185
Acta Chim. Slov. 1998, 45(2), pp. 185-198 (Received 28.1.1998)
Volumetric Properties of Alkali Metal p-Toluenesulphonates in Water
as a Function of Temperature
C. Pohar and S. Skale
Faculty of Chemistry and Chemical Technology, University of Ljubljana, 1000
Ljubljana, Slovenia
Abstract
Density data are presented for alkaline salts of p-toluenesulphonic acid at temperatures from 5 to 40 C up to concentrations of ~2 mol/kg. The apparent molar volumes, V20, were calculated for these solutions from the density measurements. The apparent molar volumes were fitted to the equation of Redlich and Meyer to determine two important parameters: i) the apparent molar volume at infinite dilution, V20, and ii) the deviation constant by. At 25 C the additivity rule of the individual ionic contributions was confirmed. Further, V2<p increases with increasing temperature for all the salts, while the parameters by monotonically decrease from positive to negative values (in the order Li<Na<K<Rb<Cs) as the temperature is increased. The effect of temperature on the apparent molar volumes of the p-toluenesulphonates in water at infinite dilution is similar to that of other simple electrolytes.
Key words: Alkaline p-Toluenesulphonates; Apparent Molar Volume; Density; Apparent Molar Expansibility.
Dedicated to the memory of Prof. Savo Lapanje
186
Introduction
Thermodynamic properties of electrolyte solutions expressed as apparent or partial molar quantities are useful in characterizing solute-solvent and solute-solute interactions. One approach toward a deeper understanding of interactions in polyelectrolyte solutions is to study the monomer system. It is reasonable to expect the electrochemical properties of the sulphonic group in polystyrenesulfonate solutions to be similar to those in low molecular analogues, i.e. various substituted benzenesulphonic acids and their salts [1]. Study of the monomer system is, moreover, facilitated by the fact that accurate theories are available for the analysis of experimental data on solutions of simple electrolyte.
The excess thermodynamic properties of electrolyte solutions, i.e. osmotic coefficients, heats of dilution, or volume changes on dilution, are determined by the ion-ion and ion-solvent interactions. Additional information about interactions in solution may be obtained by studying the system at various temperatures since different interaction potentials have different temperature dependencies [2]. Recently, the heats of dilution (AHD, e—»0.002 mole-dm" ) at various temperatures have been measured [3] for aqueous solutions of the alkaline salts of p-toluenesulphonic acid. In the another publication [4], a preliminary theoretical analysis of the osmotic coefficients, heats of dilution and volume changes on dilution based on Friedman's theory [5] was presented. Unfortunately, except for the osmotic coefficients and heats of dilution, a complete investigation of the concentration dependence of other properties of the alkali p-toluenesulphonates is lacking. In the literature we found the partial molar volume data of p-toluenesulphonic acid and its sodium salt for the temperature of 25 °C [6], but no measurements for other temperatures were presented so far. Since the concentration dependence of the apparent or partial molar volume over a sufficiently wide range of temperature is needed to verify the theoretical models of electrolyte solution, we measured the densities of Li, Na, K, Rb and Cs salts of p-toluenesulphonic acid in water at 5, 15, 25, and 40 °C. From the concentration dependence of the apparent molai volumes and with the use of the Redlich-Meyer equation [7], the apparent molai volumes at infinite dilution and the parameter by were determined. The differences in values of these quantities between various salts were interpreted with respect to
187
structural interactions [8-10]. Note that extensive reviews of the volumetric properties of electrolyte solutions have been published by Millero [11,12].
Experimental
Toluene-4-sulphonic acid monohydrate (or p-toluenesulphonic acid monohydrate, abbreviated to HTS.H20, Merck 99%) was used as a starting material for preparation of alkaline (Li, Na, K, Rb, Cs) p-toluenesulphonates (TS). All salts were prepared by neutralization of an acid solution by the corresponding metal hydroxide or carbonate until a pH of about 5 was obtained. The concentration of the acid stock solution was determined by Potentiometrie titration, while the concentrations of stock salt solutions were measured spectrophotometrically. In all the experiments water doubly distilled in quartz was used.
The densities of solution d were measured at a given temperature using a Paar digital precision density meter, Model DMA 620, with a reproducibility of 10" g-cm" . About 10 measurements at each concentration were carried out for each solution. Calibrations at each temperature were made with pure water [13], and with dry air at least twice a day. The temperature of the cell compartment was controlled to ±0.01 °C using a Heto circulating thermostat. The temperature was measured in a water bath with a platinum resistance thermometer (Degusa PtlOOO) and a thermistor inserted into the cell of the density meter. The water bath and the density meter were located so that a stream of water at constant temperature travelled between them.
The apparent molar volumes V20 were calculated from the densities fusing [12]
M     I000(d°-d) d           mdd°
where d ° is the density of pure water, m the molality and M the molar mass of the
solute.
The  experimental  error  in   V20,  which  stems  from  uncertainties   in  the  density
measurements, exceeds that from the uncertainties in concentration. The error was
188
T                         1
estimated to be < ± 1 cm -mol"  at the lowest measured concentration and decreases
with increasing concentration.
Results
Experimentally obtained densities are given in Table I for each of the salts and the acid, as a function of molality and temperature. Table I also lists the apparent molar volumes calculated by Equation (1).
TABLE  I.     Densities  and  Apparent  Molar  Volumes  of Aqueous  Alkaline  p-Toluenesulphonate Solutions as a Function of Concentration at Various Temperatures.
HTS 5 UC                                                   HTS 15 UC
ma	db	V2*c	m	d	V20
0.0104	1.00055	115.56	0.0094	0.99961	118.42
0.0505	1.00280	115.66	0.0466	1.00159	118.61
0.1053	1.00582	115.86	0.0764	1.00316	118.64
0.5559	1.02913	116.34	0.2959	1.01434	118.96
1.0573	1.05208	116.82	0.6487	1.03109	119.14
1.1815	1.05752	116.77	0.8232	1.03892	119.15
1.3301	1.06360	116.92	1.0903	1.05034	119.16
1.4162	1.06717	116.89	1.4221	1.06360	119.22
1.6218	1.07514	117.05	1.8729	1.08042	119.16
			2.1339	1.08952	119.13
a Units: mol-kg'
b            -3
g-cm ccm -mol" .
HTS 25 UC                                                 HTS 40 UC
m	d	V20	m	d	V20
0.0095	0.99754	120.69	0.0479	0.99462	122.38
0.0471	0.99946	120.90	0.0776	0.99608	122.50
0.0775	1.00099	121.07	0.3024	1.00680	122.76
0.2984	1.01177	121.28	0.6540	1.02235	123.01
0.6561	1.02801	121.47	0.8312	1.02980	122.97
0.8321	1.03548	121.56	1.1198	1.04118	123.06
1.1057	1.04664	121.55	1.4590	1.05380	123.04
1.4359	1.05937	121.46	1.9248	1.06967	123.07
1.9029	1.07577	121.50	2.2040	1.07871	122.97
2.1728	1.08473	121.44			
189
LiTS 5UC
m	d
0.0109	1.00065
0.0505	1.00313
0.1021	1.00631
0.4326	1.02575
0.9349	1.05262
1.2196	1.06659
1.3115	1.07085
1.5196	1.08043
1.6724	1.08713
1.9019	1.09687
LiTS 25 UC
m	d
0.0105	0.99766
0.0520	1.00004
0.1067	1.00315
0.5777	1.02817
0.9725	1.04729
1.2742	1.06087
1.4570	1.06879
1.5987	1.07463
1.7865	1.08219
1.9264	1.08777
NaTS 5UC
m	d
0.0107	1.00081
0.0509	1.00397
0.1004	1.00781
0.4287	1.03190
0.9321	1.06507
1.0858	1.07434
1.2408	1.08343
1.5461	1.10020
2.0830	1.12727
LiTS
v20	m
114.94	0.0105
115.08	0.0515
115.23	0.1069
115.54	0.5756
115.72	0.9694
115.79	1.2667
115.87	1.4204
115.86	1.5718
115.91	1.7285
115.94	1.8988
LiTS 40
V20	m
120.13	0.0106
120.36	0.0517
120.42	0.1073
120.69	0.5774
120.61	0.9804
120.56	1.2777
120.46	1.4318
120.47	1.5950
120.43	1.7701
120.34	1.9185
NaTS 15
V20	m
114.78	0.0186
115.05	0.2563
115.17	0.5133
115.98	0.7930
116.74	1.0755
116.98	1.3229
117.13	1.4769
117.56	1.6947
118.04	1.8991
	2.0779
°c
d                     V20
0.99973	117.92
1.00218	118.04
1.00544	118.13
1.03129	118.45
1.05104	118.46
1.06510	118.29
1.07192	118.31
1.07846	118.31
1.08518	118.22
1.09236	118.07
C
d____________V20
0.99282	121.38
0.99515	121.60
0.99825	121.69
1.02277	122.03
1.04182	122.04
1.05494	121.96
1.06146	121.90
1.06806	121.91
1.07507	121.81
1.08080	121.76
d____________V20
1.00052	117.72
1.01797	118.35
1.03561	118.76
1.05359	119.03
1.07055	119.27
1.08448	119.49
1.09276	119.61
1.10408	119.72
1.11412	119.88
1.12258	119.99
190
NaTS 25 UC
m	d
0.0186	0.99843
0.2559	1.01535
0.5114	1.03243
0.7846	1.04949
1.0731	1.06634
1.3143	1.07963
1.4768	1.08819
1.6828	1.09855
1.8873	1.10851
2.0727	1.11714
KTS 5 UC
m	d
0.0096	1.00080
0.0514	1.00436
0.1008	1.00854
0.4309	1.03479
0.8165	1.06248
0.9504	1.07153
1.0973	1.08107
1.2625	1.09121
1.4109	1.10022
1.5724	1.10956
KTS 25 UC
m	d
0.0134	0.99811
0.0645	1.00214
0.1342	1.00752
0.6682	1.04536
0.8250	1.05547
1.0109	1.06698
1.1432	1.07484
1.2709	1.08215
1.4134	1.09013
1.6321	1.10183
NaTS
v20	m
119.93	0.0184
120.57	0.2519
120.86	0.5025
121.15	0.7816
121.37	1.0474
121.49	1.2918
121.56	1.4386
121.69	1.6535
121.74	1.8519
121.80	2.0246
KTS 15
V20	m
123.81	0.0133
124.10	0.0639
124.18	0.1337
125.13	0.6580
125.85	0.8195
125.98	1.0002
126.15	1.1277
126.48	1.2541
126.55	1.4055
126.71	1.6109
___________KTSUC
V20___________m
130.57           0.0132
130.83           0.1319
131.00           0.6596
131.79           0.8025
131.94           0.9908
132.06           1.1161
132.14           1.4031
132.26           1.6158 132.31 132.41
°C
d                     V20
0.99357	120.78
1.01010	121.40
1.02677	121.64
1.04413	121.86
1.05966	122.00
1.07319	122.07
1.08099	122.10
1.09191	122.19
1.10167	122.19
1.10983	122.21
d____________V20
1.00020	127.59
1.00433	127.79
1.00992	128.01
1.04850	128.90
1.05931	129.09
1.07092	129.25
1.07882	129.33
1.08641	129.43
1.09512	129.59
1.10656	129.70
d____________V20
0.99327	131.43
1.00245	131.80
1.03964	132.58
1.04896	132.54
1.06058	132.72
1.06799	132.84
1.08422	133.00
1.09578	132.96
191
RbTS 5UC                                              RbTS 15 UC
m	d	V20	m	d		V20
0.0097	1.00120	129.67	0.0090	1.00021		133.79
0.0500	1.00626	129.86	0.0505	1	00526	134.05
0.0976	1.01216	130.11	0.4023	1	04562	134.79
0.2107	1.02586	130.40	0.7966	1	08633	135.38
0.3192	1.03854	130.76	1.0107	1	10672	135.61
0.4261	1.05073	130.89	1.0935	1	11433	135.67
0.5645	1.06587	131.26	1.2118	1	12500	135.71
0.6937	1.07957	131.44	1.3905	1	14036	135.91
0.8371	1.09415	131.74	1.5548	1	15397	136.02
RbTS 25 UC                                             RbTS 40 UC
m	d	V20	m	d	V20
0.0091	0.99814	136.09	0.0089	0.99329	136.59
0.0500	1.00303	136.30	0.0499	0.99816	136.88
0.1370	1.01320	136.55	0.1374	1.00835	137.19
0.3981	1.04220	137.12	0.3959	1.03701	137.55
0.7859	1.08163	137.49	0.7809	1.07606	137.95
1.0100	1.10259	137.71	0.9964	1.09632	138.06
1.0788	1.10878	137.80	1.0692	1.10296	138.06
1.2127	1.12056	137.88	1.1935	1.11387	138.20
1.3959	1.13617	137.92	1.3824	1.13000	138.24
			1.5304	1.14200	138.37
CsTS5uC                                               CsTS 15 UC
m	d	V20	m	d		V20
0.0099	1.00160	137.62	0.0104	1.00078		141.37
0.0385	1.00633	137.84	0.0495	1	00709	141.54
0.0665	1.01091	137.99	0.1116	1	01694	141.77
0.3009	1.04777	138.60	0.7055	1	10246	142.83
0.4405	1.06854	138.89	0.8002	1	11487	142.88
0.5578	1.08530	139.23	0.9184	1	12981	143.06
0.6888	1.10344	139.44	1.0216	1	14251	143.19
0.8348	1.12290	139.66	1.1136	1	15360	143.23
1.2457	1.17346	140.44	1.2552	1	17014	143.32
192
CsTS25uC                                             CsTS 40 UC
m	d	V20	m	d		V20
0.0494	1.00492	143.65	0.0103	0.99387		143.59
0.1099	1.01437	143.88	0.0490	1	00001	143.78
0.3445	1.04945	144.39	0.1099	1	00953	144.03
0.6945	1.09759	144.76	0.3434	1	04443	144.43
0.7977	1.11085	144.95	0.6904	1	09217	144.84
0.9103	1.12498	145.02	0.7931	1	10549	144.87
1.0184	1.13814	145.09	0.9039	1	11939	144.99
1.0955	1.14726	145.19	1.0118	1	13255	145.08
1.2307	1.16283	145.33	1.0874	1	14161	145.08
			1.2214	1	15713	145.21
The apparent molai volumes at infinite dilution V20 were calculated using Equation (2) proposed by Redlich and Meyer [7]:
VmESvcU2aV^Cbvc                                                                                      (2)
where Sy (in dm   -cm -mol"   ) is the Debye-Hückel limiting slope, which for 1:1 type electrolytes is the following function of temperature t (in °C ) [12]
Sv a 1.4447 C 1.6799xl0"2rE 8.4055x10~6t2 C 5.5153xlO~V                               (3)
and by (in cm -dm -mol" ) is the empirical deviation constant. The experimental results for LiTS and KTS are also shown graphically in Figures 1 and 2. The apparent molar volumes of alkaline p-toluenesulphonates at infinite dilution and the deviation constants by at various temperatures are collected in Table II. The possible experimental errors are given in parentheses.
193
123
r-    I2OF-
o
E
co
E . Ü
10^117^
> co
>"
114
0
0.64
c/mol dm
—3
1.28
Figure 1. Plot of V20 - SyV e   vs. molarity for LiTS in water at various temperatures; Sy from Equation (3).
194
Figure 2. Plot of V20- Sv Ve   vs. molarity for KTS in water at various temperatures; S y from Equation (3).
TABLE II. Apparent Molar Volumes of Alkaline p-Toluenesulphonates at Infinite Dilution and the Deviation Constant by at Various Temperatures.
HTS                                                                         LiTS
td	V200	by	V2»°	by
5	115.36 (0.30)	-0.08 (0.30)	114.77 (0.24)	-0.48 (0.24)
15	118.27 (0.23)	-0.77 (0.23)	117.75 (0.25)	-1.08 (0.25)
25	120.57 (0.23)	-0.90 (0.23)	119.97 (0.24)	-1.24 (0.24)
40	121.95 (0.11)	-1.02 (0.11)	121.17 (0.25)	-1.31 (0.25)
doc
NaTS                                                                         KTS
t	V200	by	V2»°	by
5	114.63 (0.26)	0.87 (0.260)	123.68 (0.34)	1.04 (0.34)
15	117.47 (0.21)	0.19 (0.21)	127.38 (0.3)	0.29 (0.30)
25	119.67 (0.21)	-0.15 (0.21)	130.36 (0.30)	-0.05 (0.30)
40	120.49 (0.22)	-0.60 (0.22)	131.14 (0.44)	-0.44 (0.44)
RbTS                                                                         CsTS
t	V200	by	V2»°	by
5	129.49 (0.96)	1.20 (0.96)	137.46 (0.64)	1.26 (0.64)
15	133.64 (0.55)	0.37 (0.55)	141.17 (0.62)	0.42 (0.62)
25	135.90 (0.47)	0.05 (0.47)	143.24 (0.60)	0.14 (0.60)
40	136.41(0.42)	-0.38 (0.42)	143.35 (0.59)	-0.32 (0.59)
Discussion
The apparent molar volumes presented in this work cannot be compared directly with literature values since, to our knowledge, no such data were published. It is possible, however, to make some comparison of the temperature dependence of V2& with those solutes for which data are available. To test the consistency of the experimental results, the additivity of the apparent molar volumes at infinite dilution at 25 °C was examined. The differences between the parameters V2<p, A are given in Table III. One can notice that the differences A for alkaline p-toluenesulphonates are very close to those for alkaline chlorides. The discrepancies lie within the experimental error of the determination of V20 . This result is not unexpected since at the infinite dilution limit the ion-ion interactions vanish and the V2<p values represent only ion-water interactions.
195
In the case of complete dissociation the A values depend only on the difference by which different ions affect the structure of water.
Table III. Differences, h, of the V20  Values for Alkaline Chlorides and Alkaline p-Toluenesulphonates at 25 °C.
Ion	CI" [10]	h	TS"
Li+	16.91	103.06	119.97
h	-0.29		-0.30
Na+	16.62	103.05	119.67
h	10.19		10.69
K+	26.81	103.55	130.36
h	5.13		5.54
Rb+	31.94	103.96	135.90
h	7.23		7.34
Cs+	39.17	104.07	143.24
To examine the effect of temperature on V20 for alkaline p-toluenesulphonates, the results for V20 were expressed as a polynomial function of temperature and the polynomial was then differentiated with respect to temperature. This way a function was obtained which allowed calculation of the apparent molar expansibility of the solute at the infinite dilution limit [12] :
F°   a
ÔV-,
20
^
(4)
Figure 3 shows E2 J for Li and K p-toluenesulphonate solutions as a function of temperature. E2®° values for LiCl and KCl [12] are included in Figure 3 for comparison. The conclusion is that the values of E20 for alkaline p-toluenesulfonate solutions decrease with increasing temperature, as in the case of other simple electrolytes.
196
-0.2
0
10
20
30
40
Figure 3. Partial molar expansibility of aqueous LiTS, KTS, LiCl and KCl at infinite dilution as a function of temperature.
There are, however, differences in the magnitude of E2® and in the shape of the curve. It seems reasonable to attribute this effect to the influence of the large aromatic anion on the structure of water. (See also Figure 4). Hepler [14] has pointed out that from the thermodynamic relation
rćžL
âP j
= -T
dr1 j
= -T
ar
(5),
where   Cp is the partial molar heat capacity at infinite dilution, one can discern the type
of effect. A positive value of
âP j
or a negative value of
JT
is evidence of the
structure breaking effect of the solute. It seems then reasonable to regard the ion of the aromatic electrolyte (cf. Figure 4) as having a dual character: it has a "structure making" effect on water on the aromatic side and a "structure breaking" effect on the side of the sulphonic group. The former effect expands, and the latter diminishes the apparent size
197
of   an ion. Both types of effect are temperature dependent. At higher temperatures électrostriction becomes more important leading to a reduction of size [12].
Figure 4. The structure of p-toluenesulphonic acid.
The values obtained for iy in Equation (2) are tabulated in Table II. Since there is no theory that covers this empirical term it is not known what significance to attach to it, although it probably has to do primarily with solute-solute interactions. One can see, however, that iy is positive at lower temperatures and becomes less positive or more negative, as the temperature rises. This behaviour is consistent with that found by Helgeson and Kirkham [15] for several inorganic salts, and recently also by Strong et al. [16] for some methyl substituted benzoic acids and their sodium salts.
Finally, it should be mentioned that direct comparison of the apparent molai volumes of polyelectrolytes with those of model electrolytes is not possible. Skerjanc [17] has demonstrated experimentally and theoretically a sharp fall of W0 with decreasing polyelectrolyte concentration. These results lead to the conclusion that W0 data obtained by linear extrapolation of W0 to zero concentration [18,19] should be accepted with a great deal of caution. Furthermore, the apparent molar volumes of polyelectrolytes are not additive, the reason being the so-called site binding of counterions [20].
198
Acknowledgments: This work was supported by the Slovenian Ministry of Science and Technology. The authors thank Professor V. Vlachy for critical reading of the manuscript and Mr. T. Zupačič nfor his excellent technical assistance.
References
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[12] F. J. Millero in Water and Aqueous solutions, R. H. Hörne ed., Wiley, New York,
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1969,2,401. [19] B. E. Conway, J. E. Desnoyers, and A. C. Smith, Phyl. Trans. Roy. Soc. London,
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Povzetek
Izmerili smo gostote raztopin alkalijskih soli p-toluensulfonske kisline pri temperaturah 5, 15, 25 in 40 °C in v koncentracijskem območju od 0.01 do 2 mol-kg"1. Iz dobljenih podatkov smo izračunali navidezne molske volumne V20 ¦ Z uporabo Redlich-Meyerjeve enačbe smo določili navidezne molske volumne pri neskončnem razredčenju V20 in deviacijske parametre by. Ugotovili smo, da velja pravilo o aditivnosti navideznih ionskih volumnov pri temperaturi 25 °C. Vrednosti V20 naraščajo, vrednosti parametrov by, pa padajo z naraščajočo temperaturo. Temperaturna odvisnost volumskih lastnosti raztopin alkalijskih p-toluensulfonatov je podobna temperaturni odvisnosti alkalijskih kloridov.