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Volumetric studies of aqueous solutions of monosodium salts of some aliphatic dicarboxylic acids at 298.15 K. A new method of data analysis
Journal of Molecular Liquids 178 (2013) 94–98
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Volumetric studies of aqueous solutions of monosodium salts of some aliphatic dicarboxylic acids at 298.15 K. A new method of data analysis Adam Bald a,⁎, Zdzisław Kinart a, Renato Tomaš b a b
Department of Physical Chemistry of Solutions, Faculty of Chemistry, University of Lodz, Pomorska 163, 90-236 Lodz, Poland Department of Physical Chemistry, Faculty of Chemistry and Technology, University of Split, Nikole Tesle 10, 21000 Split, Croatia
a r t i c l e
i n f o
Article history: Received 11 September 2012 Received in revised form 24 November 2012 Accepted 26 November 2012 Available online 11 December 2012 Keywords: Carboxylic acids Monosodium salts of dicarboxylic acid Apparent molar volume
a b s t r a c t The apparent molar volumes, Vϕ, of monosodium salts of aliphatic dicarboxylic acids of the HOOC(CH2)n(COOH)2 [n=0–5] types in dilute aqueous solution have been determined by precise density measurements, at T= 298.15 K. Densities were measured using a vibrating-tube densimeter (DMA 5000, Anton Paar, Austria) at T= 298.15 K. These results were used to calculate the apparent molar volumes of each solute over the concentration range 0.0050≤ m/(mol·kg−1) ≤0.3000. A new method for determining the values of partial molar volume of the electrolyte of NaHA type has been proposed. This method takes into account all equilibrium occurring in the solution. The variations of Vϕ0 values with aliphatic chain length of analyzed salts were determined. © 2012 Elsevier B.V. All rights reserved.
1. Introduction This work is a continuation of volumetric studies of aqueous solutions of mono- and dicarboxylic acids [1] and sodium salts of these acids [2] and viscosimetric studies of these solutions [3–6]. Research on the properties of anions \OOC(CH2)nCOOH and \OOC(CH2)nCOO\in water is necessary to understand the properties of aqueous solutions of dicarboxylic acids HOOC(CH2)nCOOH. Studies of the properties of these anions can be carried out by investigations of solutions of salts Na2A and NaHA. This method is much more convenient and simpler because these salts are strong electrolytes. Usually it is assumed that in solutions of Na2A, there is no equilibrium which may affect the quantities of anions and the appearance of new anions or molecules [2]. In the case of salt solutions such Na2A hydrolysis can be quantitatively omitted if the range of concentrations of solutions of these salts is properly selected, as shown in our previous work [2]. In the case of solutions of Na2A,hydrolysis can be quantitatively omitted if the range of concentrations of solutions of salt is properly selected, as shown in our previous work [2]. But in the case of research of solutions of NaHA, the situation is more complex. Review of literature shows that only one author tried to determine the values of apparent molar volume of some monosodium salt of dicarboxylic acids in water [7]. In this work, monosodium sodium salts of dicarboxylic acids were treated only as typical strong electrolyte of type 1-1 and chemical equilibria occurring in the solutions were not considered. Therefore, the purpose on the present study was to
⁎ Corresponding author. Tel.: +48 426355846. E-mail address: [email protected] (A. Bald). 0167-7322/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2012.11.029
determine the densities of monosodium salts of the dicarboxylic acids [HOOC(CH2)nCOOH, n = 0–5] in water, at T = 298.15 K. These results were used to calculate the apparent molar volumes (Vϕ) of each solute over the concentration range 0.0050 ≤ m/(mol·kg−1) ≤0.3000. Using a new method that takes into account all the equilibrium present in solution the values of apparent molar volumes Vϕ0 of NaHA at infinite concentration have been determined. The variations of both Vϕ0 with aliphatic chain length of analyzed carboxylic acids were determined.
2. Experimental 2.1. Materials The sources of chemicals were described in our previous papers [1–4]. Double-distilled water additionally was purified by ion exchange and stored under argon. The specific conductivity of water was less than 0.3·10−6 Ω−1 cm−1. Aqueous solutions of the monosodium salt of selected aliphatic dicarboxylic acids were prepared by dissolving equimolar mixture of carboxylic acids and their disodium salts. Used dicarboxylic acids and their disodium salts were prepared as described in the literature [1–6].
2.2. Apparatus and procedures The densities of solutions were measured using an Anton Paar model DMA 5000 densimeter with precision of ±1·10−6 g cm−3, and accuracy ±5·10−6 g cm−3. The instrument was equipped with Peltier-type thermostating unit and temperature was kept constant with accuracy
A. Bald et al. / Journal of Molecular Liquids 178 (2013) 94–98
Table 1 Apparent molal volumes (Vϕ), molarity (c) and molality (m) and fractions α and γ of monosodium salts of aliphatic carboxylic acids in water at 298.15 K. ρ g⋅cm−3
Vϕ cm3 ⋅mol−1
α
γ
Monosodium salts of ethanedioic acid 0 0 0.997043 0.01999 0.02002 0.998460 0.03963 0.03964 0.999847 0.05940 0.05933 1.001240 0.07946 0.07925 1.002650 0.09938 0.09898 1.004048 0.11892 0.11828 1.005417 0.13885 0.13791 1.006812 0.15857 0.15728 1.008190 0.17801 0.17632 1.009546 0.19774 0.19560 1.010920
– 41.25 41.39 41.49 41.57 41.65 41.72 41.78 41.84 41.90 41.96
– 0.075566 0.064984 0.061167 0.059342 0.058463 0.057990 0.057825 0.057810 0.057851 0.057948
– 0.017487 0.023650 0.027733 0.030802 0.033251 0.035224 0.036983 0.038504 0.039813 0.041003
Monosodium salts of propanedioic acid 0 0 0.997043 0.00571 0.00573 0.997443 0.01068 0.01072 0.997791 0.01869 0.01877 0.998351 0.03982 0.04002 0.999825 0.06237 0.06277 1.001394 0.07982 0.08042 1.002604 0.09903 0.09989 1.003934 0.11862 0.11979 1.005288 0.13912 0.14067 1.006702 0.15790 0.15984 1.007997 0.17800 0.18041 1.009382 0.19737 0.20028 1.010714 0.21629 0.21973 1.012004 0.23603 0.24007 1.013362 0.25524 0.25993 1.014671 0.27511 0.28051 1.016031 0.29408 0.30023 1.017323
– 56.13 56.19 56.24 56.34 56.45 56.55 56.63 56.71 56.79 56.85 56.91 56.97 57.07 57.10 57.18 57.24 57.30
– 0.044339 0.043207 0.042442 0.039871 0.035219 0.028143 0.015548 0.007329 0.006997 0.006749 0.006527 0.006343 0.006187 0.006043 0.005918 0.005802 0.005701
– 0.034408 0.037283 0.038807 0.038112 0.034183 0.027488 0.015546 0.007214 0.006902 0.006667 0.006455 0.006280 0.006130 0.005992 0.005871 0.005759 0.005661
Monosodium salts of butanedioic acid 0 0 0.997043 0.01982 0.01991 0.998437 0.04134 0.04158 0.999944 0.06014 0.06057 1.001260 0.08048 0.08117 1.002676 0.10023 0.10124 1.004052 0.11912 0.12048 1.005364 0.13821 0.13998 1.006688 0.15798 0.16023 1.008059 0.17750 0.18028 1.009404 0.19702 0.20040 1.010748 0.21671 0.22074 1.012103 0.23500 0.23968 1.013358 0.25516 0.26064 1.014740 0.27371 0.27996 1.016007 0.29355 0.30069 1.017360
– 69.95 70.10 70.16 70.28 70.35 70.42 70.49 70.55 70.64 70.72 70.79 70.85 70.92 70.99 71.07
– 0.014290 0.010975 0.009685 0.008828 0.008254 0.007841 0.007509 0.007229 0.006997 0.006798 0.006624 0.006481 0.006340 0.006224 0.006110
– 0.014242 0.010956 0.009673 0.008820 0.008248 0.007836 0.007505 0.007225 0.006994 0.006796 0.006622 0.006479 0.006338 0.006222 0.006108
Monosodium salts of pentanedioic acid 0 0 0.997043 0.01912 0.01921 0.998356 0.04054 0.04080 0.999821 0.05412 0.05453 1.000744 0.07886 0.07963 1.002427 0.08974 0.09071 1.003166 0.11916 0.12075 1.005159 0.13761 0.13968 1.006406 0.15796 0.16062 1.007781 0.17722 0.18051 1.009080 0.19644 0.20043 1.010368 0.21516 0.21990 1.011621 0.23391 0.23946 1.012875 0.25375 0.26023 1.014199 0.27295 0.28041 1.015483 0.29186 0.30033 1.016736
– 85.69 85.82 85.96 86.08 86.12 86.24 86.31 86.37 86.43 86.52 86.60 86.67 86.74 86.80 86.88
– 0.018533 0.014143 0.012835 0.011376 0.010930 0.010040 0.009629 0.009258 0.008965 0.008714 0.008501 0.008311 0.008133 0.007977 0.007838
– 0.018481 0.014124 0.012821 0.011367 0.010923 0.010035 0.009625 0.009255 0.008962 0.008711 0.008498 0.008309 0.008131 0.007975 0.007836
Monosodium salts of hexanedioic acid 0 0 0.997043 0.02104 0.02114 0.998446 0.04154 0.04184 0.999807
– 101.73 101.88
– 0.017907 0.014044
– 0.017870 0.014029
c mol⋅dm−3
m mol⋅kg−1
95
Table 1 (continued) ρ g⋅cm−3
Vϕ cm3 ⋅mol−1
α
γ
Monosodium salts of hexanedioic acid 0.06227 0.06286 1.001178 0.08301 0.08397 1.002547 0.10373 0.10515 1.003909 0.12392 0.12588 1.005234 0.14446 0.14706 1.006578 0.16487 0.16821 1.007910 0.18479 0.18892 1.009206 0.19395 0.19848 1.009804
102.02 102.12 102.23 102.33 102.42 102.52 102.61 102.63
0.012277 0.011210 0.010475 0.009939 0.009509 0.009160 0.008874 0.008756
0.012267 0.011204 0.010470 0.009935 0.009505 0.009157 0.008871 0.008754
Monosodium salts of heptanedioic acid 0 0 0.997043 0.01656 0.01664 0.998119 0.03302 0.03325 0.999185 0.04921 0.04964 1.000229 0.06648 0.06720 1.001340 0.08168 0.08272 1.002316 0.09588 0.09727 1.003225 0.11317 0.11504 1.004330 0.12885 0.13124 1.005329 0.14515 0.14812 1.006367 0.15994 0.16351 1.007308
– 117.50 117.63 117.75 117.86 117.94 118.02 118.11 118.19 118.26 118.32
– 0.019523 0.015148 0.013211 0.011974 0.011222 0.010684 0.010167 0.009788 0.009458 0.009202
– 0.019480 0.015131 0.013200 0.011967 0.011217 0.010679 0.010163 0.009785 0.009455 0.009199
c mol⋅dm−3
m mol⋅kg−1
of ± 0.001 K. The densimeter was calibrated with dry air and pure water periodically. The solutions were prepared by adding a weighed amount of concentrated solutions to known amounts of pure water. All the solutions were prepared by mass using an analytical balance (Sartorius RC 210D) with an uncertainty of ±1 · 10 −5 g. 3. Results and discussion The values of apparent molar volumes were calculated based on Eq. (1) Vϕ ¼
1000·ðρ0 −ρÞ M þ m·ρ0 ·ρ ρ
ð1Þ
where: ρ—solution density, ρ0—solvent density, m—molality of solution and M—molar mass of electrolyte. All the solutions of monosodium salts of aliphatic dicarboxylic acid were made by weight and the molalities, m, were converted into molar concentrations, c, by using the following standard relation: c¼
1000·ρ·m : ð1000 þ m·M Þ
ð2Þ
The values of apparent molar volumes Vϕ, together with the values of molar concentrations, molalities and density of the solutions are summarized in Table 1.
Table 2 Values of Vϕ0 at T = 298.15 K for studied monosodium salts of acid. HOOC(CH2)nCOONa n
Vϕ0
Vϕ0 lit.
0 1 2 3 4 5
41.97 56.24 69.71 85.53 101.47 117.26
41.19 55.96 68.88 84.77 100.98 116.59
[7]a [7] [7] [7] [7] [7]
a The value calculated on the basis of the Vϕ0 for HOOC-COOK [7] and value of the difference V 0ϕK þ −V 0ϕNaþ = 10.23 cm3 mol−1 [12].
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A. Bald et al. / Journal of Molecular Liquids 178 (2013) 94–98
Table 3a The dependence of experimental and calculated values Vϕ and the values of chosen components of Eq. (17): 0.5(α − γ) V ϕH2 Aði2Þ ; 0.5(α + γ) V ϕNa2 AðiÞ ; (1 − α − γ) V ϕNaHAðiÞ ; γ V ϕH2 AðuÞ for monosodium salts of ethanedioic acid. Monosodium salts of ethanedioic acid c mol⋅dm−3
V ϕ ðex:Þ cm3 ⋅mol−1
V ϕ ðcal:Þ cm3 ⋅mol−1
0.5(α − γ) V ϕH2 Aði2Þ
0.5(α+ γ) V ϕNa2 AðiÞ
(1 − α − γ) V ϕNaHAðiÞ
γ V ϕH2 AðuÞ
0.01999 0.03963 0.05940 0.07946 0.09938 0.11892 0.13885 0.15857 0.17801 0.19774
41.25 41.39 41.49 41.57 41.65 41.72 41.78 41.84 41.90 41.96
41.08 41.40 41.55 41.65 41.72 41.77 41.81 41.84 41.86 41.89
0.77 0.55 0.44 0.38 0.33 0.30 0.28 0.26 0.24 0.22
1.12 1.07 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22
38.27 38.52 38.55 38.53 38.49 38.45 38.40 38.34 38.30 38.25
0.93 1.26 1.48 1.64 1.77 1.88 1.97 2.06 2.13 2.19
The density of water at 298.15 K was found to be 0.997043 g cm−3; this value is equal to that from the literature [8]. In the case of the solutions of monosodium salts of dicarboxylic acids should be considered in accordance with Apelblat [9], the following processes: þ
−
NaHA → Na þ HA −
þ
2−
ð4Þ
−
H þ HA ⇌ H2 A:
ð5Þ
If you enter a fraction of α and γ h α¼
A2−
;
2−
i
ð7Þ
¼ cα;
ð8Þ
½H2 A ¼ cγ;
ð9Þ
−
½HA ¼ c ð1−α–γÞ; h h
þ
H
i
þ
Na
ð10Þ
¼ c ðα–γÞ; i
K A2 ¼
ð1−α−γÞ 1 ; ¼ K D2 ½cα ð1−α−γ Þy2
ð14Þ
where KD1 and KD2 are dissociation constants. The activity coefficient quotient (y) of Eqs. (13) and (14) can be described using relations: ð15Þ
and
concentration for each forms of the electrolyte can be described as follows: A
ð13Þ
ð6Þ
½H A γ¼ 2 ; c
h
1 γ ; ¼ K D1 ½cðα−γÞð1−α−γÞy1
y1 ¼ yHþ yHA− =yH2 A ;
i
c
K A1 ¼
ð3Þ
HA ⇌ H þ A þ
The values of α and γ for each concentrations can be calculated using the association constants KA1 and KA2, described by equations:
ð11Þ
¼ c:
ð12Þ
y2 ¼ yHþ yA2− =yHA− :
ð16Þ
The activity coefficient of the undissociated acid yH2 A is equal to unity. The activity coefficients of ions can be calculated on the basis of the Debye–Hückel equation. More details related to the description of the Debye–Hückel equation may be found in our earlier work [5]. Using the numerical methods for performing successive approximations from Eqs. (12) and (13) the values α and γ for each concentration of electrolyte (c) can be determined [5]. The values of KA1 and KA2 have been taken from [10]. The calculated numerically values of α and γ are summarized in Table 1. A solution of monosodium salt of the dicarboxylic acid can be treated as a mixture of a completely dissociated electrolytes, i.e. NaHA, H2A, Na2A, with concentrations of c (1− α − γ), 1/2c (α − γ), 1/2c (α + γ)
Table 3b The dependence of experimental and calculated values Vϕ and the values of chosen components of Eq. (17): 0.5(α − γ) V ϕH2 Aði2Þ ; 0.5(α + γ) V ϕNa2 AðiÞ ; (1 − α − γ) V ϕNaHAðiÞ ; γ V ϕH2 AðuÞ for monosodium salts for monosodium salts of heptanedioic acid. Monosodium salts of heptanedioic acid c mol⋅dm−3
V ϕ ðex:Þ cm3 ⋅mol−1
V ϕ ðcal:Þ cm3 ⋅mol−1
0.5(α−γ) V ϕH2 Aði2Þ
0.5(α+γ) V ϕNa2 AðiÞ
(1−α−γ) V ϕNaHAðiÞ
γ V ϕH2 AðuÞ
0.01656 0.03302 0.04921 0.06648 0.08168 0.09588 0.11317 0.12885 0.14515 0.15994
117.50 117.63 117.75 117.86 117.94 118.02 118.11 118.19 118.26 118.32
117.58 117.70 117.80 117.90 117.97 118.03 118.11 118.17 118.24 118.29
0.0022 0.0009 0.0006 0.0004 0.0003 0.0003 0.0002 0.0002 0.0002 0.0002
1.98 1.54 1.34 1.22 1.14 1.09 1.03 0.99 0.96 0.94
112.95 114.11 114.67 115.06 115.32 115.53 115.73 115.90 116.05 116.18
2.57 1.99 1.74 1.58 1.48 1.41 1.34 1.29 1.25 1.21
A. Bald et al. / Journal of Molecular Liquids 178 (2013) 94–98
140.00
respectively and undissociated acid H2A(u) with a concentration equal to cγ. Thus, the apparent molar volume can be described by the equation:
ð17Þ
According to Redlich–Rosenfeld equation [11] 0
V ϕNaHAðiÞ ¼ V ϕNaHAðiÞ þ SVNaHAðiÞ 0
V ϕH2 Aði2Þ ¼ V ϕH2 Aði2Þ þ SVH2 Aði2Þ V ϕNa2 AðiÞ ¼
0 V ϕNa2 AðiÞ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1−α−γÞc þ bvNaHAðiÞ c
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ðα−γ Þc þ bvH2 Aði2Þ c 2
ð17aÞ
100.00 80.00
y = 15.879x + 37.881 2 R =1
60.00 40.00 20.00 0.00
ð17bÞ
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ðα þ γÞc þ bvNa2 AðiÞ c þ SVNa2 Aði Þ 2
ð17cÞ
0
V ϕH2 AðuÞ ¼ V ϕH2 AðuÞ þ bvH2 AðuÞ c:
ð17dÞ
Assuming as Millero [12] that SvNaHA(i) = 1.868, SVH2 Aði2Þ = 9.607 and SVNa2 AðiÞ = 9.607, Eq. (17) takes the form: h i pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V ϕ ¼ ð1−α−γ Þ V 0ϕNaHAðiÞ þ 1:868 ð1−α−γÞc þ bvNaHAðiÞ " # rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 0 ðα−γ Þc þ bvH2 Aði2 Þ c þ ðα−γÞ V ϕH2 Aði2Þ þ 9:607 2 2 " # rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 0 ðα þ γÞc þ bvNa2 AðiÞ c þ ðα þ γ Þ V ϕNa2 AðiÞ þ 9:607 2 2 h i 0 þγ V ϕH2 AðuÞ þ bvH2 Aðu Þ c :
ð18Þ
Values V ϕH2 Aði2 Þ 0 , V 0ϕNa2 Aði2Þ in Eq. (18) was derived from work [2] while the values V 0ϕH2 AðuÞ from work [1]. The components of 1 1 ðα−γÞbvH2 Aði2Þ c, ðα þ γÞbvNa2 Aði2Þ c and γbvH2 AðuÞ c in Eq. (2) may be 2 2 60.00
A
50.00
VΦ [cm3 mol-1]
120.00
VoNaHA [cm3 mol-1]
1 1 V ϕ ¼ ð1−α−γ ÞV ϕNaHAðiÞ þ ðα−γ ÞV ϕH2 Aði2Þ þ ðα þ γÞV ϕNa2 AðiÞ 2 2 þ γV ϕH2 AðuÞ :
97
40.00 30.00 20.00 10.00
0.00 140.00
B 120.00 100.00 80.00
0
1
2
3
4
5
6
n Fig. 2. The dependences of limiting partial volume of (VNaHA) as a function of number of carbon atoms (n) in the molecules of monosodium salts of acid NaOOC(CH2)nCOOH: ◊ the experimental values; ■ literature [7]. Vϕo =15.879+37.881×n, R2 =1.
omitted in calculations due to their small values, less than the estimated accuracy of Vϕ. Thus, Eq. (18) only determines the values V 0ϕNaHAðiÞ and bvNaHAðiÞ c. The V 0ϕNaHAðiÞ values determined on the basis of a nonlinear least-squares method are summarized in Table 2. As can be seen the values which have been obtained in this work are systematically higher than those obtained by Høiland [7]. This effect may be associated with some of the simplifications that have been adopted by Høiland [7]. He assumed that the investigated NaHA salts are strong electrolytes and their solutions contain only Na + and HA− ions. In order to determine the values of V 0ϕNaHAðiÞ , Høiland applied a simple procedure based on the extrapolation of the results to infinite dilution using a simple equation proposed by Redlich–Rosenfeld. The values of components 0.5(α−γ)∙ V ϕH2 Aði2Þ ; 0.5(α+ γ)∙V ϕNa2 AðiÞ ; (1− α− γ) V ϕNaHAðiÞ ; γ⋅V H2 AðuÞ with Eq. (17) are summarized in Tables 3a and 3b. The plots of these values as a function of concentration for the two salts [monosodium salt of ethendioic acid (n=0) and monosodium salt of heptanedioic acid (n=5)] are presented at Fig. 1. As can be seen, the part of these components in experimental values of Vϕ is important. This applies particularly to component of γ V H2 AðuÞ which is related to the presence of undissociated dicarboxylic acid in the studied solutions. The dependence of apparent molar volumes at infinite concentration (Vϕ0) as the function of the number of carbon atoms (n) in the hydrocarbon chain of aliphatic acid is presented at Fig. 2. As can be seen, increase in the number of carbon atoms (n) of one causes an increase in the value of Vϕ0 about 15.89 cm 3/mol. This means that the molar volume of the \CH2\ group is equal approximately to 15.89 cm3/mol. This value is very well correlated with the similar values which has been designated based on the studies of the following electrolytes: sodium salts of monocarboxylic acids ( V CH2 = 15.56 cm 3/mol) [2], sodium salts of dicarboxylic acids (V CH2 = 15.62 cm3/mol) [2], monocarboxylic acids (V CH2 = 15.6 cm 3/mol) [1] and dicarboxylic acids (V CH2 = 15.96 cm 3/mol) [1].
60.00
4. Conclusions 40.00 20.00 0.00 0.000
0.050
0.100
0.150
0.200
0.250
c [mol dm-3] Fig. 1. The dependence of experimental (●) and calculated (□) values of Vφ and the values of chosen components of Eq. (17):* (1 − α − γ) V ϕNaHAðiÞ ; Δ 0.5(α − γ) V ϕH2 Aði2Þ ; x 0.5(α + γ) V ϕNa2 AðiÞ ; ♦ γ V ϕH2 AðuÞ for monosodium salts of ethenedioic acid (A) and for monosodium salts of heptanedioic acid (B).
On the basis of accurate density measurements in aqueous solutions of monosodium salts of dicarboxylic acids the value of apparent molar volumes of these salts have been determined at 298.15 K. It was shown that in addition to Na+ and HA− ions, H+ and A2− ions are also present in the solution and also molecules of H2A and their concentrations have been determined. It has been shown that the analysis of apparent molar volume of the concentration should use the modified equation which takes into account all equilibrium occurring in the solution. It was found that the partial molar volumes for the salts investigated are positive and increase linear (corelation coefficient is high, R2 =1)
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A. Bald et al. / Journal of Molecular Liquids 178 (2013) 94–98
with increasing number of carbon atoms in their carbon chain. The appointed part of \CH2\ group in the partial molar volume is almost identical to that which has been designated on the basis of aqueous solutions of disodium salts of dicarboxylic acids, monocarboxylic acids, monosodium salts of monocarboxylic acids and undissociated mono-and dicarboxylic acids. References [1] A. Bald, Z. Kinart, Journal of Solution Chemistry 40 (2011) 1. [2] Z. Kinart, A. Bald, Physics and Chemistry of Liquids 49 (2011) 3.
[3] A. Chmielewska, A. Wypych-Stasiewicz, A. Bald, Journal of Molecular Liquids 122 (2005) 110. [4] A. Chmielewska, A. Wypych-Stasiewicz, A. Bald, Journal of Molecular Liquids 130 (2007) 42. [5] A. Chmielewska, A. Wypych-Stasiewicz, A. Bald, Journal of Molecular Liquids 136 (2007) 11. [6] A. Chmielewska, A. Bald, Journal of Molecular Liquids 137 (2008) 116. [7] H. Høiland, Journal of the Chemical Society, Faraday Transactions I 71 (1975) 797. [8] F. Spieweck, H. Bettin, Technisches Messen 59 (1992) 285. [9] A. Apelblat, Journal of Molecular Liquids 73 (1997) 49, (74). [10] A. Apelblat, Journal of Molecular Liquids 95 (2002) 99. [11] O. Redlich, D.M. Meyer, Chemical Reviews 64 (1964) 221. [12] F.J. Millero, Chemical Reviews 71 (1971) 147.
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Volumetric studies of aqueous solutions of monosodium salts of some aliphatic dicarboxylic acids at 298.15 K. A new method of data analysis Adam Bald a,⁎, Zdzisław Kinart a, Renato Tomaš b a b
Department of Physical Chemistry of Solutions, Faculty of Chemistry, University of Lodz, Pomorska 163, 90-236 Lodz, Poland Department of Physical Chemistry, Faculty of Chemistry and Technology, University of Split, Nikole Tesle 10, 21000 Split, Croatia
a r t i c l e
i n f o
Article history: Received 11 September 2012 Received in revised form 24 November 2012 Accepted 26 November 2012 Available online 11 December 2012 Keywords: Carboxylic acids Monosodium salts of dicarboxylic acid Apparent molar volume
a b s t r a c t The apparent molar volumes, Vϕ, of monosodium salts of aliphatic dicarboxylic acids of the HOOC(CH2)n(COOH)2 [n=0–5] types in dilute aqueous solution have been determined by precise density measurements, at T= 298.15 K. Densities were measured using a vibrating-tube densimeter (DMA 5000, Anton Paar, Austria) at T= 298.15 K. These results were used to calculate the apparent molar volumes of each solute over the concentration range 0.0050≤ m/(mol·kg−1) ≤0.3000. A new method for determining the values of partial molar volume of the electrolyte of NaHA type has been proposed. This method takes into account all equilibrium occurring in the solution. The variations of Vϕ0 values with aliphatic chain length of analyzed salts were determined. © 2012 Elsevier B.V. All rights reserved.
1. Introduction This work is a continuation of volumetric studies of aqueous solutions of mono- and dicarboxylic acids [1] and sodium salts of these acids [2] and viscosimetric studies of these solutions [3–6]. Research on the properties of anions \OOC(CH2)nCOOH and \OOC(CH2)nCOO\in water is necessary to understand the properties of aqueous solutions of dicarboxylic acids HOOC(CH2)nCOOH. Studies of the properties of these anions can be carried out by investigations of solutions of salts Na2A and NaHA. This method is much more convenient and simpler because these salts are strong electrolytes. Usually it is assumed that in solutions of Na2A, there is no equilibrium which may affect the quantities of anions and the appearance of new anions or molecules [2]. In the case of salt solutions such Na2A hydrolysis can be quantitatively omitted if the range of concentrations of solutions of these salts is properly selected, as shown in our previous work [2]. In the case of solutions of Na2A,hydrolysis can be quantitatively omitted if the range of concentrations of solutions of salt is properly selected, as shown in our previous work [2]. But in the case of research of solutions of NaHA, the situation is more complex. Review of literature shows that only one author tried to determine the values of apparent molar volume of some monosodium salt of dicarboxylic acids in water [7]. In this work, monosodium sodium salts of dicarboxylic acids were treated only as typical strong electrolyte of type 1-1 and chemical equilibria occurring in the solutions were not considered. Therefore, the purpose on the present study was to
⁎ Corresponding author. Tel.: +48 426355846. E-mail address: [email protected] (A. Bald). 0167-7322/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2012.11.029
determine the densities of monosodium salts of the dicarboxylic acids [HOOC(CH2)nCOOH, n = 0–5] in water, at T = 298.15 K. These results were used to calculate the apparent molar volumes (Vϕ) of each solute over the concentration range 0.0050 ≤ m/(mol·kg−1) ≤0.3000. Using a new method that takes into account all the equilibrium present in solution the values of apparent molar volumes Vϕ0 of NaHA at infinite concentration have been determined. The variations of both Vϕ0 with aliphatic chain length of analyzed carboxylic acids were determined.
2. Experimental 2.1. Materials The sources of chemicals were described in our previous papers [1–4]. Double-distilled water additionally was purified by ion exchange and stored under argon. The specific conductivity of water was less than 0.3·10−6 Ω−1 cm−1. Aqueous solutions of the monosodium salt of selected aliphatic dicarboxylic acids were prepared by dissolving equimolar mixture of carboxylic acids and their disodium salts. Used dicarboxylic acids and their disodium salts were prepared as described in the literature [1–6].
2.2. Apparatus and procedures The densities of solutions were measured using an Anton Paar model DMA 5000 densimeter with precision of ±1·10−6 g cm−3, and accuracy ±5·10−6 g cm−3. The instrument was equipped with Peltier-type thermostating unit and temperature was kept constant with accuracy
A. Bald et al. / Journal of Molecular Liquids 178 (2013) 94–98
Table 1 Apparent molal volumes (Vϕ), molarity (c) and molality (m) and fractions α and γ of monosodium salts of aliphatic carboxylic acids in water at 298.15 K. ρ g⋅cm−3
Vϕ cm3 ⋅mol−1
α
γ
Monosodium salts of ethanedioic acid 0 0 0.997043 0.01999 0.02002 0.998460 0.03963 0.03964 0.999847 0.05940 0.05933 1.001240 0.07946 0.07925 1.002650 0.09938 0.09898 1.004048 0.11892 0.11828 1.005417 0.13885 0.13791 1.006812 0.15857 0.15728 1.008190 0.17801 0.17632 1.009546 0.19774 0.19560 1.010920
– 41.25 41.39 41.49 41.57 41.65 41.72 41.78 41.84 41.90 41.96
– 0.075566 0.064984 0.061167 0.059342 0.058463 0.057990 0.057825 0.057810 0.057851 0.057948
– 0.017487 0.023650 0.027733 0.030802 0.033251 0.035224 0.036983 0.038504 0.039813 0.041003
Monosodium salts of propanedioic acid 0 0 0.997043 0.00571 0.00573 0.997443 0.01068 0.01072 0.997791 0.01869 0.01877 0.998351 0.03982 0.04002 0.999825 0.06237 0.06277 1.001394 0.07982 0.08042 1.002604 0.09903 0.09989 1.003934 0.11862 0.11979 1.005288 0.13912 0.14067 1.006702 0.15790 0.15984 1.007997 0.17800 0.18041 1.009382 0.19737 0.20028 1.010714 0.21629 0.21973 1.012004 0.23603 0.24007 1.013362 0.25524 0.25993 1.014671 0.27511 0.28051 1.016031 0.29408 0.30023 1.017323
– 56.13 56.19 56.24 56.34 56.45 56.55 56.63 56.71 56.79 56.85 56.91 56.97 57.07 57.10 57.18 57.24 57.30
– 0.044339 0.043207 0.042442 0.039871 0.035219 0.028143 0.015548 0.007329 0.006997 0.006749 0.006527 0.006343 0.006187 0.006043 0.005918 0.005802 0.005701
– 0.034408 0.037283 0.038807 0.038112 0.034183 0.027488 0.015546 0.007214 0.006902 0.006667 0.006455 0.006280 0.006130 0.005992 0.005871 0.005759 0.005661
Monosodium salts of butanedioic acid 0 0 0.997043 0.01982 0.01991 0.998437 0.04134 0.04158 0.999944 0.06014 0.06057 1.001260 0.08048 0.08117 1.002676 0.10023 0.10124 1.004052 0.11912 0.12048 1.005364 0.13821 0.13998 1.006688 0.15798 0.16023 1.008059 0.17750 0.18028 1.009404 0.19702 0.20040 1.010748 0.21671 0.22074 1.012103 0.23500 0.23968 1.013358 0.25516 0.26064 1.014740 0.27371 0.27996 1.016007 0.29355 0.30069 1.017360
– 69.95 70.10 70.16 70.28 70.35 70.42 70.49 70.55 70.64 70.72 70.79 70.85 70.92 70.99 71.07
– 0.014290 0.010975 0.009685 0.008828 0.008254 0.007841 0.007509 0.007229 0.006997 0.006798 0.006624 0.006481 0.006340 0.006224 0.006110
– 0.014242 0.010956 0.009673 0.008820 0.008248 0.007836 0.007505 0.007225 0.006994 0.006796 0.006622 0.006479 0.006338 0.006222 0.006108
Monosodium salts of pentanedioic acid 0 0 0.997043 0.01912 0.01921 0.998356 0.04054 0.04080 0.999821 0.05412 0.05453 1.000744 0.07886 0.07963 1.002427 0.08974 0.09071 1.003166 0.11916 0.12075 1.005159 0.13761 0.13968 1.006406 0.15796 0.16062 1.007781 0.17722 0.18051 1.009080 0.19644 0.20043 1.010368 0.21516 0.21990 1.011621 0.23391 0.23946 1.012875 0.25375 0.26023 1.014199 0.27295 0.28041 1.015483 0.29186 0.30033 1.016736
– 85.69 85.82 85.96 86.08 86.12 86.24 86.31 86.37 86.43 86.52 86.60 86.67 86.74 86.80 86.88
– 0.018533 0.014143 0.012835 0.011376 0.010930 0.010040 0.009629 0.009258 0.008965 0.008714 0.008501 0.008311 0.008133 0.007977 0.007838
– 0.018481 0.014124 0.012821 0.011367 0.010923 0.010035 0.009625 0.009255 0.008962 0.008711 0.008498 0.008309 0.008131 0.007975 0.007836
Monosodium salts of hexanedioic acid 0 0 0.997043 0.02104 0.02114 0.998446 0.04154 0.04184 0.999807
– 101.73 101.88
– 0.017907 0.014044
– 0.017870 0.014029
c mol⋅dm−3
m mol⋅kg−1
95
Table 1 (continued) ρ g⋅cm−3
Vϕ cm3 ⋅mol−1
α
γ
Monosodium salts of hexanedioic acid 0.06227 0.06286 1.001178 0.08301 0.08397 1.002547 0.10373 0.10515 1.003909 0.12392 0.12588 1.005234 0.14446 0.14706 1.006578 0.16487 0.16821 1.007910 0.18479 0.18892 1.009206 0.19395 0.19848 1.009804
102.02 102.12 102.23 102.33 102.42 102.52 102.61 102.63
0.012277 0.011210 0.010475 0.009939 0.009509 0.009160 0.008874 0.008756
0.012267 0.011204 0.010470 0.009935 0.009505 0.009157 0.008871 0.008754
Monosodium salts of heptanedioic acid 0 0 0.997043 0.01656 0.01664 0.998119 0.03302 0.03325 0.999185 0.04921 0.04964 1.000229 0.06648 0.06720 1.001340 0.08168 0.08272 1.002316 0.09588 0.09727 1.003225 0.11317 0.11504 1.004330 0.12885 0.13124 1.005329 0.14515 0.14812 1.006367 0.15994 0.16351 1.007308
– 117.50 117.63 117.75 117.86 117.94 118.02 118.11 118.19 118.26 118.32
– 0.019523 0.015148 0.013211 0.011974 0.011222 0.010684 0.010167 0.009788 0.009458 0.009202
– 0.019480 0.015131 0.013200 0.011967 0.011217 0.010679 0.010163 0.009785 0.009455 0.009199
c mol⋅dm−3
m mol⋅kg−1
of ± 0.001 K. The densimeter was calibrated with dry air and pure water periodically. The solutions were prepared by adding a weighed amount of concentrated solutions to known amounts of pure water. All the solutions were prepared by mass using an analytical balance (Sartorius RC 210D) with an uncertainty of ±1 · 10 −5 g. 3. Results and discussion The values of apparent molar volumes were calculated based on Eq. (1) Vϕ ¼
1000·ðρ0 −ρÞ M þ m·ρ0 ·ρ ρ
ð1Þ
where: ρ—solution density, ρ0—solvent density, m—molality of solution and M—molar mass of electrolyte. All the solutions of monosodium salts of aliphatic dicarboxylic acid were made by weight and the molalities, m, were converted into molar concentrations, c, by using the following standard relation: c¼
1000·ρ·m : ð1000 þ m·M Þ
ð2Þ
The values of apparent molar volumes Vϕ, together with the values of molar concentrations, molalities and density of the solutions are summarized in Table 1.
Table 2 Values of Vϕ0 at T = 298.15 K for studied monosodium salts of acid. HOOC(CH2)nCOONa n
Vϕ0
Vϕ0 lit.
0 1 2 3 4 5
41.97 56.24 69.71 85.53 101.47 117.26
41.19 55.96 68.88 84.77 100.98 116.59
[7]a [7] [7] [7] [7] [7]
a The value calculated on the basis of the Vϕ0 for HOOC-COOK [7] and value of the difference V 0ϕK þ −V 0ϕNaþ = 10.23 cm3 mol−1 [12].
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A. Bald et al. / Journal of Molecular Liquids 178 (2013) 94–98
Table 3a The dependence of experimental and calculated values Vϕ and the values of chosen components of Eq. (17): 0.5(α − γ) V ϕH2 Aði2Þ ; 0.5(α + γ) V ϕNa2 AðiÞ ; (1 − α − γ) V ϕNaHAðiÞ ; γ V ϕH2 AðuÞ for monosodium salts of ethanedioic acid. Monosodium salts of ethanedioic acid c mol⋅dm−3
V ϕ ðex:Þ cm3 ⋅mol−1
V ϕ ðcal:Þ cm3 ⋅mol−1
0.5(α − γ) V ϕH2 Aði2Þ
0.5(α+ γ) V ϕNa2 AðiÞ
(1 − α − γ) V ϕNaHAðiÞ
γ V ϕH2 AðuÞ
0.01999 0.03963 0.05940 0.07946 0.09938 0.11892 0.13885 0.15857 0.17801 0.19774
41.25 41.39 41.49 41.57 41.65 41.72 41.78 41.84 41.90 41.96
41.08 41.40 41.55 41.65 41.72 41.77 41.81 41.84 41.86 41.89
0.77 0.55 0.44 0.38 0.33 0.30 0.28 0.26 0.24 0.22
1.12 1.07 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22
38.27 38.52 38.55 38.53 38.49 38.45 38.40 38.34 38.30 38.25
0.93 1.26 1.48 1.64 1.77 1.88 1.97 2.06 2.13 2.19
The density of water at 298.15 K was found to be 0.997043 g cm−3; this value is equal to that from the literature [8]. In the case of the solutions of monosodium salts of dicarboxylic acids should be considered in accordance with Apelblat [9], the following processes: þ
−
NaHA → Na þ HA −
þ
2−
ð4Þ
−
H þ HA ⇌ H2 A:
ð5Þ
If you enter a fraction of α and γ h α¼
A2−
;
2−
i
ð7Þ
¼ cα;
ð8Þ
½H2 A ¼ cγ;
ð9Þ
−
½HA ¼ c ð1−α–γÞ; h h
þ
H
i
þ
Na
ð10Þ
¼ c ðα–γÞ; i
K A2 ¼
ð1−α−γÞ 1 ; ¼ K D2 ½cα ð1−α−γ Þy2
ð14Þ
where KD1 and KD2 are dissociation constants. The activity coefficient quotient (y) of Eqs. (13) and (14) can be described using relations: ð15Þ
and
concentration for each forms of the electrolyte can be described as follows: A
ð13Þ
ð6Þ
½H A γ¼ 2 ; c
h
1 γ ; ¼ K D1 ½cðα−γÞð1−α−γÞy1
y1 ¼ yHþ yHA− =yH2 A ;
i
c
K A1 ¼
ð3Þ
HA ⇌ H þ A þ
The values of α and γ for each concentrations can be calculated using the association constants KA1 and KA2, described by equations:
ð11Þ
¼ c:
ð12Þ
y2 ¼ yHþ yA2− =yHA− :
ð16Þ
The activity coefficient of the undissociated acid yH2 A is equal to unity. The activity coefficients of ions can be calculated on the basis of the Debye–Hückel equation. More details related to the description of the Debye–Hückel equation may be found in our earlier work [5]. Using the numerical methods for performing successive approximations from Eqs. (12) and (13) the values α and γ for each concentration of electrolyte (c) can be determined [5]. The values of KA1 and KA2 have been taken from [10]. The calculated numerically values of α and γ are summarized in Table 1. A solution of monosodium salt of the dicarboxylic acid can be treated as a mixture of a completely dissociated electrolytes, i.e. NaHA, H2A, Na2A, with concentrations of c (1− α − γ), 1/2c (α − γ), 1/2c (α + γ)
Table 3b The dependence of experimental and calculated values Vϕ and the values of chosen components of Eq. (17): 0.5(α − γ) V ϕH2 Aði2Þ ; 0.5(α + γ) V ϕNa2 AðiÞ ; (1 − α − γ) V ϕNaHAðiÞ ; γ V ϕH2 AðuÞ for monosodium salts for monosodium salts of heptanedioic acid. Monosodium salts of heptanedioic acid c mol⋅dm−3
V ϕ ðex:Þ cm3 ⋅mol−1
V ϕ ðcal:Þ cm3 ⋅mol−1
0.5(α−γ) V ϕH2 Aði2Þ
0.5(α+γ) V ϕNa2 AðiÞ
(1−α−γ) V ϕNaHAðiÞ
γ V ϕH2 AðuÞ
0.01656 0.03302 0.04921 0.06648 0.08168 0.09588 0.11317 0.12885 0.14515 0.15994
117.50 117.63 117.75 117.86 117.94 118.02 118.11 118.19 118.26 118.32
117.58 117.70 117.80 117.90 117.97 118.03 118.11 118.17 118.24 118.29
0.0022 0.0009 0.0006 0.0004 0.0003 0.0003 0.0002 0.0002 0.0002 0.0002
1.98 1.54 1.34 1.22 1.14 1.09 1.03 0.99 0.96 0.94
112.95 114.11 114.67 115.06 115.32 115.53 115.73 115.90 116.05 116.18
2.57 1.99 1.74 1.58 1.48 1.41 1.34 1.29 1.25 1.21
A. Bald et al. / Journal of Molecular Liquids 178 (2013) 94–98
140.00
respectively and undissociated acid H2A(u) with a concentration equal to cγ. Thus, the apparent molar volume can be described by the equation:
ð17Þ
According to Redlich–Rosenfeld equation [11] 0
V ϕNaHAðiÞ ¼ V ϕNaHAðiÞ þ SVNaHAðiÞ 0
V ϕH2 Aði2Þ ¼ V ϕH2 Aði2Þ þ SVH2 Aði2Þ V ϕNa2 AðiÞ ¼
0 V ϕNa2 AðiÞ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1−α−γÞc þ bvNaHAðiÞ c
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ðα−γ Þc þ bvH2 Aði2Þ c 2
ð17aÞ
100.00 80.00
y = 15.879x + 37.881 2 R =1
60.00 40.00 20.00 0.00
ð17bÞ
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ðα þ γÞc þ bvNa2 AðiÞ c þ SVNa2 Aði Þ 2
ð17cÞ
0
V ϕH2 AðuÞ ¼ V ϕH2 AðuÞ þ bvH2 AðuÞ c:
ð17dÞ
Assuming as Millero [12] that SvNaHA(i) = 1.868, SVH2 Aði2Þ = 9.607 and SVNa2 AðiÞ = 9.607, Eq. (17) takes the form: h i pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V ϕ ¼ ð1−α−γ Þ V 0ϕNaHAðiÞ þ 1:868 ð1−α−γÞc þ bvNaHAðiÞ " # rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 0 ðα−γ Þc þ bvH2 Aði2 Þ c þ ðα−γÞ V ϕH2 Aði2Þ þ 9:607 2 2 " # rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 0 ðα þ γÞc þ bvNa2 AðiÞ c þ ðα þ γ Þ V ϕNa2 AðiÞ þ 9:607 2 2 h i 0 þγ V ϕH2 AðuÞ þ bvH2 Aðu Þ c :
ð18Þ
Values V ϕH2 Aði2 Þ 0 , V 0ϕNa2 Aði2Þ in Eq. (18) was derived from work [2] while the values V 0ϕH2 AðuÞ from work [1]. The components of 1 1 ðα−γÞbvH2 Aði2Þ c, ðα þ γÞbvNa2 Aði2Þ c and γbvH2 AðuÞ c in Eq. (2) may be 2 2 60.00
A
50.00
VΦ [cm3 mol-1]
120.00
VoNaHA [cm3 mol-1]
1 1 V ϕ ¼ ð1−α−γ ÞV ϕNaHAðiÞ þ ðα−γ ÞV ϕH2 Aði2Þ þ ðα þ γÞV ϕNa2 AðiÞ 2 2 þ γV ϕH2 AðuÞ :
97
40.00 30.00 20.00 10.00
0.00 140.00
B 120.00 100.00 80.00
0
1
2
3
4
5
6
n Fig. 2. The dependences of limiting partial volume of (VNaHA) as a function of number of carbon atoms (n) in the molecules of monosodium salts of acid NaOOC(CH2)nCOOH: ◊ the experimental values; ■ literature [7]. Vϕo =15.879+37.881×n, R2 =1.
omitted in calculations due to their small values, less than the estimated accuracy of Vϕ. Thus, Eq. (18) only determines the values V 0ϕNaHAðiÞ and bvNaHAðiÞ c. The V 0ϕNaHAðiÞ values determined on the basis of a nonlinear least-squares method are summarized in Table 2. As can be seen the values which have been obtained in this work are systematically higher than those obtained by Høiland [7]. This effect may be associated with some of the simplifications that have been adopted by Høiland [7]. He assumed that the investigated NaHA salts are strong electrolytes and their solutions contain only Na + and HA− ions. In order to determine the values of V 0ϕNaHAðiÞ , Høiland applied a simple procedure based on the extrapolation of the results to infinite dilution using a simple equation proposed by Redlich–Rosenfeld. The values of components 0.5(α−γ)∙ V ϕH2 Aði2Þ ; 0.5(α+ γ)∙V ϕNa2 AðiÞ ; (1− α− γ) V ϕNaHAðiÞ ; γ⋅V H2 AðuÞ with Eq. (17) are summarized in Tables 3a and 3b. The plots of these values as a function of concentration for the two salts [monosodium salt of ethendioic acid (n=0) and monosodium salt of heptanedioic acid (n=5)] are presented at Fig. 1. As can be seen, the part of these components in experimental values of Vϕ is important. This applies particularly to component of γ V H2 AðuÞ which is related to the presence of undissociated dicarboxylic acid in the studied solutions. The dependence of apparent molar volumes at infinite concentration (Vϕ0) as the function of the number of carbon atoms (n) in the hydrocarbon chain of aliphatic acid is presented at Fig. 2. As can be seen, increase in the number of carbon atoms (n) of one causes an increase in the value of Vϕ0 about 15.89 cm 3/mol. This means that the molar volume of the \CH2\ group is equal approximately to 15.89 cm3/mol. This value is very well correlated with the similar values which has been designated based on the studies of the following electrolytes: sodium salts of monocarboxylic acids ( V CH2 = 15.56 cm 3/mol) [2], sodium salts of dicarboxylic acids (V CH2 = 15.62 cm3/mol) [2], monocarboxylic acids (V CH2 = 15.6 cm 3/mol) [1] and dicarboxylic acids (V CH2 = 15.96 cm 3/mol) [1].
60.00
4. Conclusions 40.00 20.00 0.00 0.000
0.050
0.100
0.150
0.200
0.250
c [mol dm-3] Fig. 1. The dependence of experimental (●) and calculated (□) values of Vφ and the values of chosen components of Eq. (17):* (1 − α − γ) V ϕNaHAðiÞ ; Δ 0.5(α − γ) V ϕH2 Aði2Þ ; x 0.5(α + γ) V ϕNa2 AðiÞ ; ♦ γ V ϕH2 AðuÞ for monosodium salts of ethenedioic acid (A) and for monosodium salts of heptanedioic acid (B).
On the basis of accurate density measurements in aqueous solutions of monosodium salts of dicarboxylic acids the value of apparent molar volumes of these salts have been determined at 298.15 K. It was shown that in addition to Na+ and HA− ions, H+ and A2− ions are also present in the solution and also molecules of H2A and their concentrations have been determined. It has been shown that the analysis of apparent molar volume of the concentration should use the modified equation which takes into account all equilibrium occurring in the solution. It was found that the partial molar volumes for the salts investigated are positive and increase linear (corelation coefficient is high, R2 =1)
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A. Bald et al. / Journal of Molecular Liquids 178 (2013) 94–98
with increasing number of carbon atoms in their carbon chain. The appointed part of \CH2\ group in the partial molar volume is almost identical to that which has been designated on the basis of aqueous solutions of disodium salts of dicarboxylic acids, monocarboxylic acids, monosodium salts of monocarboxylic acids and undissociated mono-and dicarboxylic acids. References [1] A. Bald, Z. Kinart, Journal of Solution Chemistry 40 (2011) 1. [2] Z. Kinart, A. Bald, Physics and Chemistry of Liquids 49 (2011) 3.
[3] A. Chmielewska, A. Wypych-Stasiewicz, A. Bald, Journal of Molecular Liquids 122 (2005) 110. [4] A. Chmielewska, A. Wypych-Stasiewicz, A. Bald, Journal of Molecular Liquids 130 (2007) 42. [5] A. Chmielewska, A. Wypych-Stasiewicz, A. Bald, Journal of Molecular Liquids 136 (2007) 11. [6] A. Chmielewska, A. Bald, Journal of Molecular Liquids 137 (2008) 116. [7] H. Høiland, Journal of the Chemical Society, Faraday Transactions I 71 (1975) 797. [8] F. Spieweck, H. Bettin, Technisches Messen 59 (1992) 285. [9] A. Apelblat, Journal of Molecular Liquids 73 (1997) 49, (74). [10] A. Apelblat, Journal of Molecular Liquids 95 (2002) 99. [11] O. Redlich, D.M. Meyer, Chemical Reviews 64 (1964) 221. [12] F.J. Millero, Chemical Reviews 71 (1971) 147.