0.00004
0.77617
1.2134
−3.2059
−2.7181
1.0000
0.00007
0.58372
1.1665
−2.6774
−2.9045
1.0000
0.00002
0.39237
1.1233
−2.1469
−3.0987
1.0000
0.00003
0.19570
1.0798
−1.5388
−3.3456
0.9999
0.00005At constant molality and pressure, equation (3) was used to acquire partial derivatives of temperature ∂ρ/∂Tp:(3)∂ρ∂Tp=A1+2A2T–273.15.Substituting equation (3) into equation (1), the thermal expansion coefficients of NaAsO2 aqueous solution were calculated with various molalities at different temperatures. According to the calculated data, the relation of the thermal expansion coefficient and the molality at temperature intervals of 5 K from 283.15 to 363.15 K is plotted in Figure 2. It can be seen that the thermal expansion coefficient for NaAsO2 aqueous solution increased with the increasing of temperature at the constant molality. Also, with the increasing of molality, the thermal expansion coefficient increased obviously at T = 283.15 to 333.15 K, almost unchanged at T = 338.15 to 348.15 K, and decreased lightly at T = 353.15 to 363.15 K.Figure 2
Thermal expansion coefficient (α) of NaAsO2 (aq) against the molality (m) at different temperatures.


## 3.3. Apparent Molar Volume and Pitzer Parameter of NaAsO2

The apparent molar volumes of NaAsO2 aqueous solution were calculated using measured densities of pure water and the sample solutions by the following equation:(4)Vϕ=1000ρw−ρsmi⋅ρw⋅ρ+Miρ,where mi is the molality (mol·kg−1) of the solute in the aqueous solution, Mi is the molar mass (kg·mol−1) of the solute, and ρw and ρ are the densities (g·cm−3) of pure water and sample solution, respectively. The calculated apparent molar volumes of NaAsO2 with an uncertainty of 0.0030 cm3·mol−1 are listed in Table 3, and the 3D surfaces (mi, T, VΦ) of apparent molar volume of NaAsO2 versus temperature and molality are plotted in Figure 3. The results indicate that apparent molar volume of NaAsO2 universally increased with increasing temperature at low molality, and it foremost increased and then decreased with the increasing temperature at high molality.Figure 3
Apparent molar volumes of NaAsO2 aqueous solution against temperature and molality at atmospheric pressure.Pitzer’s electrolyte solution theory is based on the model of ion interaction and statistical mechanics. It can accurately express the thermodynamic properties of electrolyte aqueous solution. The apparent molar volumes of NaAsO2 were calculated using the following Pitzer equation to construct the Pitzer model [16, 17]:(5)VΦ+υwnr=Vmrnr+υZMZXAV2bln1+bI1+bIr+2υMυXRTmBMXυm−mrBMXυmr+υMzMCM,Xυm2−mr2.The relationship betweenBM,Xυ(m) and ionic strength I of aqueous solution was employed as follows: (6)BM,Xυ=βM,X0υ+βM,X1υgαB1I+βM,X2υgαB2I,(7)gt=21–1+texp−tt2,where m (mol·kg−1) is the molality of NaAsO2 aqueous solution, υw is the volume of 1 kg pure water, V(mr) is the volume of a certain solution of reference molality mr = 1.5 mol·kg−1 containing 1 kg of water, nr = 1.5 mol is the moles number of this certain solution, Av is the Debye–Hückel limiting-law slope for the apparent molar volume, zM and zX are the charges of the cation and anion for NaAsO2 (zM = 1, zX = 1), υM and υX are the stoichiometric numbers of M and X ions formed by stoichiometric dissociation of one molecule of MX, and υ = υM + υX, as for NaAsO2 (υM = 1, υX = 1, υ = 2), αB1  = 1.4 kg1/2 mol1/2, αB2  = 9.3 kg1/2 mol1/2, b = 1.2 kg1/2 mol−1/2, and I (mol·kg−1) is the ionic strength of the aqueous solution calculated as (1/2)Σmizi2, R (cm3·MPa·K−1·mol−1) is the gas constant, and T is the temperature. The temperature-dependent and pressure-dependent volumetric ion-interaction parameters are BM,Xυ(m) and CM,Xυ(m).The Pitzer ion-interaction parameters of the volumetric properties are expressed as functionsF(i, p, T):(8)βM,X0υ=F0,p,T,(9)βM,X1υ=F1,p,T,(10)βM,X2υ=F2,p,T,(11)CM,Xv=F3,p,T,with F(i, p, T) represented as(12)Fi,P,T=a1+a2lnT298.15+a3T−298.15+a4620−T+a5T−227,where T is the temperature in Kelvin, p is the pressure in MPa, and ai are the polynomial coefficients. All the thermodynamic and dielectric properties involved were calculated by the IAPWS-95 equation from Ref. [18].On the basis of equations (5) to (7), the single-salt parameters βM,X0v, βM,X1v, βM,X2v, and CM,Xv for NaAsO2 at each temperature were fitted and are listed in Table 5. The temperature relation coefficients ai in equations (8) to (12) were fitted and are listed in Table 6, and the fitted results of each single-salt parameter βM,X0v, βM,X1v, βM,X2v, and CM,Xv of NaAsO2 were in good agreement with the experimental values, which indicated that the Pitzer model we constructed is suitable to describe the volumetric properties of the binary system NaAsO2 + H2O. On the basis of temperature-dependent coefficients and calculated Pitzer single-salt parameters, the apparent molar volume for NaAsO2 aqueous solution at each temperature from 283.15 to 363.15 K could be predicted, not only for the experimental temperature, which are meaningful for the actual application.Table 5
The pitzer single-salt parameters of NaAsO2 at different temperatures.
T (K)
β
0
v
β
1
v
β
2
v
C
0
v
283.15
−0.0252
0.1036
9.6726
0.0026
288.15
−0.0245
0.1008
9.5275
0.0025
293.15
−0.0239
0.0982
9.3899
0.0025
298.15
−0.0233
0.0956
9.2592
0.0024
303.15
−0.0229
0.0938
9.1245
0.0023
308.15
−0.0223
0.0916
9.0005
0.0023
313.15
−0.0217
0.0895
8.8891
0.0022
318.15
−0.0213
0.0878
8.7694
0.0021
323.15
−0.0209
0.0860
8.6669
0.0021
328.15
−0.0204
0.0841
8.5631
0.0020
333.15
−0.0200
0.0826
8.4661
0.0020
338.15
−0.0195
0.0809
8.3752
0.0019
343.15
−0.0191
0.0792
8.2921
0.0019
348.15
−0.0189
0.0781
8.2003
0.0019
353.15
−0.0186
0.0769
8.1137
0.0019
358.15
−0.0182
0.0755
8.0237
0.0018
363.15
−0.0174
0.0729
7.9326
0.0017Table 6
The temperature-dependent equation coefficients of Pitzer parameters of NaAsO2.
Polynomial coefficient
Pitzer parameters
β
0
v
β
1
v
β
2
v
C
0
v
α
1
−1.6307 × 10−1
4.8917 × 10−1
3.2765 × 101
3.6363 × 10−2
α
2
5.4520 × 10−1
−1.5004 × 100
−1.0041 × 102
−1.3276 × 10−1
α
3
−2.0407 × 10−3
5.6413 × 10−3
3.6187 × 101
5.0425 × 10−4
α
4
4.2987 × 101
−1.2384 × 102
−7.1663 × 103
−1.0344 × 101
α
5
4.3834 × 10−1
−6.0862 × 10−1
−8.8443 × 101
−1.3035 × 10−1


## 4. Conclusion

The densities and apparent molar volumes of NaAsO2 aqueous solution from 283.15 to 363.15 K at atmospheric pressure were obtained for the first time. Apparent molar volumes and thermal expansion coefficient were calculated, and the Pitzer single-salt parameters (βM,X0υ, βM,X1υ, βM,X2υ, and CM,Xυ) were parameterized from the Pitzer ion-interaction model. The temperature-dependent equation coefficients were obtained on account of the least-squares method. It is essential to study the thermodynamic properties, especially apparent molar volume, and construct a model of thermodynamic for solving environmental geochemical arsenic pollution.



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*Source: 9478365-2020-01-11.xml*