Article pubs.acs.org/jced
Thermodynamic Study of the NaNO3−Cd(NO3)2−H2O Ternary System at 298.15 K by the Potential Difference Method Dan Wang,†,‡ Xiao-Hui Wen,†,‡ Wen-Yao Zhang,†,‡ and Shi-Hua Sang*,†,‡ †
College of Materials and Chemistry & Chemical Engineering, Chengdu University of Technology, Chengdu 610059, P. R. China Mineral Resources Chemistry Key Laboratory of Sichuan Higher Education Institutions, Chengdu 610059, P. R. China
‡
ABSTRACT: In this work, we have made some thermodynamic investigations about the NaNO3−Cd(NO3)2−H2O ternary system. The potential difference method of the battery cell, Na−ISE|NaNO3 (m1), Cd(NO3)2 (m2)|NO3−ISE, was used to study the activity coefficients in this mixed system at 298.15 K in the total ionic strengths range 0.0100− 1.0000 mol·kg−1 with different ionic strength fractions yb of Cd(NO3)2 with yb = (0, 0.2, 0.4, 0.6, and 0.8). There was a good Nernst response between Na−ISE and NO3−ISE in this work, and the mean activity coefficients of NaNO3 can be interpreted well by the Pitzer models. Furthermore, the mixing Pitzer ion interaction parameters of θNa,Cd and ψNa,Cd,NO3 were fitted from Pitzer’s equation, and the two parameters were applied to compute the values of the mean activity coefficients of Cd(NO3)2, the osmotic coefficients, the solvent activity, and the excess Gibbs free energy in this mixed system. The CoCl2−CoSO4−H2O system has been determined by Pournaghdy et al.1 Cs and Ca salts were thermodynamically investigated by Hu et al.,11−13 and the activity coefficients of the NaCl−Na2SO4−H2O14,15 and KI−KNO3−H2O16 systems were also studied by researchers. In the early stage, our group performed some research on mixed solutions, for example: the mean activity coefficients of KBr in the KBr−K2SO4−H2O17 and in KBr−K2B4O7−H2O ternary systems,18 those of NaBr in NaBr−Na2B4O7− H2O19and NaBr−SrBr2−H2O ternary systems,20 and those of KCl in KCl−K2B4O7−H2O.21 Although the thermodynamic properties have been widely studied by scholars for more than 100 years,22−28 there are many relevant data of the electrolytic system, which are not reported, especially the rare reports of the activity coefficients of the low concentration of heavy metals. The investigation of heavy metals is important in the natural environment due to contamination from petroleum cracking catalysts released as refinery waste products, and in the process of mining and the process of making leather, and heavy metals can also get mobilized into groundwater and surface water from soils and ores through both natural processes and anthropogenic activities. Heavy metal elements are widely distributed in nature, and heavy metal contamination in natural water poses a great threat to millions of people in many regions of the world. Therefore, the main goals of this work were to use the potential difference method to measure the activity coefficients of NaNO3 and Cd(NO3)2 in ternary mixed solutions and activities of water, excess Gibbs free energies, and osmotic coefficient
1. INTRODUCTION Thermodynamic properties of ternary mixed solutions play important roles in fields such as food processing, biology, atmospheric science, and so on. These properties also form significant information for the operation and design of several chemical desalination processes.1 The studies of these areas listed above need knowledge of the thermodynamic properties of the water−salt system, such as the activity coefficient, permeability coefficient, excess free energy, and so on. For example, the thermodynamic properties of the study lay a foundation for the research on phase equilibrium, and the infinite dilution activity coefficients can also be applied to the calculation of solubility. Researchers use those properties to handle related problems in different areas. Activity coefficients of electrolyte solutions have been detected by the kinetic method, the conductivity method, the equal pressure method, gas−liquid chromatography, the ion selective electrode method, and so on. An ion selective electrode is a kind of electrochemical sensor, which can measure the activity of some ions in solution, reaching 10−6. Ion selective electrodes have caused concern to humans,2−4 and over 30 kinds of those have been found. Research reports about calculating the activity coefficients by making use of Pitzer equations are increasing rapidly. That is, individual ionic activity coefficients of sodium halides in glucose−water solutions, and osmotic coefficients and activity coefficients in aqueous aminoethanoic acid−NaCl mixtures at 298.15 K were measured5,6 Dinane A have studied the NaCl−KCl−NH4Cl−H2O and LiCl−KCl−NH4Cl−H2O systems;7,8 Roy et al. studied the InCl3−HCl−H2O system9 and Xie et al. studied the activity coefficients of o-, m-, p-xylene in aqueous salt solutions.10 © XXXX American Chemical Society
Received: September 7, 2016 Accepted: February 10, 2017
A
DOI: 10.1021/acs.jced.6b00790 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
in the total ionic strengths range of 0.0100−1.0000 mol·kg−1 at 298.15 K. The parameters of θNa,Cd and ψNa,Cd,NO3 were also fitted in these ternary mixed solutions.
3. RESULTS AND DISCUSSIONS 3.1. Performance of the electrode. For cell (a), the γ0 of pure NaNO329 and each corresponding potential (Ea) had the following relations:
2. EXPERIMENTAL SECTION 2.1. Chemical reagents. Deionized water with the conductivity of 10−6 S·cm−1, Cd(NO3)2, and NaNO3 were G.R. level reagents. Cadmium nitrate tetrahydrate (Cd(NO3)2· 4H2O) (purity is 99.99%) and sodium nitrate (NaNO3) (purity is 99.5%) were made by Chinese Medicine Group Chemical Reagent Co, Ltd. NaNO3 was heated at 388.15 K in an oven for several hours until constant weight, and afterward stored over silica gel in desiccators for use (see Table 1).
Ea ± NaNO3 = E±0 NaNO3 + κ±NaNO3 ln m02γ02± NaNO3
We measured Ea and m0, in line accordance with the solution of single salt NaNO3, and the related molarities and potential difference are listed in Table 3. Figure 1 showed that there was Table 3. Potential Differences, Activity Coefficients, and Uncertainties of the NaNO3 Criterion Solution at 298.15 K and 101.325 kPa
Table 1. Sample Description Table
Chemical Name
Initial Mole Fraction Purity
Purification Method
Final Mole Fraction Purity
NaNO3a
99.5%
oven heating
99.9%
Cd(NO3)2·4H2Oa
99.99%
none
Analysis Method Potential Difference Method Potential Difference Method
The source of chemicals: NaNO3 and Cd(NO3)2·4H2O, Chinese Medicine Group Chemical Reagent Co Ltd..
a
2.2. Measuring Instrument. The main instruments are listed in Table 2, and according to the instructions for the electrodes, we made the electrodes excited and washed them to a blank potential.
AL104 electronic balance Pxsj-216 ion meter a JB-1 blender PNO3-1-01 ion selective electrode 217 reference electrode 6801-01 sodium ion selective electrode Bilon-HW-05
m0a /mol·kg−1
γ0±NaNO329
2 ln α ± NaNO3
Eab /mV
0.0011 0.0020 0.0050 0.0100 0.0201 0.0500 0.1000 0.2000 0.3001 0.4000 0.5000 0.6001 0.7000 0.8000 0.9000 1.0001
0.965 0.951 0.926 0.900 0.867 0.811 0.76 0.702 0.666 0.639 0.618 0.600 0.585 0.571 0.559 0.549
−13.6853 −12.5293 −10.7457 −9.4304 −8.0999 −6.4101 −5.1542 −3.9263 −3.2204 −2.7282 −2.3486 −2.0429 −1.7857 −1.5671 −1.3737 −1.1990
−315.4 −288.4 −243.5 −210.2 −178.4 −133.1 −102.9 −71.3 −51.8 −40.5 −31.8 −24.2 −16.5 −14.4 −4.6 0.9
a m0a indicates the molalities of NaNO3 as single salts in water at 101.325 kPa and standard uncertainties u with 0.68 level of confidence are follows: u (m0) = 0.0001 mol·kg−1, u(T) = 0.1 K. bThe average uncertainties of the potential difference were calculated according to data scatter at 101.325 kPa: u(Ea) = 1.6 mV.
Table 2. Main Instruments Instrument name
(1)
Source U.S. Mettler-Toledo Group Leici Precision Scientific Instrument Co, Ltd.
Beijing Bi-Lang Co, Ltd.
Na−ISE | NaNO3 (m 0) | NO3−ISE
(a)
Na−ISE | NaNO3 (m1), Cd(NO3)2 (m2) | NO3−ISE
(b)
2.3. The cell arrangements. These cells contained no liquid junction, where m0 was the molality of NaNO3 in binary solutions. The m1 and m2 were the molalities of NaNO3 and Cd(NO3)2 in ternary mixed solutions, respectively. In cell (a), we carried on the experiment with m0 from low to high within the molality range 0.0010−1.0000 mol·kg−1 to get the data: 0 potential difference E±NaNO3 and practical response slope κ±NaNO3. Then cell (b) was measured in sequence of ionic strength score yb (yb = 3m2/I) = (0.8, 0.6, 0.4, 0.2, 0) of Cd(NO3)2 in the solution and with I (I = m1 + 3m2) range of 0.0100−1.0000 mol·kg−1. The whole process was kept at temperature within (298.15 ± 0.1) K and regarded the potential difference showing an internal fluctuation at most 0.1 mV in 3 min as balanced.
Figure 1. Plot of Ea vs ln α±NaNO3 for calibration of the sodium and nitrate selective electrode pair at 298.15 K.
a good linear response between E0±NaNO3 and ln α±NaNO3, and E0±NaNO3 was 28.252 mV and κ±NaNO3 was 25.255 mV and the coefficient of determination (R2) is 0.9998 through a linear regression method. The value of κ±NaNO3 approached the theoretical Nernst slope (25.69 mV). We can conclude that Na−ISE and NO3−ISE electrodes have a wonderful Nernst reponse and linear relation, and are well suitable for measurment in ternary mixed solutions. B
DOI: 10.1021/acs.jced.6b00790 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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Table 4. Mean Activity Coefficients of NaNO3 in the NaNO3−Cd(NO3)2−H2O Ternary System and Uncertainties at 298.15 K and 101.325 kPa Ia,c/mol·kg−1
yb
m1a,c/mol·kg−1
m2a,c/mol·kg−1
Ebb,c/mV
γ±NaNO3b,c
0.0100 0.0101 0.0101 0.0099 0.0100 0.0500 0.0498 0.0500 0.0500 0.0501 0.1000 0.1001 0.0999 0.1000 0.1001 0.2001 0.2001 0.1999 0.2001 0.2000 0.2999 0.3001 0.3000 0.3000 0.3000 0.4000 0.3999 0.4000 0.4000 0.4001 0.5001 0.5000 0.5002 0.5000 0.5000 0.5999 0.6001 0.5999 0.6001 0.6000 0.7001 0.7002 0.7001 0.6997 0.7000 0.7998 0.8000 0.7960 0.7999 0.8002 0.9000 0.8998 0.9001 0.9000 0.8999 0.9999 1.0001 1.0000 1.0001
0.0000 0.2019 0.4008 0.5957 0.7795 0.0000 0.1991 0.4001 0.5996 0.7999 0.0000 0.2006 0.3995 0.6006 0.8003 0.0000 0.2000 0.4001 0.5996 0.7996 0.0000 0.2001 0.4001 0.5999 0.8000 0.0000 0.1999 0.4001 0.6000 0.7998 0.0000 0.1999 0.4001 0.6000 0.8000 0.0000 0.2000 0.4000 0.5999 0.8001 0.0000 0.2000 0.4000 0.6000 0.8001 0.0000 0.2001 0.3971 0.6000 0.7999 0.0000 0.1999 0.4000 0.6000 0.8000 0.0000 0.2001 0.3999 0.6000
0.0100 0.0081 0.0060 0.0040 0.0022 0.0500 0.0399 0.0300 0.0200 0.0100 0.1000 0.0800 0.0600 0.0399 0.0200 0.2001 0.1601 0.1199 0.0801 0.0401 0.2999 0.2401 0.1800 0.1200 0.0600 0.4000 0.3200 0.2400 0.1600 0.0801 0.5001 0.4000 0.3001 0.2000 0.1000 0.5999 0.4800 0.3600 0.2401 0.1199 0.7001 0.5601 0.4201 0.2799 0.1399 0.7998 0.6399 0.4799 0.3200 0.1601 0.9000 0.7200 0.5401 0.3600 0.1800 0.9999 0.8000 0.6001 0.4001
0.0000 0.0007 0.0013 0.0020 0.0026 0.0000 0.0033 0.0067 0.0100 0.0134 0.0000 0.0067 0.0133 0.0200 0.0267 0.0000 0.0133 0.0267 0.0400 0.0533 0.0000 0.0200 0.0400 0.0600 0.0800 0.0000 0.0267 0.0534 0.0800 0.1067 0.0000 0.0333 0.0667 0.1000 0.1333 0.0000 0.0400 0.0800 0.1200 0.1600 0.0000 0.0467 0.0933 0.1399 0.1867 0.0000 0.0534 0.1054 0.1600 0.2133 0.0000 0.0600 0.1200 0.1800 0.2400 0.0000 0.0667 0.1333 0.2000
−204.4 −210.4 −218.1 −229.2 −243.5 −127 −132.1 −139.1 −148.9 −165.5 −94.3 −99 −106.3 −116.4 −134.6 −63.5 −68.3 −75.3 −85.6 −103.2 −45.3 −49.6 −56.6 −67 −85 −32.5 −37.4 −44.5 −54.8 −72.8 −22.8 −28.4 −36 −47 −65.3 −16.9 −22.4 −30.3 −41.4 −60.4 −10 −16.3 −24.2 −35.2 −53.1 −5 −11.5 −19.3 −29.6 −47.1 −1.5 −7.5 −15.2 −26.3 −44.9 2.3 −4.6 −12.7 −24
0.8932 0.9150 0.9451 0.9830 1.0340 0.8108 0.8513 0.8883 0.9353 0.9975 0.7657 0.8085 0.8415 0.8813 0.9118 0.6971 0.7348 0.7691 0.8012 0.8398 0.6632 0.7053 0.7377 0.7678 0.7989 0.6378 0.6711 0.7003 0.7305 0.7592 0.6163 0.6397 0.6608 0.6802 0.7035 0.5763 0.5991 0.6156 0.6319 0.6452 0.5648 0.5782 0.5941 0.6116 0.6374 0.5450 0.5556 0.5731 0.5966 0.6264 0.5185 0.5339 0.5505 0.5655 0.5815 0.5025 0.5084 0.5203 0.5322
C
DOI: 10.1021/acs.jced.6b00790 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 4. continued Ia,c/mol·kg−1
yb
m1a,c/mol·kg−1
m2a,c/mol·kg−1
Ebb,c/mV
γ±NaNO3b,c
1.0000
0.8001
0.1999
0.2667
−43.2
0.5411
I, m1, and m2 indicate the total ionic strength for the NaNO3−Cd(NO3)2−H2O ternary system and the molalities of NaNO3 and Cd(NO3)2 in the mixture, respectively. Standard uncertainties u with 0.68 level of confidence are as follows: u(I) = 0.0001 mol·kg−1, u(m1) = 0.0001 mol·kg−1, u(m2) = 0.0001 mol·kg−1, u(T) = 0.1 K. bThe average uncertainties of emf were calculated according to data scatter: u(Eb) = 1.5 mV, u(γ±NaNO3) = 0.063. c Aqueous solution. a
ln γNO − = F + mNa(2BNa , NO3 + ZCNa , NO3) 3
+ mCd (2BCd, NO3 + ZCCd, NO3) + mNamCd ψNa , Cd , NO + mNamCl CNa , NO3 3
+ mCd mNO3CCd, NO3
(7)
and ln γCd2+ = 4F + mNO3(2BCd, NO3 + ZCCd, NO3) + 2mNamNO3CNa , NO3 + mCd mNO3CCd, NO3 Figure 2. Plot of ln γ±NaNO3 vs yb for different ionic strengths I.
+ mNa(2ΦCd , Na + mNO3ψNa , Cd , NO )
Table 5. Values of the Pitzer’s Pure-Electrolyte Parameters β(0), β(1), and Cϕ for NaNO3 and Cd(NO3)2 electrolyte
β(0)/ kg· mol−1
β(1)/ kg· mol−1
Cϕ/kg2·mol−2
σ
ref
NaNO3 Cd(NO3)2
0.00388 0.2865
0.21151 1.668
0.00006 −0.02565
0.00073 0.0020
30 31
where ⎡ ⎤ ⎛2⎞ I1/2 ′ , NO3 F = − Aϕ⎢ + ⎜ ⎟ ln(1 + bI1/2)⎥ + mNamNO3BNa 1/2 ⎝b⎠ ⎣ (1 + bI ) ⎦ ′ NO3 + mNamCd Φ′Cd , Na + mCd mNO3BCd,
I/mol·kg−1
θNa,Cd
ψNa,Cd,NO3
σ
R2
ref
0.01∼1
−0.7940
0.0231
0.0015
0.9846
This work
In these equations (eqs 4−9), the constants b = 1.2 mol−1/2· kg , a = 2.0 mol−1/2·kg1/2, and Aϕ = 0.391475 mol−1/2·kg1/2 for an aqueous solution at 298.15 K. The β(0), β(1), and Cϕ are parameters of the Pitzer equation for a single salt electrolyte solution taken from the literature and are presented in Table 5, and Z is given by Z = mNa + 2mCd + mNO3; and mNa = m1; mCd = m2; and mNO3 = m1 + 2m2. And
3.2. Experimental mean activity coefficient of NaNO3 in the mixture system. The γ±NaNO3 and Eb had the following relations in the cell (b): 3
⎛ ⎞⎡ ⎛ −AϕI 3/2 ⎞ 1 ⎟⎟⎢2⎜ ⎟ Φ = 1 + ⎜⎜ 1/2 ⎝ mNa + mCd + mNO3 ⎠⎢⎣ ⎝ 1 + bI ⎠ ϕ + mNamNO3(BNaNO + ZCNa , NO3) 3
(2)
ϕ + mCd mNO3(BCd , NO3 + ZCCd , NO3)
after arrangements, it became
⎤ + mNamCd {ΦϕNa , Cd + mNO3ψNa , Cd , NO }⎥ 3 ⎥ ⎦
ln γ±NaNO = (E b ± NaNO3 − E±0 NaNO3)/2κ±NaNO3 3
− 1/2 ln m1(m1 + 2m2)
(3)
We can use eq 3 to compute the mean activity coefficients of NaNO3 in the aqueous mixture on the basis of the measurement of Eb±NaNO3 and E0±NaNO3 and κ±NaNO3 previously, and we list the corresponding results in Table 4 and show them in Figure 2. 3.3. Pitzer equation. In these mixed solutions, the γ±NaNO3 and γ±Cd(NO3)2 and Φ can be obtained as follows (eqs 4−9): (γ±NaNO )2 = γNa+· γNO − 3
2
(γ±Cd(NO ) ) = (γCd2 +)·(γNO −) 3 2
ϕ (0) (1) BCA = βCA + βCA exp( −αI1/2)
⎪
⎪
⎪
⎪
(12)
ln γNa+ = F + mNO3(2BNa , NO3 + ZCNa , NO3) + mCd (2ΦCd , Na + mNO3ψNa , Cd , NO ) + mCd mNO3CCd, NO3 3
+ mNamNO3CNa , NO3
(11)
⎧ [1 − (1 + αI1/2) exp( −αI1/2)] ⎫ (0) (1) ⎬ ⎨2 + βCA BCA = βCA α 2I ⎭ ⎩
(5)
3
(10)
The quantities BϕCA, BCA, CCA, and B′CA are defined as the following dependences on ionic strength (C denotes Na+ or Cd2+ and A denotes NO3−; ZC and ZA are the valences of ions C and A):
(4)
3
3
(9)
1/2
Table 6. Values of the Pitzer Mixing Interaction Parameters θNa,Cd and ψNa,Cd,NO3 for the NaNO3−Cd(NO3)2−H2O Ternary System at 298 K
Eb ± NaNO3 = E±0 NaNO3 + κ±NaNO3 ln m1(m1 + 2m2)· γ±2NaNO
(8)
3
CCA =
(6) D
ϕ CCA
(2 |ZCZA|1/2 )
(13) DOI: 10.1021/acs.jced.6b00790 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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Table 7. Mean Activity Coefficients ln γ±Cd(NO3)2, Osmotic Coefficients Φ, Solvent Activity αw, and Excess Gibbs Free Energies GE at T = 298.15 K yb
Ia/mol·kg−1
γ±Cd(NO3)2b
Φb
αwb
GEb/kJ·mol−1
yb
Ia/mol·kg−1
γ±Cd(NO3)2b
Φb
α wb
GEb/kJ·mol−1
0 0 0 0 0 0 0 0 0 0 0 0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.4 0.4 0.4
0.0100 0.0500 0.0500 0.2001 0.2999 0.4000 0.5001 0.5999 0.7001 0.7998 0.9000 0.9999 0.0101 0.0498 0.1001 0.2001 0.3001 0.3999 0.5000 0.6001 0.7002 0.8000 0.8998 1.0001 0.0101 0.0500 0.0999 0.1999 0.3000 0.4000
0.7208 0.6484 0.6484 0.4772 0.4245 0.3867 0.3577 0.3342 0.3147 0.2982 0.2841 0.2719 0.7228 0.6556 0.5756 0.4919 0.4422 0.4070 0.3799 0.3581 0.3400 0.3248 0.3118 0.3006 0.8094 0.6620 0.5860 0.5068 0.4605 0.4280
0.9667 0.9369 0.9369 0.9018 0.8903 0.8818 0.8749 0.8692 0.8642 0.8597 0.8557 0.8520 0.9624 0.9297 0.9107 0.8891 0.8751 0.8645 0.8558 0.8486 0.8424 0.8372 0.8328 0.8290 0.9580 0.9218 0.9013 0.8776 0.8622 0.8503
0.9997 0.9983 0.9983 0.9935 0.9904 0.9874 0.9844 0.9814 0.9784 0.9755 0.9726 0.9698 0.9997 0.9985 0.9970 0.9942 0.9915 0.9889 0.9862 0.9836 0.9811 0.9785 0.9760 0.9735 0.9997 0.9987 0.9974 0.9950 0.9926 0.9902
−0.0004 −0.0036 −0.0036 −0.0252 −0.0435 −0.0639 −0.0858 −0.1090 −0.1333 −0.1585 −0.1847 −0.2116 −0.0004 −0.0037 −0.0098 −0.0255 −0.0442 −0.0651 −0.0878 −0.1119 −0.1373 −0.1637 −0.1911 −0.2194 −0.0004 −0.0037 −0.0097 −0.0253 −0.0440 −0.0649
0.4 0.4 0.4 0.4 0.4 0.4 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
0.5002 0.5999 0.7001 0.7960 0.9001 1.0000 0.0099 0.0500 0.1000 0.2001 0.3000 0.4000 0.5000 0.6001 0.6997 0.7999 0.9000 1.0001 0.0100 0.0501 0.1001 0.2000 0.3000 0.4001 0.5000 0.6000 0.7000 0.8002 0.8999 1.0000
0.4032 0.3834 0.3670 0.3534 0.3416 0.3316 0.8131 0.6685 0.5958 0.5217 0.4792 0.4498 0.4276 0.4100 0.3958 0.3838 0.3738 0.3653 0.8139 0.6745 0.6054 0.5367 0.4983 0.4723 0.4532 0.4383 0.4263 0.4165 0.4084 0.4016
0.8407 0.8327 0.8259 0.8207 0.8156 0.8118 0.9531 0.9132 0.8916 0.8678 0.8526 0.8412 0.8320 0.8244 0.8181 0.8129 0.8088 0.8055 0.9468 0.9034 0.8819 0.8605 0.8483 0.8399 0.8336 0.8286 0.8248 0.8219 0.8198 0.8185
0.9880 0.9857 0.9835 0.9813 0.9791 0.9769 0.9998 0.9988 0.9978 0.9958 0.9936 0.9916 0.9896 0.9876 0.9857 0.9837 0.9818 0.9799 0.9998 0.9990 0.9981 0.9963 0.9945 0.9928 0.9910 0.9893 0.9876 0.9859 0.9842 0.9825
−0.0876 −0.1117 −0.1371 −0.1626 −0.1912 −0.2195 −0.0004 −0.0036 −0.0096 −0.0271 −0.0429 −0.0631 −0.0850 −0.1083 −0.1326 −0.1581 −0.1845 −0.2117 −0.0004 −0.0035 −0.0093 −0.0238 −0.0409 −0.0598 −0.0801 −0.1015 −0.1238 −0.1470 −0.1708 −0.1952
I indicates the total ionic strength for the NaNO3−Cd(NO3)2−H2O ternary system. Standard uncertainties u with a 0.68 level of confidence are as follows: u(I) = 0.0001 mol·kg−1. bThe average uncertainties of the emf were calculated according to data scatter: u(γ±Cd(NO3)2) = 0.0005, u(Φ) = 0.0003, u(αw) = 0.0002, u(GE) = 0.0003. a
Figure 3. Plot of osmotic coefficient Φ of water against total ionic strength I of the NaNO3−Cd(NO3)2−H2O ternary system at different ionic strength fractions yb of Cd(NO3)2 in the mixture at T = 298.15 K.
Figure 4. Plot of the value of the mean activity coefficient for Cd(NO3)2 against the total ionic strength I of the NaNO3− Cd(NO3)2−H2O ternary system at different ionic strength fractions yb of Cd(NO3)2 in the mixture at T = 298.15 K.
⎤ 2 ⎞ ⎧ ⎡ ⎛ 1/2 α I 1/2 ⎫ ⎪ 2⎢⎢⎣1 − ⎜⎝1 + αI + 2 ⎟⎠ exp(−αI )⎥⎥⎦ ⎪ (1) ⎬ βCA ⎨ − α 2I
′ = BCA
⎪ ⎩
⎪ ⎭
I
and
(14)
′ , Cd Φ′Na , Cd = E θNa
and ′ , Cd ΦϕNa , Cd = θNa , Cd + E θNa , Cd + E IθNa
(15)
ΦNa , Cd = θNa , Cd + Eθ Na , Cd
(16)
E
θ Na , Cd =
(17)
J(χNa , Na ) J(χCd , Cd ) ⎤ ⎛ ZNaZCd ⎞⎡ ⎥ ⎜ ⎟⎢J (χ ) − − ⎝ 4I ⎠⎢⎣ Na , Cd ⎥⎦ 2 2 (18)
E
DOI: 10.1021/acs.jced.6b00790 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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3.4. Excess Gibbs free energy and activity of water. GE and αw were calculated from the following relations: GE = RT[2m1(1 − Φ + ln γ±NaNO )] 3
+ 3m2(1 − Φ + ln γ±Cd(NO ) ) 3 2
⎡⎛ 18.0513 ⎞ ⎤ ⎟(2m + 3m )Φ αw = exp⎢⎜ − ⎥ 1 2 ⎝ ⎠ ⎣ ⎦ 1000 Figure 5. Plot of the solvent activity αw for Cd(NO3)2 against total ionic strength I of the NaNO3−Cd(NO3)2−H2O ternary system at different ionic strength fractions yb of Cd(NO3)2 in the mixture at T = 298.15 K.
(b) When we keep yb constant, with I increasing, γ±NaNO3 and γ±Cd(NO3)2 are decreasing. The possible reasons are as follows: (i) In the electrolyte solution, with the concentration increasing and ions close to each other, the force occurs between the ions, mainly the electrostatic attraction, and ion chemical potential decreases; thus, the activity coefficient decreases. (ii) With I increasing, association of ions is significant, a mixed salt system is formed of three ionic species (Na+−NO3−−Cd2+), and the activity coefficient reduces. (3) In Figure 5 and Figure 6, the changes of αw and GE are reduced with increasing total ionic strength.
⎛ Eθ ⎞ ⎛Z Z ⎞ Na , Cd ⎟⎟ + ⎜ Na 2Cd ⎟ ′ , Cd = −⎜⎜ θNa I ⎝ ⎠ ⎝ 8I ⎠ ⎡ χNa , Na J′(χNa , Na ) + ⎢χNa , Cd J′(χNa , Cd ) − ⎢⎣ 2 −
χCd , Cd J′(χCd , Cd ) ⎤ ⎥ ⎥⎦ 2
(19)
where χNa , Cd = 6ZNaZCdAϕI1/2
(20)
J(χ ) = χ[4 + C1χ −C2 exp(−C3χ C4 )]−1
(21)
4. CONCLUSION The thermodynamic investigation of the ternary mixedelectrolyte system NaNO3−Cd(NO3)2−H2O was undertaken at 298.15 K by the potential difference method from the battery cell without a liquid junction, a Na ion-selective electrode (ISE) and a NO3 ion-selective electrode (ISE), and the concentration range 0.0100−1.0000 mol·kg−1 for different ionic strength fractions yb of Cd(NO3)2 with yb = (0.8, 0.6, 0.4, 0.2, 0). In addition, we also obtained some data, for instance the Pitzer ion interaction parameters θNa,Cd and ψNa,Cd,NO3; we used the two parameters to calculate the activity coefficients of Cd(NO3)2, the osmotic coefficients Φ and excess Gibbs free energies of the system GE, and the activities of water αw. In this paper, the investigation showed both that the Pitzer model can be used to describe this aqueous system satisfactorily and that this study provided basic thermodynamic reference data for further research applications.
J′(χ ) = [4 + C1χ −C2 exp(−C3χ C4 )]−1 + [4 + C1χ −C2 exp( −C3χ C4 )]−2 ×[C1χ exp( −C3χ C4 )(C2χ −C2 − 1 + C3C4χ C4 − 1 χ −C2 )] (22)
J ′(χ ) = [4 + C1χ
−C 2
C4
−1
exp(−C3χ )]
+ [4 + C1χ −C2 exp(−C3χ C4 )]−2 ×[C1χ exp( −C3χ C4 )(C2χ −C2 − 1 + C3C4χ C4 − 1 χ −C2 )]
(25)
where m1 and m2 are the total number of anions and cations of the electrolyte produced by dissociation of one molecule of Cd(NO3)2 and NaNO3, respectively. The results of GE and αw are listed in Table 7. We use those data shown in Table 7, and draw four groups of graphics, Figure 3, Figure 4, Figure 5, and Figure 6. (1) In Figure 3, Φ decreases as I ranges from 0.0100 to 1.0000 mol·kg−1. The curve of yb = 0.6 reduces the amplitude the most obviously. And when I is constant, the osmotic coefficient with increasing ionic strength fractions decreases in turn. (2) Comparing Figure 2 and Figure 4, we can get the information as follows: (a) When we keep I constant, with yb increasing, γ±NaNO3 and γ±Cd(NO3)2 are reducing.
Figure 6. Plot of the excess Gibbs free energy GE for a mixed electrolyte solution against total ionic strength I of the NaNO3− Cd(NO3)2−H2O ternary system at different ionic strength fractions yb of Cd(NO3)2 in the mixture at T = 298.15 K. E
(24)
(23)
where C1 = 4.581; C2 = 0.7237; C3 = 0.0120; and C4 = 0.528. Through eqs 4−23, using the multiple linear regression technique, we obtained the mixing ionic parameters θNa,Cd and ψNa,Cd,NO3, which are shown in Table 6. F
DOI: 10.1021/acs.jced.6b00790 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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AUTHOR INFORMATION
Corresponding Author
*Tel: 13032845233, E-mail:
[email protected]. ORCID
Shi-Hua Sang: 0000-0002-5948-3882 Notes
The authors declare no competing financial interest. Funding
This project was supported by the National Natural Science Foundation of China (U1407108, 41373062), and scientific research and innovation team in Universities of Sichuan Provincial Department of Education (15TD0009).
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LIST OF SYMBOLS m molality R gas constant T gas constant E potential difference F Faraday constant I ionic strength GE excess Gibbs free energy αw activity of water θ,ψ Pitzer mixing parameters Φ osmotic coefficients β(0), β(1), CΦ parameters of the Pitzer equation α, b empirical constants AΦ Debye−Hü ckel coefficient for the osmotic coefficient yb fraction of the ionic strength of the electrolyte b in the mixture κ Nernst slope BΦ, B the second virial coefficients B′ B differential of ionic strength ΦΦ, Φ, Φ′ the second virial coefficients J ion of short-range interaction potential between group integral J′ the first order derivative of J Z the sum of products of the absolute value of the charge and the molality χ a function of the ionic strength I Greek Letters
γ±i ionic mean activity coefficients of the electrolyte i in the mixture γ0±i ionic mean activity coefficients of the electrolyte i pure
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DOI: 10.1021/acs.jced.6b00790 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
