Article pubs.acs.org/jced
Estimation of the Partial Molal Adiabatic Compressibility of Ions in Mixed Electrolyte Solutions Using the Pitzer Equations Frank J. Millero* and Jonathan D. Sharp Rosenstiel School of Marine and Atmospheric Science University of Miami Miami, Florida 33149, United States ABSTRACT: The Pitzer equations have been used to fit the apparent molal adiabatic compressibility of electrolytes in water as a function of temperature. The equations have been used to estimate the partial molal compressibility for a number of cations and anions in 0.725 m NaCl and average seawater (S = 35 g kg−1). The calculated results for electrolytes are in good agreement with direct measurements in 0.725 m NaCl and seawater. The partial molal compressibilities estimated from the model can be used to make more reliable estimates of the effect of pressure on activity coefficients and ionic equilibria in seawater and other mixed electrolyte solutions at high pressures. Values of κ0̅ , βMX(0)κ, βMX(1)κ, and CκMX are available for the major seasalts (NaCl, Na2SO4, MgCl2, and MgSO4) from (0 to 95) °C.7 A typical example of the Pitzer fits are shown for NaCl solutions from (5 to 35) °C in Figure 1. The apparent molal compressibilities (ϕκMX) examined in this study were determined from sound speed measurements.8−20 The sound speeds were measured at 2 MHz to a precision of ±0.02 m sec−1 with a Nusonic “sing-around” velocimeter. Details of the system are given elsewhere.8 The values of ϕκMX have been calculated from the sound speed (U) using the equation
1. INTRODUCTION The Pitzer1 ionic interaction model has been shown to be very useful in fitting the volume properties of electrolytes, as a function of concentration and temperature.2 The partial molal volumes of ions in mixed electrolyte solutions determined from these Pitzer equations can also be used to estimate the effect of pressure on activity coefficients3 and ionic equilibrium in mixed electrolytes.4 Only limited studies have been made on the compressibility of mixed electrolyte solutions. In this study we have fit the compressibility of a number of salts to the Pitzer equations. We also demonstrate how these results can be used to estimate the partial molal compressibility in 0.725 m NaCl and seawater.
ϕ
κ MX = 1000(βSρ0 − βS0ρ)/mρρ0 + (βSM )/ρ
where βS is the adiabatic compressibility, ρ is the density, m is the molality and M is the molecular weight. The superscript zero is used to indicate the values are for pure water.2 The adiabatic compressibility was determined from the sound speed using βS = 1/(ρU2). The Pitzer compressibility parameters. Values of κ0̅ , β(0)κ MX , (1)κ βMX , and CκMX for a number of salts at 25 °C are given in Tables A1, A2, and A3 in the Appendix. The effect of temperature on the parameters (0 °C to 50 °C or 0 °C to 90 °C) have been fitted to the equation
2. CALCULATIONS The Pitzer1 equations for apparent molal compressibility (ϕκMX = −∂ϕVMX/∂P) for an electrolyte (υ = υM + υX) are given by5 ϕ
0 0.5 κ MX = κMX ̅ + υ|Z MZ X|(Aκ /2b) ln(1 + bI )
+ 2υMυX RT[mBκ MX + mC κ MX ]
(1)
The κ0M ̅ X is the partial molal compressibility of a salt (MυM XυX) in pure water. The value of BκMX is given by κ BMX = βMX(0)κ + βMX(1)κ g (α1I 0.5) + βMX(2)κ g (α2I 0.5)
(2)
Y = Y (25 °C) +
The value of υ = υM + υX and R and T have their normal definitions, and I is the ionic strength. The g(x) term is given by 2
g (x) = (2/x )[1 − (1 + x) exp(−x)]
(3)
104A κ ,S = −2.187 − 0.105314t + 1.46994·10−03t 2 − 7.82165·10−05t 3
Received: August 13, 2013 Accepted: November 5, 2013
+ 1.70244·10−06t 4 − 2.253236·10−08t 5 + 1.51313·10−10t 6
(4) © XXXX American Chemical Society
(6)
where Yi are adjustable parameters, T is the absolute temperature and TR = 298.15 K is the reference temperature.2,21 The coefficients for eq 6 for some of the salts are given in Tables A4 and A5 in the Appendix. Only limited Pitzer Coefficients are available for sulfates and carbonates needed to make reliable estimates in seawater. The partial molal volume of a cation (M) or anion (X) in a mixed electrolyte solution with cations c and anions a can be
0.5
− 4.1478·10−13t 7
∑ Yi(T − TR )i i
where x = α1I or α2I . The values of b = 1.2 and α1 = 2.0 are used for 1−1, 2−1, 3−1, and 1−2 electrolytes and b = 1.2, α1 = 1.4, and α2 = 12.0 are used for 2−2 electrolytes. The Debye− Hückel limiting law slope for adiabatic compressibility (Aκ,S) is given by6 0.5
(5)
A
dx.doi.org/10.1021/je400734v | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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molal compressibility of cation (M) or anion (X) in a mixed electrolyte solution5 neglecting higher order interaction terms22 0 2 κ κM̅ = κM ̅ − Z M DH κ κ + 2RT ∑ ma [BM,a + (∑ m ion|Zi|)CM,a ] i
a
+ RT ∑ ∑ c
2 κ mcma [Z M (Bc,a )′
κ + Z MCc,a ]
(12)
a
κ κ κX̅ = κ X̅ 0 − Z X2 DHκ + 2RT ∑ mc[Bc,a + (∑ m ion|Zi|)Cc,a ] i
c
+ RT ∑ ∑ c
κ mcma [Z X2(Bc,a )′
+
κ Z XCc,a ]
(13)
a
It should be pointed out that in the earlier paper by Krumgalz et al.,22 the RT term was not considered. The (Bκc,a)′ term is defined as V κ (Bc,a )′ = −∂(Bc,a )′/∂P (1)κ (2)κ = −(βc,a )∂g (x1)/∂I − (βc,a )∂g (x 2)/∂I
B(1)κ c,a
−∂β(1)V c,a /∂P
β(2)κ c,a
where = and The DHκ term is given by Figure 1. Plots of the values of 104 Kϕ (cm3 mol−1 bar−1) for NaCl solutions as a function of molality and temperature.
ln(1 + 1.2I 0.5)}
estimated from the simplified equations of Monnin that neglect the higher order interaction terms21 V + 2RT ∑ ma [BM,a + (∑ m ion|Zi|)CM,a] i
+ RT ∑ ∑ c
VX̅ =
V̅X0
+
V + Z MCc,a ]
a
(7)
Table 1. Measured Partial Molal Adiabatic Compressibilities (cm3 mol−1 bar−1) of Cations in Water, 0.725m NaCl and S = 35 g kg−1 Seawater at 25°C
Z X2 DHV
V V + 2RT ∑ mc[Bc,X + (∑ m ion|Zi|)Cc,X )] V V + RT ∑ ∑ mcma [Z X2(Bc,a )′ + Z XCc,a ] c
water
i
c
a
DHV = (Av/4){(I 0.5/(1 + 1.2I 0.5) + (2/1.2) (9)
The limiting slope AV is given by
6
A V = 1.50619 + 0.0130073t + 4.8307·10−05t 2 + 8.95087·10−07t 3 − 3.7279·10−09t 4 + 2.3942·10−11t 5
The
(BVc,a)′
(10)
term in eqs 6 and 7 are given by
V V (Bc,a )′ = (∂Bc,a /∂I ) (1)V (2)V = (βc,a )∂g (x1)/∂I + (βc,a )∂g (x 2)/∂I
(11)
where x1 = α1I and x2 = α2I and (∂g(xi/∂I) = − (1 + xi + xi2/2) exp(−xi)]. The differentiation of eqs 7 and 8 with respect to pressure can yield equations that can be used to estimate the partial 0.5
0.5
−(2/xi2I)[1
B
0.725 m NaCl
seawater S = 35g/kg
ion
−κ̅ ·10
−κ*·10 ̅
4 −κ*·10 ̅
+
0 28.8 41.3 34.6 31.1 27.4 12.1 77.7 74.6 89.7 89.5 76.2 84.9 89.6 97.2 86.1 64.0 101.7 130.1 123.1 114.7 120.3
0.0 29.6 38.1 32.4 29.2 27.0 9.7 76.0 72.9 85.5 85.8 76.3 81.2 85.0 82.2 84.0 63.4
0.0 29.3 38.8 32.0 28.2 25.5 9.8 73.4
H Li+ Na+ K+ Rb+ Cs+ NH4+ Mg2+ Ca2+ Sr2+ Ba2+ Mn2+ Co2+ Ni2+ Cu2+ Zn2+ Cd2+ Fe3+ La3+ Nd3+ Sm3+ Dy3+
(8)
where DHV is given by ln(1 + 1.2I 0.5)}
(15)
The measured partial molal compressibilities for a number of cations and anions at 25 °C in water, 0.725 m NaCl23−25 and seawater SP = 3526,27 are tabulated in Tables 1 and 2. They were calculated from chloride and sodium salts on the conventional scale, κ̅ (H+) = 0 cm3 mol−1 bar−1. The cation values in 0.725 m NaCl are in reasonable agreement with the limited results in seawater. Indicating that 0.725 m NaCl is a reasonable model
2 VM̅ = V̅M0 − Z M DHV
2 V mcma [Z M (Bc,a )′
=
DHκ = (A κ ,S /4){(I 0.5/(1 + 1.2I 0.5) + (2/1.2)
5
a
(14)
−∂β(2)V c,a /∂P
0
4
4
dx.doi.org/10.1021/je400734v | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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Table 2. Measured Partial Molal Adiabatic Compressibility (cm3 mol−1 bar−1) of Anions Measured in Water, 0.725 m NaCl and S = 35 g kg−1 Seawater at 25°C water ion −
F Cl− Br− I− OH− NO3− B(OH)4− HCO3− ClO4− BrO3− CH3COO− CO32‑ SO42‑ S2O32‑ H2PO4− HPO42‑ PO43‑
−κ̅ ·10 0
32.2 7.7 −0.7 −10.0 40.3 −2.4 60.2 31.8 −11.7 10.4 15.7 68.6 66.9 11.1 47.7 89.2 120.9
4
Table 3. The Measured and Calculated Partial Molal Adiabatic Compressibility (cm3 mol−1 bar−1) of Cations in 0.725 m NaCl at 25°C
0.725 m NaCl
seawater S = 35
measured
calculated
delta
−κ*·10 ̅
−κ*·10 ̅
ion
−κ̅ ·10
−κ*·10 ̅
4 −κ*·10 ̅
+
0.0 29.6 38.1 32.4 29.2 27.0 9.7 76.0 72.9 85.5 85.8 76.3 81.2 85.0 82.2 84.0 63.4
0.0 26.0 37.9 30.0 28.4 22.2 7.7 74.8 69.7 86.1 83.5 69.7 78.7 81.7 36.1 83.5 50.9
0.0 3.6 0.2 2.4 0.8 4.8 2.0 1.2 3.2 −0.6 2.3 6.6 2.5 3.3 46.1 0.5 12.5
4
23.3 1.5 −4.4 −14.6 30.3 −9.4 39.9 14.1
47.8 39.1
4
H Li+ Na+ K+ Rb+ Cs+ NH+4 Mg2+ Ca2+ Sr2+ Ba2+ Mn2+ Co2+ Ni2+ Cu2+ Zn2+ Cd2+
1.5 −4.9 −14.2 −7.0 −6.7
38.2
51.3 38.2 30.7
0
4
4
Table 4. The Measured and Calculated Partial Molal Adiabatic Compressibility (cm3 mol−1 bar−1) of Anions in 0.725 m NaCl at 25°C ion F− Cl− Br− I− OH− NO3− B(OH)4− HCO3− ClO4− BrO3− CH3COO− CO32‑ SO42‑ S2O32‑ H2PO4− HPO42‑ PO43‑
measured
calculated
delta
−κ0̅ ·104
4 −κ*·10 ̅
4 −κ*·10 ̅
23.3 1.5 −4.4 −14.6 30.3 −9.4 39.9 14.1 12.8 3.6 −1.6 47.8 39.1 56.0 51.3 38.2 30.7
22.7 1.7 −5.6 −16.4 28.9 −8.7 29.4 16.3
0.6 −0.2 1.2 1.8 1.4 −0.7 10.5 −2.2
45.5 41.9
2.3 −2.8
30.3 36.8 59.3
21.0 1.4 −28.6
in Tables 3 and 4. The calculated results are in reasonable agreement (average of ± 3.3 cm3 mol−1 bar−1) for most of the cations. The larger errors for Cd2+ and Cu2+ may be due to the limited concentration data used for the Pitzer fits. The measured values for Cu2+ may also be in error due to it being plated on the sound speed probe.14 The differences for the anions are much larger (average of ± 8 cm3 mol−1 bar−1). The larger delta for B(OH)4− is due to the higher measured value in 0.725m NaCl and has been attributed to the increase in the formation of the complex between Na+ and B(OH)4− in 0.725m NaCl.22 The larger errors for H2PO4− and PO43‑ may be related to the limited concentration sound speed measurements in water and changes in the hydrolysis in 0.725 m NaCl.13 Further sound speed studies are needed to examine the compressibility of the phosphate system.
Figure 2. The partial molal compressibilities (cm3 mol−1bar−1) of cations and anions in 0.725 m NaCl and water at 25 °C.
for average seawater. As shown in Figure 2, the cation values of κ̅ (i) in 0.725 m NaCl show a linear relationship with the values in water with the exception of Cu2+. The anion values of κ̅ (i) in 0.725 m NaCl of the simple monatomic ions also are linear related to the values in water. The oxy-anions show an offset from the linear behavior. This is probably related to difference in the hydration of these anions in the two media. Equations 12 and 13 have been used to estimate the partial molal compressibility of a number of cations and anions in 0.725 m NaCl at 25 °C. The estimated values of κ̅ (i) for cations and anions at 25 °C are compared to measured values C
dx.doi.org/10.1021/je400734v | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table A1. Pitzer Coefficients for the Partial Molal Adiabatic Compressibility Chloride Salts in Water at 25°C salt HCl LiCl NaCl KCl RbCl CsCl NH4Cl MgCl2 CaCl2 SrCl2 BaCl2 MnCl2 CoCl2 NiCl2 CuCl2 ZnCl2 CdCl2 FeCl3 LaCl3 NdCl3 SmCl3 DyCl3
−104 κ0̅ 7.7 36.5 49.0 42.3 38.8 35.1 19.8 93.1 90.0 105.1 104.9 91.6 100.4 105.0 112.7 101.5 79.4 124.8 153.2 146.2 137.8 143.5
β(0)MXκ
β(1)MXκ −09
−4.975·10 5.525·10−10 8.936·10−09 2.302·10−09 1.498·10−08 2.754·10−09 −1.348·10−08 1.803·10−08 1.857·10−08 2.507·10−08 2.235·10−08 1.249·10−08 1.547·10−08 1.306·10−08 −7.354·10−08 1.418·10−07 1.531·10−08 8.0146·10−08 2.5546·10−08 3.8786·10−08 3.5857·10−08 3.4878·10−08
−08
4.129·10 4.924·10−08 3.769·10−08 5.953·10−08 2.660·10−08 5.220·10−08 8.403·10−08 9.381·10−08 1.100·10−07 8.775·10−08 1.117·10−07 1.272·10−07 1.206·10−07 1.352·10−07 6.673·10−07 −1.875·10−08 1.808·10−07 1.0994·10−06 2.7164·10−07 1.4416·10−07 1.7734·10−07 1.7324·10−07
CκMX
std error
max m
1.843·10−09 1.357·10−09 −3.759·10−10 1.310·10−09 −3.149·10−09 3.987·10−09 5.982·10−09 −1.348·10−09 −1.748·10−09 −3.427·10−09 −2.576·10−09 1.338·10−09 3.275·10−10 1.735·10−09 3.517·10−08 −5.986·10−08 −8.950·10−10 −2.0216·10−06 −3.0569·10−10 −7.7954·10−09 −7.1470·10−09 −5.9808·10−09
0.04 0.01 0.07 0.05 0.07 0.07 0.03 0.26 0.16 0.03 0.06 0.45 0.14 0.06 1.75 0.56 1.07 0.16 0.57 0.19 0.13 0.14
1.3 1.1 6.1 1.0 1.0 0.6 1.0 5.5 1.0 1.0 1.0 1.0 1.0 1.0 0.7 1.0 1.0 0.1 1.1 1.3 1.0 0.9
Table A2. Pitzer Coefficients for the Partial Molal Adiabatic Compressibility Sodium and Potassium Salts in Water at 25°C salt NaF NaCl NaBr NaI NaOH NaNO3 NaB(OH)4 NaHCO3 NaClO4 NaBrO3 NaCH3CO2 Na2CO3 Na2SO4 Na2S2O3 NaH2PO4 Na2HPO4 Na3PO4 KF KCl KBr KI KNO3 KHCO3 K2CO3 K2SO4 KH2PO4 K2HPO4 K3PO4 NH4Br
−104 κ0̅ 73.5 49 40.7 31.3 81.7 38.9 101.5 73.1 29.61 51.65 57.02 151.3 149.6 134.96 89 171.9 245 63 42.3 33.8 22.9 28.8 59.8 144.3 132.4 84.8 157.3 225.8 12.3
βMX(0)κ
βMX(1)κ
βMX(2)κ
std error
max m
1.237·10−08 8.936·10−09 3.139·10−09 −1.831·10−08 7.846·10−09 −5.147·10−09 −6.973·10−08 −1.017·10−08 1.311·10−07 1.251·10−08 1.969·10−08 3.158·10−08 3.362·10−08 9.688·10−08 2.438·10−08 −1.019·10−08 4.503·10−08 −9.192·10−10 2.302·10−09 1.881·10−09 8.692·10−09 7.076·10−08 1.065·10−08 2.210·10−08 3.619·10−08 −1.398·10−07 1.049·10−08 2.716·10−08 −1.482·10−08
5.345·10−08 3.769·10−08 3.828·10−08 8.280·10−08 7.053·10−08 6.161·10−08 3.106·10−07 1.290·10−07 −1.803·10−07 4.391·10−08 4.995·10−08 1.836·10−07 1.964·10−07 −1.788·10−07 9.437·10−08 3.801·10−07 5.741·10−07 7.721·10−08 5.953·10−08 4.602·10−08 1.897·10−08 −1.111·10−07 7.706·10−08 −6.523·10−08 1.760·10−07 4.410·10−07 3.218·10−07 5.548·10−07 8.121·10−08
3.778·10−11 −3.759·10−10 1.294·10−09 8.092·10−09 2.786·10−09 3.911·10−09 3.544·10−08 8.881·10−09 −9.587·10−08 2.220·10−09 −4.600·10−09 −3.703·10−09 −4.469·10−09 −1.527·10−08 −3.059·10−09 3.397·10−08 −7.129·10−09 3.761·10−09 1.310·10−09 1.601·10−09 −1.612·10−09 −2.573·10−08 3.536·10−10 −7.666·10−09 −6.940·10−09 6.667·10−08 8.095·10−09 4.810·10−09 5.199·10−09
0.02 0.07 0.01 0.03 0.06 0.09 0.34 0.03 0.04 0.20 0.09 0.64 0.13 0.19 0.36 0.18 0.12 0.06 0.05 0.01 0.05 0.30 0.03 0.04 0.01 0.85 0.28 0.26 0.01
0.80 6.10 1.00 1.00 0.90 1.00 0.90 0.80 0.50 1.00 1.00 0.90 1.60 1.00 1.10 0.50 0.70 1.10 1.00 1.00 1.00 1.00 1.00 0.90 0.50 1.00 1.00 0.70 1.00
are needed for some of the Na+ salts over a range of temperatures in 0.725 m NaCl to compare to the estimates using the Pitzer equations. Estimation of the Partial Molal Compressibility of Ions in S = 35 g/kg seawater. For seawater, the Pitzer equations
Since the Pitzer parameters for the major salts are known from (0 to 95) °C, and a few from (0 to 50) °C, it is possible to determine reasonable estimates of the partial molal compressibilities for some of the ions over a wide range of temperatures. More experimental compressibility measurements D
dx.doi.org/10.1021/je400734v | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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Table A3. Pitzer Coefficients for the Partial Molal Adiabatic Compressibility Sulfates in Water at 25°C −104 κ0̅
salt MgSO4 MnSO4 CoSO4 NiSO4 ZnSO4 CdSO4
144.0 143.1 151.9 156.6 153.1 131
βMX(0)κ
βMX(1)κ
−08
βMX(2)κ −07
1.3705·10 −6.7119·10−08 −6.6764·10−08 −6.9937·10−08 −4.8600·10−08 −8.0738·10−08
−06
4.3540·10 6.9876·10−07 7.1334·10−07 7.2681·10−07 6.5818·10−07 7.0823·10−07
5.4995·10 7.6687·10−06 7.3981·10−06 8.6122·10−06 9.8084·10−06 3.2353·10−06
CκMX
std error
max m
3.2920·10−09 3.7223·10−08 3.9060·10−08 4.1567·10−08 2.8390·10−08 4.6576·10−07
0.32 0.40 0.52 0.28 0.22 0.24
2.4 1.1 1.0 0.9 1.0 0.9
Table A4. Pitzer Coefficients for the Partial Molal Adiabatic Compressibility (cm3 mol−1 bar−1) Salts Fit to eq 5 from 0 to 50 °C Y(25 °C)
Y1
Y2
Y3
7.7 −4.9750·10−09 4.1291·10−08 1.8430·10−09 81.7 7.8458·10−09 7.0526·10−08 2.7861·10−09 101.5 −6.9728·10−08 3.1063·10−07 3.5440·10−08 73.1 −1.017·10−08 1.290·10−07 8.881·10−09 151.3 3.1583·10−08 1.8363·10−07 −3.7026·10−09
4.1311·10−05 4.0089·10−09 −8.7038·10−09 −1.6733·10−09 0.00011489 4.8088·10−09 −1.2017·10−08 −2.0952·10−09 9.4215·10−05 −6.0810·10−09 1.1968·10−08 2.4742·10−09 −0.0001124 −4.682·10−08 1.0976·10−07 1.7865·10−08 0.0004655 2.9388·10−08 −1.1981·10−07 −1.6235·10−08
−5.8587·10−07 2.4950·10−12 −6.5352·10−12 −2.4903·10−13 −8.88·10−07 6.4201·10−11 −1.6853·10−10 −2.5177·10−11 −2.004·10−06 −4.3089·10−11 1.2440·10−10 2.1653·10−11 −7.944·10−07 −1.282·10−10 3.4744·10−10 4.0899·10−11 −5.554·10−06 −9.1574·10−11 5.3134·10−10 5.1010·10−11
−3.2880·10−08 −1.2785·10−11 2.8557·10−11 5.2999·10−12 −8.528·10−08 −1.4838·10−11 3.6702·10−11 6.1251·10−12 4.4399·10−08 9.7241·10−12 −2.0909·10−11 −4.2685·10−12 4.7514·10−07 1.1398·10−10 −2.671·10−10 −4.3968·10−11 −7.326·10−07 −7.4051·10−11 2.9580·10−10 4.0615·10−11
salt HCl
NaOH
NaB(OH)4
NaHCO3
Na2CO3
−104 β(0)κ MX β(1)κ MX CκMX −104 β(0)κ MX β(1)κ MX CκMX −104 β(0)κ MX β(1)κ MX CκMX −104 β(0)κ MX β(1)κ MX CκMX −104 β(0)κ MX β(1)κ MX CκMX
κ0̅
κ0̅
κ0̅
κ0̅
κ0̅
Table A5. Pitzer Coefficients for the Partial Molal Adiabatic Compressibility (cm3 mol−1 bar−1) Salts Fit to eq 5 from 0 to 95 °C Y (25 °C)
Y1
Y2
Y3
49.0 8.9362·10−09 3.7688·10−08 −3.7593·10−10 149.6 3.3616·10−08 1.9641·10−07 −4.4691·10−09 93.1 1.8025·10−08 9.3810·10−08 −1.3479·10−09 143.96 1.3705·10−08 4.3540·10−07 5.4995·10−06 3.2920·10−09
6.2368·10−05 −1.3820·10−10 9.8551·10−11 8.0419·10−12 0.00016056 −3.9070·10−10 −5.2718·10−10 1.0458·10−10 9.2213·10−05 −1.6024·10−10 1.2538·10−09 1.6641·10−11 −0.0003637 1.7221·10−10 −9.5297·10−10 2.8705·10−06 −9.6678·10−11
−1.149·10−06 1.6866·10−12 1.6714·10−11 −9.7664·10−15 −2.942·10−06 7.7371·10−12 7.2927·10−11 −2.2790·10−12 −1.822·10−06 5.5779·10−12 7.2820·10−12 −5.3710·10−13 −1.669·10−05 −4.6579·10−12 9.4839·10−11 7.5565·10−08 3.0244·10−12
7.1325·10−09 7.6565·10−15 −1.8757·10−13 −1.7721·10−15 2.3003·10−08 −4.8848·10−14 −4.9191·10−13 1.9121·10−14 1.0005·10−08 −3.8028·10−14 1.9609·10−13 4.1006·10−15 −5.863·10−08 6.0188·10−14 −4.6478·10−13 1.7815·10−10 −3.3463·10−14
salt NaCl
Na2SO4
MgCl2
MgSO4
−104 β(0)κ MX % CκMX −104 β(0)κ MX β(1)κ MX CκMX −104 β(0)κ MX β(1)κ MX CκMX −104 β(0)κ MX β(1)κ MX β(2)κ MX CκMX
κ0̅
κ0̅
κ0̅
κ0̅
needed to determine the partial molal compressibilities are more complicated, and largely related to the major cations and anions in seawater
κX̅ = κ x̅ 0 − Z2x DH + 2RTmNa [(B κNa,X + mNa C κNa,X )] + 2RTmMg [(BκMg,X + mSO4 CκMg,X )] κ + 2RTmCa [(BCa,X + mCa CκM,HCO3)]
0 2 κ κ κM̅ = κM ̅ − Z MDH + 2RTmCl [(BM,Cl + mCl CM,Cl )]
Estimates for the partial molal compressibility of ions in seawater are limited since Pitzer parameters for sulfate and bicarbonate parameters are only available for Na+ and Mg2+ salts.
+ 2RTmSO4 [(BκM,SO4 + mSO4 CκM,SO4 )] + 2RTmHCO3[(BκM,HCO3 + mSO4 CκM,HCO3)]
(17)
(16) E
dx.doi.org/10.1021/je400734v | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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(16) Millero, F. J.; Rico, J.; Schreiber, D. R. PVT properties of concentrated aqueous electrolytes. II. Compressibilities and apparent molar compressibilities of aqueous NaCl, Na2SO2, MgCl2, and MgSO4 from dilute solution to saturation and from 0 to 50 °C. J. Solution Chem. 1982, 11, 671−686. (17) Hershey, J. P.; Sotolongo, S.; Millero, F. J. Densities and compressibilities of aqueous sodium carbonate and bicarbonate from 0 to 45 °C. J. Solution Chem. 1983, 12, 233−254. (18) Hershey, J. P.; Damesceno, R.; Millero, F. J. Densities and compressibilities of aqueous HCl and NaOH from 0 to 45 °C. The effect of pressure on the ionization of water. J. Solution Chem. 1984, 13, 825−848. (19) Dedick, E.; Stade, D.; Sotolongo, S.; Hershey, J. P.; Millero, F. J.. The PVT properties of concentrated aqueous electrolytes. IX. The volume properties of KCl and K2SO4 and their mixtures with NaCl and Na2SO4 as a function of temperature. J. Solution Chem. 1990, 19, 353−374. (20) Millero, F. J.; Lampreia, M. I. The PVT properties of concentrated aqueous electrolytes. IV. Changes in the compressibilities of mixing the major sea salts at 25°C. J. Solution Chem. 1985, 14, 853− 864. (21) Krumgalz, B. S.; Starinsky, A.; Pitzer, K. S. Ion-interactions approach: Pressure effect on the solubility of some minerals in Submarine brines. J. Solution Chem. 1999, 28, 667−292. (22) Ward, G. K.; Millero, F. J. The effect of pressure on the ionization of boric acid in sodium chloride and seawater from molal volume data at 0 and 25°C. Geochim. Cosmochim. Acta 1975, 39, 1595−1604. (23) Millero, F. J.; Kembro, A.; Lo Surdo, A. Adiabatic partial molal compressibilities of electrolytes in 0.725m NaCl solutions at 25 °C. J. Phys. Chem. 1980, 84, 2728−2734. (24) Millero, F. J.; Huang, F.; Lo Surdo, A.; Vinokurova, F. Partial molal volumes and compressibilities of phosphoric acid and sodium phosphates in 0.725 m NaCl at 25°C. J. Phys. Chem. B 2010, 114, 16099−16104. (25) Millero, F. J.; Ward, G. K.; Lo Surdo, A.; Huang, F. Effect of pressure on the dissociation constant of boric acid in water and seawater. Geochim. Cosmochim. Acta 2011, 76, 83−92. (26) Millero, F. J.; Huang, F. The effect of pressure on transition metals in seawater. Deep-Sea Res. I 2011, 58, 298−305. (27) Millero, F. J.; Huang, F. The partial molal volume and compressibility of salts in seawater. Geochim. Cosmochim. Acta 2013, 104, 19−28.
APPENDIX (1)κ κ + − The values of κ0̅ , β(0)κ MX , βMX , and CMX for Na and Cl salts at 25 °C are given in Tables A1 and A2. The values for sulfates are given in Table A3. The effect of temperature on the parameters fit to eq 6 from 0 to 50 °C and 0 to 95 °C are tabulated in Tables A4 and A5.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Funding
The authors wish to acknowledge the support of the oceanographic section of the National Science Foundation and the National Oceanic and Atmospheric Administration Office for supporting our Marine Physical Chemistry work. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Pitzer, K. S. Activity Coefficients in Electrolyte Solutions; CRC Press: Boca Raton, FL, 1991. (2) Rodriguez, C.; Millero, F. J. Estimating the densities and compressibilities of seawater to high temperatures using the Pitzer equations. Aqua. Geochem. 2013, 19, 115−133. (3) Millero, F. J. Effects of pressure and temperature on activity coefficients; In Activity Coefficients in Electrolyte Solutions; CRC Press: Boca Raton, FL, 1991; Chapter 2, pp 63−151. (4) Millero, F. J. Influence of pressure on chemical processes in the sea. In Chemical Oceanography, 2nd ed.; Riley, J. P., Chester, R., Eds., Academic Press: San Diego, CA, 1983; Vol. 8, pp 1−88, . (5) Monnin, C. The influence of pressure on the activity coefficients of the solutes and on the solubility of minerals in the system Na-CaCl-SO4-H2O to 200°C and 1 kbar and to high NaCl concentration. Geochim. Cosmochim. Acta 1990, 54, 3265−3282. (6) Pierrot, D.; Millero, F. J. The apparent molal volume and compressibility of seawater fit to the Pitzer equations. J. Solution Chem. 2000, 29, 719−742. (7) Millero, F. J.; Vinokurova, F.; Fernandez, M.; Hershey, J. P. PVT properties of concentrated electrolytes. VI. The speed of sound and apparent molal compressibilities of NaCl, Na2SO4, MgCl2 and MgSO4 solutions from 0 to 100°C. J. Solution Chem. 1987, 16, 269−284. (8) Millero, F. J.; Kubinski, T. Speed of sound in seawater as a function of temperature and salinity at one atmosphere. J. Acoust. Soc. Am. 1975, 57, 312−319. (9) Millero, F. J.; Gomar, F.; Oster, J. The partial molal volume and compressibility change for the formation of the calcium sulfate ion pair at 25°C. J. Solution Chem. 1977, 6, 269−280. (10) Chen, C.-T.; Millero, F. J. The volume and compressibility change for the formation of LaSO4+ ion pair at 25°C. J. Solution Chem. 1977, 6, 589−607. (11) Millero, F. J.; Ward, G. K.; Chetirkin, P. V. Relative sound velocities of sea salts at 25 °C. J. Acoust. Soc. Am. 1977, 61, 1492− 1498. (12) Chen, C. -T.; Chen, L. -S.; Millero, F. J. The speed of sound in NaCl, MgCl2, Na2SO4 aqueous solutions as functions of concentration, temperature and pressure. J. Acoust. Soc. Am. 1978, 63, 1795−1800. (13) Lo Surdo, A.; Bernstrom, K.; Jonsson, C. −A.; Millero, F. J. Molal volume and adiabatic compressibility of aqueous phosphate solutions at 25 °C. J. Phys. Chem. 1979, 83 (10), 1255−1262. (14) Lo Surdo, A.; Millero, F. J. The volume and compressibility change for the formation of transition metal sulfate ion pairs at 25 °C. J. Solution Chem. 1980, 9, 163−181. (15) Lo Surdo, A.; Millero, F. J. Apparent molal volumes and adiabatic compressibilities of aqueous transition metal chlorides at 25 °C. J. Phys. Chem. 1980, 84, 710−715. F
dx.doi.org/10.1021/je400734v | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
