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Hygrometric determination of the water activities and the osmotic and activity coefficients of (ammonium chloride + sodium chloride + water) atT = 298.15 K
J. Chem. Thermodynamics 2002, 34, 783–793 doi:10.1006/jcht.2002.0954 Available online at http://www.idealibrary.com on
Hygrometric determination of the water activities and the osmotic and activity coefficients of (ammonium chloride + sodium chloride + water) at T = 298.15 K Abderrahim Dinane, Mohamed El Guendouzi,a and Abdelfetah Mounir Laboratoire de Chimie Physique, D´epartment de Chimie, Facult´e des Sciences Ben M’sik, Universit´e Hassan II Mohammedia, B.P 7955, Casablanca, Maroc
The mixed aqueous electrolyte system of ammonium and sodium chlorides has been studied by the hygrometric method at the temperature 298.15 K. The relative humidities of this system were measured at total molalities from 0.3 mol · kg−1 to 6 mol · kg−1 for different ionic-strength fractions of NH4 Cl with y = (0.33, 0.50, and 0.67). The data obtained allow the deduction of new water activities and osmotic coefficients. The experimental results are compared with the predictions of the extended composed additivity model proposed in our previous work, the Robinson–Stokes, Reilly–Wood– Robinson, and Lietzke–Stoughton models. From these measurements, the new Pitzer mixing ionic parameters were determined and used to predict the solute activity coefficients c 2002 Elsevier Science Ltd. All rights reserved. in the mixture. KEYWORDS: aqueous mixed-electrolyte; ammonium and sodium chloride solutions; relative humidity; water activity; osmotic coefficient; activity coefficient; Pitzer’s model; extended composed additivity (ECA)
1. Introduction Investigation of the thermodynamic properties of aqueous mixed electrolyte solutions is of great interest. Much of this interest arises from the importance of the electrolytes in areas such as desalination, oceanography, biology, geochemistry, atmospheric processes, and the environment. The most common methods for the determination of thermodynamic properties in mixed electrolyte solutions are the isopiestic vapour pressure, (1–4) vapour pressure lowering, (5–7) and e.m.f. techniques. (8–13) In this work, we use the hygrometric method, described in a E-mail: [email protected]
0021–9614/02
c 2002 Elsevier Science Ltd. All rights reserved.
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our previous paper, (14) that yields directly the water activity in aqueous electrolytes. This method has been used for determining thermodynamic properties of binary aqueous solutions (15, 16) and ternary mixed chloride electrolytes. (17) This paper is the continuation of the research on ternary aqueous mixtures of chlorides. The main objectives are to determine thermodynamic properties for the ternary solutions of (ammonium chloride + sodium chloride + water) by the hygrometric method. The thermodynamic behaviour of this system has not been extensively studied. Kirgintsev et al. (18) measured the osmotic coefficients of (ammonium chloride + sodium chloride + water) for different ionicstrength fractions at T = 295.85 K. Meada et al. (19) also measured the osmotic coefficients of this system for x(NaCl) = x(NH4 Cl) = x(H2 O) = 0.33 in the range of total ionic strength I < 5.94 mol · kg−1 by the isopiestic method. Recently, water activities were determined with an electrodynamic balance by Ha et al. (20) for n(NaCl)/n(NH4 Cl) = (1 and 3) in the range of water activity from 0.4 to 0.8. In this work, the measurements of relative humidities for the total molality range from 0.3 mol · kg−1 to 6 mol · kg−1 were performed for the aqueous ternary solution (ammonium chloride + sodium chloride + water) for different ionic-strength fractions from 0.33 to 0.67 at temperature of 298.15 K. The osmotic coefficients were also evaluated for these solutions from the relative humidities. We have used the extended composed additivity (ECA) model proposed in our previous paper (17) to predict water activities of this system. The results are compared with values from three commonly used thermodynamic models. The experimental values are used for the calculation of solute activity coefficients by Pitzer’s model with our newly obtained ionic mixing parameters.
2. Experimental The water activity was determined by a hygrometric method described in our earlier work. (14) The apparatus used in this study of mixed electrolyte solutions is essentially the same as that used for the investigation of aqueous single-electrolyte solutions. It is based on the measurement of the relative humidity over aqueous solutions of non-volatile electrolytes. The apparatus used is a hygrometer in which a droplet of salt solution is maintained on a thin thread. Measurements of the diameter of the previously calibrated droplet permit the calculation of the relative humidity of aqueous solutions. The droplets of a reference solution of NaCl(aq) or LiCl(aq) are deposited on the very thin thread by pulverisation. This thread is stretched over a Perspex support, which is fixed to a cup containing the solution to be studied. The cup is then placed in a thermostatted box. The droplet diameter is measured by a microscope with an ocular-equipped with the micrometer screw. In general, the relative humidity is equivalent to the water activity aw . From measurements of the reference droplet diameters D{aw(ref) } above the reference solution and the same diameters D(aw ) above the studied solution, we calculate the ratio of growth K = D{aw(ref) }/D(aw ) and determine graphically the water activity based upon the variation of the ratio K as a function of the water activity of reference solutions of NaCl(aq) or
Thermodynamic properties of (ammonium chloride + sodium chloride + water) at T = 298.15 K785
LiCl(aq). (14, 15) Generally, the reference relative humidity is 0.84. It is 0.98 for solutions in the medium range of dilution.
3. Results and discussion In this work, measurements of the water activity were made for this mixture as a function of total molality ranging from 0.3 mol · kg−1 to 6 mol · kg−1 , for different ionic-strength fractions of NH4 Cl, y = I (NH4 Cl)/{I (NH4 Cl) + I (NaCl)}, with y = (0.33, 0.50, and 0.67) at the temperature 298.15 K. The solutions were prepared from Merck extrapur-grade chemicals (mass fraction > 0.99) and deionised distilled water. The reference solution is NaCl(aq). The experimental values of water activity are listed in table 1. The experimental uncertainty is between ±2 · 10−4 and ±2 · 10−3 over the experimental molality range. Figure 1 is a plot of aw against total molality m for the different ionic-strength fractions y with the limiting cases of y corresponding to the pure electrolytes. In comparing the relative magnitudes of these water activities at different ionic-strength fractions, we note a relative lowering in the order aw (NH4 Cl)(y=0) > aw(y=0.33) > aw(y=0.50) > aw(y=0.67) > aw (NaCl)(y=1) . From experimental data, we evaluated the molalities of NH4 Cl and NaCl at different constant water activities of the ternary mixture. The dependence of the molality of NaCl against the molality of NH4 Cl at constant water activity is represented in figure 2. The application of the theory to the calculation of thermodynamic properties often involves equations highly complex in form and containing interaction parameters which are not always readily available for mixed electrolytes at the concentration of practical interest. We have proposed in our earlier work (17) a simple rule which allows the properties of mixed electrolyte solutions to be predicted from those of the aqueous solutions of the individual component salts. This ECA “extended composed additivity” model predicts the water activity in mixed electrolyte solutions as: aw = −1 + aw(MX) + aw(NX) − m MX m NX λ − m MX m NX mδ,
(1)
where mMX, mNX, and m are, respectively, the molalities of the electrolytes MX NX in the mixture, and the total molality. Here, aw , aw(MX) , and aw(NX) are, respectively, the water activities of the ternary solution of MX and NX, the water activity of the binary solution of MX at the molality m MX , and the water activity of NX at the molality m NX . The parameters λ and δ, determined experimentally for each system, characterise the deviation from ideality in the mixture of MX and NX for concentrated solution. In dilute solutions, λ = 0 and δ = 0. In general, these quantities depend on the composition and the water activity. In most cases, however, these parameters are fairly constant and arithmetical mean values over a water activity range are used. The unknowns λ and δ may be estimated by a graphical procedure that uses a modified version of equation (1): 1aw /m MX m NX = −λ − mδ,
(2)
where 1aw is the difference between the experimental values of water activity aw and the sum of water activities in the binaries. The quantity on the left is plotted against the total molality m to obtain a linear plot with intercept λ and slope δ.
786
A. Dinane et al. TABLE 1. Ratios of growth K of the NaCl(aq) droplets, water activities aw , and osmotic coefficients φ of mixtures of aqueous ammonium chloride and sodium chloride at total molalities m for different ionic strength fractions y a m(NH4 Cl) mol · kg−1
m(NaCl) mol · kg−1
m mol · kg−1
0.1
0.2
0.3
K
aw
φ
(1.261)
0.9900
0.930
y = 0.33 0.2
0.4
0.6
1.873
0.9800
0.935
0.3
0.6
0.9
1.658
0.9711
0.936
0.5
1.0
1.5
1.391
0.950
0.949
1.0
2.0
3.0
1.123
0.897
1.006
1.5
3.0
4.5
1.000
0.840
1.075
2.0
4.0
6.0
0.920
0.777
1.167
0.908
y = 0.50 0.2
0.2
0.4
(1.166)
0.9870
0.4
0.5
1.0
1.604
0.9680
0.903
0.6
1.0
2.0
1.278
0.934
0.947
1.0
1.5
3.0
1.134
0.900
0.975
2.0
2.0
4.0
1.046
0.864
1.014
3.0
2.5
5.0
0.979
0.826
1.061
4.0
3.0
6.0
0.934
0.790
1.108
y = 0.67 0.2
0.1
0.3
(1.261)
0.9900
0.930
0.4
0.2
0.6
1.873
0.9800
0.887
0.6
0.3
0.9
1.658
0.9701
0.904
1.0
0.5
1.5
1.410
0.952
0.910
2.0
1.0
3.0
1.134
0.900
0.975
3.0
1.5
4.5
1.016
0.849
1.010
4.0
2.0
6.0
0.940
0.777
1.061
a The reference water activity is 0.84; numbers in parentheses are for a reference water activity of 0.98.
We have applied this model to {NH4 Cl(aq) + NaCl(aq)}, and the mean values determined by the graphical procedure are λ = −0.001107 and δ = 0.00007. The standard deviation for the fit is σ (aw ) = 0.0017. Extensive tests on the validity of equation (1) have been carried out and show that aw calculated by employing the assigned values of λ and δ are in good agreement with experiment (figure 3). Three models for the prediction of water activity of the mixtures were used to evaluate the performance of our ECA model. Calculations of the thermodynamic properties of
Thermodynamic properties of (ammonium chloride + sodium chloride + water) at T = 298.15 K787 1.0
aw
0.9
0.8
0.7
0
1
2
3
4
5
6
7
m /(mol . kg − 1)
FIGURE 1. Water activity aw of (ammonium chloride + sodium chloride)(aq) against total molality m at different ionic strength fractions y of NH4 Cl. H, y = 0; +, y = 0.33; ×, y = 0.50; 1, y = 0.67; N, y = 1. 5 y = 0.67
m(NaCl) /(mol . kg − 1)
4 y = 0.50
3 y = 0.33
2
1
0
0
1
2
3
4
5
6
m(NH4Cl) /(mol . kg − 1)
FIGURE 2. Molality of NaCl against the molality of NH4 Cl in mixed (ammonium chloride + sodium chloride)(aq) at constant water activity aw . N, aw = 0.98; H, aw = 0.96; , aw = 0.94; , aw = 0.92; ♦, aw = 0.90; ×, aw = 0.88; +, aw = 0.86; 1, aw = 0.84; , aw = 0.82; , aw = 0.80; , aw = 0.78.
◦ •
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A. Dinane et al. 1.000 y = 0.33 0.950
aw
0.900 0.850 0.800 0.750 0
1
2
3 4 m /(mol . kg − 1)
5
6
7
1.000 y = 0.50 0.950
aw
0.900 0.850 0.800 0.750
0
1
2
3 4 m /(mol . kg − 1)
5
6
7
1.000 y = 0.67 0.950
aw
0.900 0.850 0.800 0.750
0
1
2
3
4
5
6
7
m /(mol . kg − 1)
FIGURE 3. Water activity aw of (ammonium chloride + sodium chloride)(aq) against total molality m at different ionic strength fractions y of 0.33, 0.50, and 0.67. , experimental points; +, present model; 1, RWR model; ×, LS model; ♦, RS model.
•
Thermodynamic properties of (ammonium chloride + sodium chloride + water) at T = 298.15 K789
mixed-electrolyte systems generally require those of the pure component at the same ionic strength I as the mixture. In the case of NH4 Cl(aq) and NaCl(aq), the required quantities were calculated from results obtained in our previous work. (15) Robinson and Stokes (1) proposed a form of the vapour pressure of the mixture involves the additivity lowering solvent vapour pressures of the solutes and extended into the following form: (6) (1 − aw(m) ) = {(1 − aw(MX,m) )(m MX /m) + (1 − aw(NX,m) )(m NX /m)},
(3)
where aw(m) , aw(MX,m) , and aw(NX,m) are, respectively, the water activities of the ternary solutions of MX and NX, and the water activities of the binary solutions of MX and NX at the same molality m as the mixed solution. Another model of a mixed electrolyte solution is that developed by Reilly et al. (RWR). (21) For a solution of molality m MX and m NX , the RWR method predicts the osmotic coefficient of the mixed-electrolyte solution by: (m MX + m NX )(1 − φ) = m MX (1 − φMX ) + m NX (1 − φNX ) + X X (m MX m NX /2){gMN + m∂(gMN )/∂m},
(4)
where φMX and φNX are, respectively, the osmotic coefficients of the solution of MX and X is a quantity that involves interactions NX at the ionic strength I of the mixture, and gMN between pairs of electrolytes. The Lietzke and Stoughton model (22, 23) (LS II) predicts the osmotic coefficient of a multicomponent solution by: (νMX m MX + νNX m NX )φ = νMX m MX φMX + νNX m NX φNX ,
(5)
where νMX is the number of ions released by the complete dissociation of one molecule of component MX, m MX is its molality, and φMX is the osmotic coefficient of the binary solution of component MX at the total ionic strength of the multicomponent solution. The comparison of the water activities calculated with our proposed model ECA, equation (1), and those predicted by the four models shows good agreement (figure 3). The average difference is less than ±0.0005 between our model and the other three. On the basis of the experimental data obtained for the water activity, we evaluated the osmotic coefficients obtained for different ionic-strength fractions y. The obtained osmotic coefficients are listed in table 1 and plotted against m 1/2 in figure 4. The calculations of the osmotic coefficients by the ECA method has been generalised for different mixtures (figure 4). The standard deviation for the osmotic coefficient is σ (φ) = 0.018. The comparison of our results with those of the three models is shown in figure 4. The predictions by the ECA method are very similar to those of the other models at medium and high molalities, but the deviations of ECA become quite large at low total molality. The discrepancy in this region is attributed to the parameters λ and δ, which are, generally, introduced for the middle to higher concentrations, and also to the aw φ relationship by the term 1000/6i νi m i Mw which becomes greater for m < 0.5 mol · kg−1 and yields large deviations for the lower variation of water activity. Figure 5 is a plot of φ calculated from equation (1) as a function of m 1/2 at different ionic strength fractions y. As can be seen from these curves, the values of φ fall in regular and
790
A. Dinane et al. 1.2 y = 0.33 1.1
1.0
0.9
0.8 0.5
1.0
1.5
2.0
2.5
2.0
2.5
2.0
2.5
{m /(mol . kg − 1)}1/2 1.2 y = 0.50 1.1
1.0
0.9
0.5
1.0
1.5 {m /(mol . kg − 1)}1/2
1.2 y = 0.67 1.1
1.0
0.9
0.8 0.5
1.0
1.5 {m /(mol . kg − 1)}1/2
FIGURE 4. Osmotic coefficient φ of (ammonium chloride + sodium chloride)(aq) against m 1/2 at different ionic strength fractions y of 0.33, 0.50, and 0.67. , experimental points; +, present model; 4, RWR model; ×, LS model; ♦, RS model.
•
Thermodynamic properties of (ammonium chloride + sodium chloride + water) at T = 298.15 K791 1.4
1.2
1.0
0.8 0.5
1.0
1.5 {m /(mol . kg − 1)}1/2
2.0
2.5
FIGURE 5. Osmotic coefficients φ of (ammonium chloride + sodium chloride)(aq) against m 1/2 at different ionic strength fractions y of NH4 Cl. , y = 1; , y = 0; 1, y = 0.67; ×, y = 0.50; +, y = 0.33.
•
decreasing order from pure NaCl(aq) to pure NH4 Cl(aq): φ(y = 0) > φ(y = 0.33) > φ(y = 0.50) > φ(y = 0.67) > φ(y=1). The curves at different y are indeed quite similar in their dependence on molality. Pitzer’s model (24–27) provides the simplest and most convenient procedure for calculating the thermodynamic properties of mixed-electrolyte solutions. The activity coefficient γMX of MX in a common-ion mixture of two 1-1 electrolytes is given by Pitzer’s model as ∗ ln γMX = ln γMX + y · 1φ ∗ + y · m[θMN + m · {1 − (y/2)}ψMNX ],
1φ ∗
∗ (φNX
∗ ) φMX
(6)
∗
where is − and the superscript denotes pure components at the same molality as the total molality of the mixture. Here, 1φ ∗ can be expressed as: (0)
(0)
φ
(1)
(1)
1φ ∗ = m{βNX − βMX + h 1 (βNX − βMX ) + m 2 (CNX − CMX )},
(7)
γ∗
where is the solute activity coefficient determined by the ion-interaction model. For component NX, γNX is given by a similar equation: ∗ ln γNX = ln γNX + (1 − y)1φ ∗ + (1 − y)m[θMN + m · {1 − (y/2)}ψMNX ].
β (0) ,
β (1) ,
Cφ
(8)
Values of the ionic parameters and of the pure electrolytes NH4 Cl(aq) and NaCl(aq) were obtained from Pitzer’s expressions by fits of the experimental osmotic coefficients given in our previous work. (15) The corresponding values are β (0) = 0.0738, β (1) = 0.2712, and C φ = 0.00167 for NaCl(aq), and β (0) = 0.0527, β (1) = 0.2011, and C φ = −0.00306 for NH4 Cl(aq).
792
A. Dinane et al.
From the osmotic coefficients determined from the experimental water activities of the mixture studied at different ionic strength fractions, it is possible to determine the unknown Pitzer mixing ionic parameters θ(NH4 ,Na) and ψ(NH4 ,NaCl) , which are not given in the literature. These parameters may be used to predict the solute activity coefficients in the mixture. Both θ(NH4Na) and ψ(NH4NaCl) are estimated by a graphical procedure. This procedure defines the quantity 1φ as the difference between the experimental values φ(expt) and that calculated from equation (1), φ(calc). This yields: m/m(NaCl) · m(NH4 Cl) = θ(NH4 ,Na) + ψ(NH4 ,NaCl) · m,
(9)
so that a plot of 1φ against total molality m should give a straight line with intercept θ(NH4 ,Na) and slope ψ(NH4 ,NaCl) . The values of these ionic parameters are θ(NH4 ,Na) = 0.0159 and ψ(NH4 ,NaCl) = −0.0048, and the standard deviation is σ (1φ) = 0.001. The activity coefficients of NH4 Cl(aq) and NaCl(aq) in the mixture, listed in table 2, were calculated by Pitzer’s equation with the ionic mixing parameters obtained in this work. Figure 6 is the plot of γNH4 Cl and γNaCl as a function of m 1/2 . The extremes of composition are illustrated in this figure, i.e., the activity coefficients of the pure components. The γ (NaCl) decreases rapidly enough with increasing molality, goes through a minimum which varies between total molalities of (1.5 and 2.0) mol · kg−1 , and then increases. The γ (NH4 Cl) decreases with increasing molality over the entire total concentration range. 1.2
1.0
0.8
0.6
0.4 0.5
1.0
1.5
2.0
2.5
3.0
{m / (mol . kg − 1)}1/2
FIGURE 6. Activity coefficients γ (NH4 Cl) and γ (NaCl) against m 1/2 at different ionic strength fractions y of NH4 Cl. Upper curves are for NaCl, and lower curves are for NH4 Cl. , y = 1; , y = 0; 1, y = 0.67; ×, y = 0.50; +, y = 0.33.
•
Thermodynamic properties of (ammonium chloride + sodium chloride + water) at T = 298.15 K793 TABLE 2. Activity coefficients γ NH4 Cl(aq) and (NaCl)(aq) of NaCl(aq) in (ammonium chloride + sodium chloride)(aq) at total molality m for different ionic-strength fractions of NH4 Cl y = 0.33 y = 0.50 y = 0.67 m/(mol · kg−1 ) γ (NH4 Cl) γ (NaCl) m/(mol · kg−1 ) γ (NH4 Cl) γ (NaCl) m/(mol · kg−1 ) γ (NH4 Cl) γ (NaCl) 0.3 0.6 0.9 1.5 3.0 4.5 6.0
0.681 0.829 0.601 0.569 0.529 0.497 0.458
0.704 0.667 0.651 0.645 0.688 0.774 0.896
0.4 1.0 2.0 3.0 4.0 5.0 6.0
0.660 0.596 0.557 0.536 0.519 0.501 0.480
0.686 0.646 0.649 0.680 0.728 0.790 0.864
0.3 0.6 0.9 1.5 3.0 4.5 6.0
0.683 0.632 0.605 0.575 0.544 0.526 0.505
0.702 0.664 0.647 0.639 0.673 0.743 0.837
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.
Robinson, R. A; Stokes, R. H. Electrolyte Solutions. Butterworth: London. 1955. Rard, J. A.; Clegg, S. L.; Palmer, D. A. J. Solution Chem. 2000, 29, 1–49. Holmes, H. F.; Mesmer, R. E. J. Chem. Thermodynamics 1996, 28, 67–81. Todorovic, M.; Ninkovic, R. J. Chem. Thermodynamics 1996, 28, 491–496. Gokcen, N. A. Report of Investigations RI8372. U. S. Dept. of the Interior. Bureau of Mines, 1979. El Golli, S.; Arnaud, G.; Bricard, J.; Treiner, C. J. Aerosol Sci. 1977, 8, 39–54. Michielsen, M.; Loix, G. Y.; Gilbert, J.; Cleas, P. J. Chim. Phys. 1982, 79, 247–252. Harned, H. N.; Owen, B. B. The Physical Chemistry of Electrolyte Solutions. Reinhold: New York. 1958. Roy, R. N.; Rice, R. A.; Vogel, K. M.; Roy, L. N. J. Phys. Chem. 1990, 94, 7706–7710. Sarada, S.; Ananthaswamy, J. J. Chem. Soc. Faraday Trans. 1990, 86, 81–84. Downes, C. J. J. Phys. Chem. 1970, 74, 2153–2160. Lanier, R. D. J. Phys. Chem. 1965, 69, 3992–3998. Lietzke, M. H.; O’Brien, H. A. Jr. J. Phys. Chem. 1968, 72, 4408–4414. El Guendouzi, M.; Dinane, A. J. Chem. Thermodynamics 2000, 32, 297–313. El Guendouzi, M.; Dinane, A.; Mounir, A. J. Chem. Thermodynamics (in press). El Guendouzi, M.; Mounir, A.; Dinane, A. J. Chem. Thermodynamics (accepted for publication). Dinane, A.; El Guendouzi, M.; Mounir, A. J. Chem. Thermodynamics (in press). Kirgint’sev, A. N.; Luk’yanov, A. V. Russ. J. Phys. Chem. 1963, 37, 1501–1502. Maeda, M.; Hisada, O.; Ito, K.; Kinjo, Y. J. Chem. Soc. Faraday Trans. 1 1989, 85, 2555–2562. Ha, Z.; Choy, L.; Chan, C. K. J. Geophys. Res. 2000, 105, 11699–11709. Reilly, P. J.; Wood, R. H.; Robinson, R. A. J. Phys. Chem. 1971, 75, 1305–1314. Lietzke, M. H.; Stoughton, R. W. J. Solution Chem. 1972, 1, 299–308. Lietzke, M. H.; Stoughton, R. W. J. Inorg. Nucl. Chem. 1974, 36, 1315–1324. Pitzer, K. S. J. Phys. Chem. 1973, 77, 268–277. (a) Pitzer, K. S.; Kim, J. J. J. Am. Chem. Soc. 1974, 96, 5701–5707; (b) Lu, X.; Maurer, G. AIChE J. 1993, 39, 1527–1538.. Pitzer, K. S.; Mayorga, G. J . Phys. Chem. 1973, 77, 2300–2307. Pitzer, K. S. Thermodynamics: 2nd revision of 1st edition. Lewis, G. N.; Randall, M.: editors. McGraw-Hill: New York. 1993. (Received 8 March 2001; in final form 15 August 2001)
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Hygrometric determination of the water activities and the osmotic and activity coefficients of (ammonium chloride + sodium chloride + water) at T = 298.15 K Abderrahim Dinane, Mohamed El Guendouzi,a and Abdelfetah Mounir Laboratoire de Chimie Physique, D´epartment de Chimie, Facult´e des Sciences Ben M’sik, Universit´e Hassan II Mohammedia, B.P 7955, Casablanca, Maroc
The mixed aqueous electrolyte system of ammonium and sodium chlorides has been studied by the hygrometric method at the temperature 298.15 K. The relative humidities of this system were measured at total molalities from 0.3 mol · kg−1 to 6 mol · kg−1 for different ionic-strength fractions of NH4 Cl with y = (0.33, 0.50, and 0.67). The data obtained allow the deduction of new water activities and osmotic coefficients. The experimental results are compared with the predictions of the extended composed additivity model proposed in our previous work, the Robinson–Stokes, Reilly–Wood– Robinson, and Lietzke–Stoughton models. From these measurements, the new Pitzer mixing ionic parameters were determined and used to predict the solute activity coefficients c 2002 Elsevier Science Ltd. All rights reserved. in the mixture. KEYWORDS: aqueous mixed-electrolyte; ammonium and sodium chloride solutions; relative humidity; water activity; osmotic coefficient; activity coefficient; Pitzer’s model; extended composed additivity (ECA)
1. Introduction Investigation of the thermodynamic properties of aqueous mixed electrolyte solutions is of great interest. Much of this interest arises from the importance of the electrolytes in areas such as desalination, oceanography, biology, geochemistry, atmospheric processes, and the environment. The most common methods for the determination of thermodynamic properties in mixed electrolyte solutions are the isopiestic vapour pressure, (1–4) vapour pressure lowering, (5–7) and e.m.f. techniques. (8–13) In this work, we use the hygrometric method, described in a E-mail: [email protected]
0021–9614/02
c 2002 Elsevier Science Ltd. All rights reserved.
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A. Dinane et al.
our previous paper, (14) that yields directly the water activity in aqueous electrolytes. This method has been used for determining thermodynamic properties of binary aqueous solutions (15, 16) and ternary mixed chloride electrolytes. (17) This paper is the continuation of the research on ternary aqueous mixtures of chlorides. The main objectives are to determine thermodynamic properties for the ternary solutions of (ammonium chloride + sodium chloride + water) by the hygrometric method. The thermodynamic behaviour of this system has not been extensively studied. Kirgintsev et al. (18) measured the osmotic coefficients of (ammonium chloride + sodium chloride + water) for different ionicstrength fractions at T = 295.85 K. Meada et al. (19) also measured the osmotic coefficients of this system for x(NaCl) = x(NH4 Cl) = x(H2 O) = 0.33 in the range of total ionic strength I < 5.94 mol · kg−1 by the isopiestic method. Recently, water activities were determined with an electrodynamic balance by Ha et al. (20) for n(NaCl)/n(NH4 Cl) = (1 and 3) in the range of water activity from 0.4 to 0.8. In this work, the measurements of relative humidities for the total molality range from 0.3 mol · kg−1 to 6 mol · kg−1 were performed for the aqueous ternary solution (ammonium chloride + sodium chloride + water) for different ionic-strength fractions from 0.33 to 0.67 at temperature of 298.15 K. The osmotic coefficients were also evaluated for these solutions from the relative humidities. We have used the extended composed additivity (ECA) model proposed in our previous paper (17) to predict water activities of this system. The results are compared with values from three commonly used thermodynamic models. The experimental values are used for the calculation of solute activity coefficients by Pitzer’s model with our newly obtained ionic mixing parameters.
2. Experimental The water activity was determined by a hygrometric method described in our earlier work. (14) The apparatus used in this study of mixed electrolyte solutions is essentially the same as that used for the investigation of aqueous single-electrolyte solutions. It is based on the measurement of the relative humidity over aqueous solutions of non-volatile electrolytes. The apparatus used is a hygrometer in which a droplet of salt solution is maintained on a thin thread. Measurements of the diameter of the previously calibrated droplet permit the calculation of the relative humidity of aqueous solutions. The droplets of a reference solution of NaCl(aq) or LiCl(aq) are deposited on the very thin thread by pulverisation. This thread is stretched over a Perspex support, which is fixed to a cup containing the solution to be studied. The cup is then placed in a thermostatted box. The droplet diameter is measured by a microscope with an ocular-equipped with the micrometer screw. In general, the relative humidity is equivalent to the water activity aw . From measurements of the reference droplet diameters D{aw(ref) } above the reference solution and the same diameters D(aw ) above the studied solution, we calculate the ratio of growth K = D{aw(ref) }/D(aw ) and determine graphically the water activity based upon the variation of the ratio K as a function of the water activity of reference solutions of NaCl(aq) or
Thermodynamic properties of (ammonium chloride + sodium chloride + water) at T = 298.15 K785
LiCl(aq). (14, 15) Generally, the reference relative humidity is 0.84. It is 0.98 for solutions in the medium range of dilution.
3. Results and discussion In this work, measurements of the water activity were made for this mixture as a function of total molality ranging from 0.3 mol · kg−1 to 6 mol · kg−1 , for different ionic-strength fractions of NH4 Cl, y = I (NH4 Cl)/{I (NH4 Cl) + I (NaCl)}, with y = (0.33, 0.50, and 0.67) at the temperature 298.15 K. The solutions were prepared from Merck extrapur-grade chemicals (mass fraction > 0.99) and deionised distilled water. The reference solution is NaCl(aq). The experimental values of water activity are listed in table 1. The experimental uncertainty is between ±2 · 10−4 and ±2 · 10−3 over the experimental molality range. Figure 1 is a plot of aw against total molality m for the different ionic-strength fractions y with the limiting cases of y corresponding to the pure electrolytes. In comparing the relative magnitudes of these water activities at different ionic-strength fractions, we note a relative lowering in the order aw (NH4 Cl)(y=0) > aw(y=0.33) > aw(y=0.50) > aw(y=0.67) > aw (NaCl)(y=1) . From experimental data, we evaluated the molalities of NH4 Cl and NaCl at different constant water activities of the ternary mixture. The dependence of the molality of NaCl against the molality of NH4 Cl at constant water activity is represented in figure 2. The application of the theory to the calculation of thermodynamic properties often involves equations highly complex in form and containing interaction parameters which are not always readily available for mixed electrolytes at the concentration of practical interest. We have proposed in our earlier work (17) a simple rule which allows the properties of mixed electrolyte solutions to be predicted from those of the aqueous solutions of the individual component salts. This ECA “extended composed additivity” model predicts the water activity in mixed electrolyte solutions as: aw = −1 + aw(MX) + aw(NX) − m MX m NX λ − m MX m NX mδ,
(1)
where mMX, mNX, and m are, respectively, the molalities of the electrolytes MX NX in the mixture, and the total molality. Here, aw , aw(MX) , and aw(NX) are, respectively, the water activities of the ternary solution of MX and NX, the water activity of the binary solution of MX at the molality m MX , and the water activity of NX at the molality m NX . The parameters λ and δ, determined experimentally for each system, characterise the deviation from ideality in the mixture of MX and NX for concentrated solution. In dilute solutions, λ = 0 and δ = 0. In general, these quantities depend on the composition and the water activity. In most cases, however, these parameters are fairly constant and arithmetical mean values over a water activity range are used. The unknowns λ and δ may be estimated by a graphical procedure that uses a modified version of equation (1): 1aw /m MX m NX = −λ − mδ,
(2)
where 1aw is the difference between the experimental values of water activity aw and the sum of water activities in the binaries. The quantity on the left is plotted against the total molality m to obtain a linear plot with intercept λ and slope δ.
786
A. Dinane et al. TABLE 1. Ratios of growth K of the NaCl(aq) droplets, water activities aw , and osmotic coefficients φ of mixtures of aqueous ammonium chloride and sodium chloride at total molalities m for different ionic strength fractions y a m(NH4 Cl) mol · kg−1
m(NaCl) mol · kg−1
m mol · kg−1
0.1
0.2
0.3
K
aw
φ
(1.261)
0.9900
0.930
y = 0.33 0.2
0.4
0.6
1.873
0.9800
0.935
0.3
0.6
0.9
1.658
0.9711
0.936
0.5
1.0
1.5
1.391
0.950
0.949
1.0
2.0
3.0
1.123
0.897
1.006
1.5
3.0
4.5
1.000
0.840
1.075
2.0
4.0
6.0
0.920
0.777
1.167
0.908
y = 0.50 0.2
0.2
0.4
(1.166)
0.9870
0.4
0.5
1.0
1.604
0.9680
0.903
0.6
1.0
2.0
1.278
0.934
0.947
1.0
1.5
3.0
1.134
0.900
0.975
2.0
2.0
4.0
1.046
0.864
1.014
3.0
2.5
5.0
0.979
0.826
1.061
4.0
3.0
6.0
0.934
0.790
1.108
y = 0.67 0.2
0.1
0.3
(1.261)
0.9900
0.930
0.4
0.2
0.6
1.873
0.9800
0.887
0.6
0.3
0.9
1.658
0.9701
0.904
1.0
0.5
1.5
1.410
0.952
0.910
2.0
1.0
3.0
1.134
0.900
0.975
3.0
1.5
4.5
1.016
0.849
1.010
4.0
2.0
6.0
0.940
0.777
1.061
a The reference water activity is 0.84; numbers in parentheses are for a reference water activity of 0.98.
We have applied this model to {NH4 Cl(aq) + NaCl(aq)}, and the mean values determined by the graphical procedure are λ = −0.001107 and δ = 0.00007. The standard deviation for the fit is σ (aw ) = 0.0017. Extensive tests on the validity of equation (1) have been carried out and show that aw calculated by employing the assigned values of λ and δ are in good agreement with experiment (figure 3). Three models for the prediction of water activity of the mixtures were used to evaluate the performance of our ECA model. Calculations of the thermodynamic properties of
Thermodynamic properties of (ammonium chloride + sodium chloride + water) at T = 298.15 K787 1.0
aw
0.9
0.8
0.7
0
1
2
3
4
5
6
7
m /(mol . kg − 1)
FIGURE 1. Water activity aw of (ammonium chloride + sodium chloride)(aq) against total molality m at different ionic strength fractions y of NH4 Cl. H, y = 0; +, y = 0.33; ×, y = 0.50; 1, y = 0.67; N, y = 1. 5 y = 0.67
m(NaCl) /(mol . kg − 1)
4 y = 0.50
3 y = 0.33
2
1
0
0
1
2
3
4
5
6
m(NH4Cl) /(mol . kg − 1)
FIGURE 2. Molality of NaCl against the molality of NH4 Cl in mixed (ammonium chloride + sodium chloride)(aq) at constant water activity aw . N, aw = 0.98; H, aw = 0.96; , aw = 0.94; , aw = 0.92; ♦, aw = 0.90; ×, aw = 0.88; +, aw = 0.86; 1, aw = 0.84; , aw = 0.82; , aw = 0.80; , aw = 0.78.
◦ •
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A. Dinane et al. 1.000 y = 0.33 0.950
aw
0.900 0.850 0.800 0.750 0
1
2
3 4 m /(mol . kg − 1)
5
6
7
1.000 y = 0.50 0.950
aw
0.900 0.850 0.800 0.750
0
1
2
3 4 m /(mol . kg − 1)
5
6
7
1.000 y = 0.67 0.950
aw
0.900 0.850 0.800 0.750
0
1
2
3
4
5
6
7
m /(mol . kg − 1)
FIGURE 3. Water activity aw of (ammonium chloride + sodium chloride)(aq) against total molality m at different ionic strength fractions y of 0.33, 0.50, and 0.67. , experimental points; +, present model; 1, RWR model; ×, LS model; ♦, RS model.
•
Thermodynamic properties of (ammonium chloride + sodium chloride + water) at T = 298.15 K789
mixed-electrolyte systems generally require those of the pure component at the same ionic strength I as the mixture. In the case of NH4 Cl(aq) and NaCl(aq), the required quantities were calculated from results obtained in our previous work. (15) Robinson and Stokes (1) proposed a form of the vapour pressure of the mixture involves the additivity lowering solvent vapour pressures of the solutes and extended into the following form: (6) (1 − aw(m) ) = {(1 − aw(MX,m) )(m MX /m) + (1 − aw(NX,m) )(m NX /m)},
(3)
where aw(m) , aw(MX,m) , and aw(NX,m) are, respectively, the water activities of the ternary solutions of MX and NX, and the water activities of the binary solutions of MX and NX at the same molality m as the mixed solution. Another model of a mixed electrolyte solution is that developed by Reilly et al. (RWR). (21) For a solution of molality m MX and m NX , the RWR method predicts the osmotic coefficient of the mixed-electrolyte solution by: (m MX + m NX )(1 − φ) = m MX (1 − φMX ) + m NX (1 − φNX ) + X X (m MX m NX /2){gMN + m∂(gMN )/∂m},
(4)
where φMX and φNX are, respectively, the osmotic coefficients of the solution of MX and X is a quantity that involves interactions NX at the ionic strength I of the mixture, and gMN between pairs of electrolytes. The Lietzke and Stoughton model (22, 23) (LS II) predicts the osmotic coefficient of a multicomponent solution by: (νMX m MX + νNX m NX )φ = νMX m MX φMX + νNX m NX φNX ,
(5)
where νMX is the number of ions released by the complete dissociation of one molecule of component MX, m MX is its molality, and φMX is the osmotic coefficient of the binary solution of component MX at the total ionic strength of the multicomponent solution. The comparison of the water activities calculated with our proposed model ECA, equation (1), and those predicted by the four models shows good agreement (figure 3). The average difference is less than ±0.0005 between our model and the other three. On the basis of the experimental data obtained for the water activity, we evaluated the osmotic coefficients obtained for different ionic-strength fractions y. The obtained osmotic coefficients are listed in table 1 and plotted against m 1/2 in figure 4. The calculations of the osmotic coefficients by the ECA method has been generalised for different mixtures (figure 4). The standard deviation for the osmotic coefficient is σ (φ) = 0.018. The comparison of our results with those of the three models is shown in figure 4. The predictions by the ECA method are very similar to those of the other models at medium and high molalities, but the deviations of ECA become quite large at low total molality. The discrepancy in this region is attributed to the parameters λ and δ, which are, generally, introduced for the middle to higher concentrations, and also to the aw φ relationship by the term 1000/6i νi m i Mw which becomes greater for m < 0.5 mol · kg−1 and yields large deviations for the lower variation of water activity. Figure 5 is a plot of φ calculated from equation (1) as a function of m 1/2 at different ionic strength fractions y. As can be seen from these curves, the values of φ fall in regular and
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A. Dinane et al. 1.2 y = 0.33 1.1
1.0
0.9
0.8 0.5
1.0
1.5
2.0
2.5
2.0
2.5
2.0
2.5
{m /(mol . kg − 1)}1/2 1.2 y = 0.50 1.1
1.0
0.9
0.5
1.0
1.5 {m /(mol . kg − 1)}1/2
1.2 y = 0.67 1.1
1.0
0.9
0.8 0.5
1.0
1.5 {m /(mol . kg − 1)}1/2
FIGURE 4. Osmotic coefficient φ of (ammonium chloride + sodium chloride)(aq) against m 1/2 at different ionic strength fractions y of 0.33, 0.50, and 0.67. , experimental points; +, present model; 4, RWR model; ×, LS model; ♦, RS model.
•
Thermodynamic properties of (ammonium chloride + sodium chloride + water) at T = 298.15 K791 1.4
1.2
1.0
0.8 0.5
1.0
1.5 {m /(mol . kg − 1)}1/2
2.0
2.5
FIGURE 5. Osmotic coefficients φ of (ammonium chloride + sodium chloride)(aq) against m 1/2 at different ionic strength fractions y of NH4 Cl. , y = 1; , y = 0; 1, y = 0.67; ×, y = 0.50; +, y = 0.33.
•
decreasing order from pure NaCl(aq) to pure NH4 Cl(aq): φ(y = 0) > φ(y = 0.33) > φ(y = 0.50) > φ(y = 0.67) > φ(y=1). The curves at different y are indeed quite similar in their dependence on molality. Pitzer’s model (24–27) provides the simplest and most convenient procedure for calculating the thermodynamic properties of mixed-electrolyte solutions. The activity coefficient γMX of MX in a common-ion mixture of two 1-1 electrolytes is given by Pitzer’s model as ∗ ln γMX = ln γMX + y · 1φ ∗ + y · m[θMN + m · {1 − (y/2)}ψMNX ],
1φ ∗
∗ (φNX
∗ ) φMX
(6)
∗
where is − and the superscript denotes pure components at the same molality as the total molality of the mixture. Here, 1φ ∗ can be expressed as: (0)
(0)
φ
(1)
(1)
1φ ∗ = m{βNX − βMX + h 1 (βNX − βMX ) + m 2 (CNX − CMX )},
(7)
γ∗
where is the solute activity coefficient determined by the ion-interaction model. For component NX, γNX is given by a similar equation: ∗ ln γNX = ln γNX + (1 − y)1φ ∗ + (1 − y)m[θMN + m · {1 − (y/2)}ψMNX ].
β (0) ,
β (1) ,
Cφ
(8)
Values of the ionic parameters and of the pure electrolytes NH4 Cl(aq) and NaCl(aq) were obtained from Pitzer’s expressions by fits of the experimental osmotic coefficients given in our previous work. (15) The corresponding values are β (0) = 0.0738, β (1) = 0.2712, and C φ = 0.00167 for NaCl(aq), and β (0) = 0.0527, β (1) = 0.2011, and C φ = −0.00306 for NH4 Cl(aq).
792
A. Dinane et al.
From the osmotic coefficients determined from the experimental water activities of the mixture studied at different ionic strength fractions, it is possible to determine the unknown Pitzer mixing ionic parameters θ(NH4 ,Na) and ψ(NH4 ,NaCl) , which are not given in the literature. These parameters may be used to predict the solute activity coefficients in the mixture. Both θ(NH4Na) and ψ(NH4NaCl) are estimated by a graphical procedure. This procedure defines the quantity 1φ as the difference between the experimental values φ(expt) and that calculated from equation (1), φ(calc). This yields: m/m(NaCl) · m(NH4 Cl) = θ(NH4 ,Na) + ψ(NH4 ,NaCl) · m,
(9)
so that a plot of 1φ against total molality m should give a straight line with intercept θ(NH4 ,Na) and slope ψ(NH4 ,NaCl) . The values of these ionic parameters are θ(NH4 ,Na) = 0.0159 and ψ(NH4 ,NaCl) = −0.0048, and the standard deviation is σ (1φ) = 0.001. The activity coefficients of NH4 Cl(aq) and NaCl(aq) in the mixture, listed in table 2, were calculated by Pitzer’s equation with the ionic mixing parameters obtained in this work. Figure 6 is the plot of γNH4 Cl and γNaCl as a function of m 1/2 . The extremes of composition are illustrated in this figure, i.e., the activity coefficients of the pure components. The γ (NaCl) decreases rapidly enough with increasing molality, goes through a minimum which varies between total molalities of (1.5 and 2.0) mol · kg−1 , and then increases. The γ (NH4 Cl) decreases with increasing molality over the entire total concentration range. 1.2
1.0
0.8
0.6
0.4 0.5
1.0
1.5
2.0
2.5
3.0
{m / (mol . kg − 1)}1/2
FIGURE 6. Activity coefficients γ (NH4 Cl) and γ (NaCl) against m 1/2 at different ionic strength fractions y of NH4 Cl. Upper curves are for NaCl, and lower curves are for NH4 Cl. , y = 1; , y = 0; 1, y = 0.67; ×, y = 0.50; +, y = 0.33.
•
Thermodynamic properties of (ammonium chloride + sodium chloride + water) at T = 298.15 K793 TABLE 2. Activity coefficients γ NH4 Cl(aq) and (NaCl)(aq) of NaCl(aq) in (ammonium chloride + sodium chloride)(aq) at total molality m for different ionic-strength fractions of NH4 Cl y = 0.33 y = 0.50 y = 0.67 m/(mol · kg−1 ) γ (NH4 Cl) γ (NaCl) m/(mol · kg−1 ) γ (NH4 Cl) γ (NaCl) m/(mol · kg−1 ) γ (NH4 Cl) γ (NaCl) 0.3 0.6 0.9 1.5 3.0 4.5 6.0
0.681 0.829 0.601 0.569 0.529 0.497 0.458
0.704 0.667 0.651 0.645 0.688 0.774 0.896
0.4 1.0 2.0 3.0 4.0 5.0 6.0
0.660 0.596 0.557 0.536 0.519 0.501 0.480
0.686 0.646 0.649 0.680 0.728 0.790 0.864
0.3 0.6 0.9 1.5 3.0 4.5 6.0
0.683 0.632 0.605 0.575 0.544 0.526 0.505
0.702 0.664 0.647 0.639 0.673 0.743 0.837
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.
Robinson, R. A; Stokes, R. H. Electrolyte Solutions. Butterworth: London. 1955. Rard, J. A.; Clegg, S. L.; Palmer, D. A. J. Solution Chem. 2000, 29, 1–49. Holmes, H. F.; Mesmer, R. E. J. Chem. Thermodynamics 1996, 28, 67–81. Todorovic, M.; Ninkovic, R. J. Chem. Thermodynamics 1996, 28, 491–496. Gokcen, N. A. Report of Investigations RI8372. U. S. Dept. of the Interior. Bureau of Mines, 1979. El Golli, S.; Arnaud, G.; Bricard, J.; Treiner, C. J. Aerosol Sci. 1977, 8, 39–54. Michielsen, M.; Loix, G. Y.; Gilbert, J.; Cleas, P. J. Chim. Phys. 1982, 79, 247–252. Harned, H. N.; Owen, B. B. The Physical Chemistry of Electrolyte Solutions. Reinhold: New York. 1958. Roy, R. N.; Rice, R. A.; Vogel, K. M.; Roy, L. N. J. Phys. Chem. 1990, 94, 7706–7710. Sarada, S.; Ananthaswamy, J. J. Chem. Soc. Faraday Trans. 1990, 86, 81–84. Downes, C. J. J. Phys. Chem. 1970, 74, 2153–2160. Lanier, R. D. J. Phys. Chem. 1965, 69, 3992–3998. Lietzke, M. H.; O’Brien, H. A. Jr. J. Phys. Chem. 1968, 72, 4408–4414. El Guendouzi, M.; Dinane, A. J. Chem. Thermodynamics 2000, 32, 297–313. El Guendouzi, M.; Dinane, A.; Mounir, A. J. Chem. Thermodynamics (in press). El Guendouzi, M.; Mounir, A.; Dinane, A. J. Chem. Thermodynamics (accepted for publication). Dinane, A.; El Guendouzi, M.; Mounir, A. J. Chem. Thermodynamics (in press). Kirgint’sev, A. N.; Luk’yanov, A. V. Russ. J. Phys. Chem. 1963, 37, 1501–1502. Maeda, M.; Hisada, O.; Ito, K.; Kinjo, Y. J. Chem. Soc. Faraday Trans. 1 1989, 85, 2555–2562. Ha, Z.; Choy, L.; Chan, C. K. J. Geophys. Res. 2000, 105, 11699–11709. Reilly, P. J.; Wood, R. H.; Robinson, R. A. J. Phys. Chem. 1971, 75, 1305–1314. Lietzke, M. H.; Stoughton, R. W. J. Solution Chem. 1972, 1, 299–308. Lietzke, M. H.; Stoughton, R. W. J. Inorg. Nucl. Chem. 1974, 36, 1315–1324. Pitzer, K. S. J. Phys. Chem. 1973, 77, 268–277. (a) Pitzer, K. S.; Kim, J. J. J. Am. Chem. Soc. 1974, 96, 5701–5707; (b) Lu, X.; Maurer, G. AIChE J. 1993, 39, 1527–1538.. Pitzer, K. S.; Mayorga, G. J . Phys. Chem. 1973, 77, 2300–2307. Pitzer, K. S. Thermodynamics: 2nd revision of 1st edition. Lewis, G. N.; Randall, M.: editors. McGraw-Hill: New York. 1993. (Received 8 March 2001; in final form 15 August 2001)
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