Interactions of potassium fluoride with coexistent components in water–dimethyl sulfoxide mixed solvent at different temperatures

Thermochimica Acta 525 (2011) 197–205

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Thermochimica Acta journal homepage: www.elsevier.com/locate/tca

Interactions of potassium fluoride with coexistent components in water–dimethyl sulfoxide mixed solvent at different temperatures K. Rajagopal a,∗ , S. Edwin Gladson b,1 a b

Department of Physics, Government College of Engg., Tirunelveli 627007, Tamil Nadu, India Department of Physics, St. Xavier’s Catholic College of Engg., Chunkankadai 629003, Tamil Nadu, India

a r t i c l e

i n f o

Article history: Received 22 January 2011 Received in revised form 9 August 2011 Accepted 11 August 2011 Available online 19 August 2011 Keywords: Potassium fluoride Dimethyl sulfoxide Partial molal volume Partial molal compressibility Viscosity B-coefficient

a b s t r a c t Apparent molal volumes (Vϕ ), apparent molal compressibilities (Kϕ ) and viscosity A and B-coefficients of potassium fluoride in aqueous solutions of dimethyl sulfoxide (DMSO), have been evaluated at T = 303.15, 308.15, 313.15 and 318.15 K from density, velocity and viscosity data, respectively. The standard partial molal volumes (Vϕ 0 ), standard partial molal volumes of transfer (Vϕ 0 ), standard partial molal compressibilities (Kϕ 0 ) and standard partial molal compressibilities of transfer (Kϕ 0 ) have been determined and interpreted in terms of solute–solvent interactions. Hepler’s coefficient (∂2 Vϕ 0 /∂T2 ) and variation of B coefficient with temperature (dB/dT) have been interpreted in terms of the structure-making/structurebreaking effects of potassium fluoride in the mixture. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Electrolytes play significant role in chemical laboratories, industries and biological processes of living organisms. The electrolytes, which are significantly soluble in water without bringing about a major change in the solution pH affect electrostatic interactions in macromolecules like proteins. There are extensive thermodynamic studies of electrolytes in aqueous solutions [1–5]. However, literature survey reveals that there have not been many reports about studies on interactions of electrolytes with solvents. It appears that limiting apparent molal volume [6] and limiting apparent molal compressibility [6,7] still remain powerful tools for probing the hydrational state of the solute in the solution. Volumetric properties are useful for the elucidation of noncovalent interactions occurring in solutions and characterizing the structure and properties of solutions [8]. Consequently, the study on the volumetric properties of electrolytes in aqueous/mixed aqueous solutions will be very useful for obtaining information about various types of interactions occurring in these solutions, which are mostly hydrophobic and electrostatic in nature. In addition to this, viscosity B-coefficients and related thermodynamic parameters are expected to highlight the role of the solute–solvent interactions

∗ Corresponding author. Tel.: +91 4622531084; fax: +91 4622554012. E-mail addresses: [email protected] (K. Rajagopal), aseg [email protected] (S. Edwin Gladson). 1 Tel.: +91 4651222197; fax: +91 4652233982. 0040-6031/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tca.2011.08.013

[9]. Since biochemical reactions are not limited to a particular temperature, investigating the temperature dependence of the above parameters is important [10]. Dimethyl sulfoxide (DMSO) was particularly chosen because of its wide range of applicability as a solvent in synthetic chemistry (carbohydrates dyer, resins, polymers), in biological processes and in pharmacy and medicine (dermatology, immunology, microbiology) [11]. It easily penetrates biological membrane, facilitates chemical transport into biological tissues and it is well known for its cryoprotective effects on biological system [12]. Fluorides reduce the ability of bacteria to make acids, and they remineralize the areas of the tooth that have been affected by acids from bacteria. K+ ion is considered as the element of life along with Na+ , Ca2+ and Mg2+ and it affects the activity and stability of enzymes more strongly than Na+ [13]. Potassium fluoride is used in the excretion of urea to maintain proper health [14]. Moreover, the effectiveness of various salts towards the destabilizing tendency of proteins has been classified in the form of a series known as Hofmeister series [15]. Also it is observed that peptide group is less salted in by potassium fluoride than sodium iodide but strongly salted in than sodium bromide [16]. Therefore in order to understand the behaviour of potassium fluoride in aqueous DMSO solution, we report the apparent molal volumes (Vϕ ), apparent molal compressibilities (Kϕ ) and viscosity A and B-coefficients of potassium fluoride (0.05, 0.1, 0.15 and 0.2 M) in aqueous DMSO solution obtained from experimentally measured densities, ultrasonic speeds and viscosities. The standard partial molal volumes (Vϕ 0 ), standard partial molal volumes of transfer (Vϕ 0 ) from pure water to water–DMSO mixed solvent,

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14

partial molal compressibilities (Kϕ 0 ), standard partial molal compressibilities of transfer (Kϕ 0 ), Hepler’s coefficient (∂2 Vϕ 0 /∂T2 ) and variation of B coefficient with temperature (dB/dT) have been determined from these data. These results have been discussed in terms of solute–solvent interactions.

13

12

3. Result The apparent molal volumes (Vϕ ) are calculated from the measured density data (given in Table 1) using the following equation: M  − 0 Vϕ = − 1000  m0

Vϕ = Vϕ 0 + Sv m

-1 3 -6

10

9

8

7

6 0.00

The limiting values Vϕ 0 of the apparent molal volume can be regarded as the partial molal volume. Sv is the slope indicative of solute–solute interactions arising from solute concentration effects (Fig. 1). However in the cases where molality dependence of Vϕ is found to be either negligible or having no definite trend, the partial molal volume at infinite dilution, Vϕ 0 are evaluated by taking

0.10

0.15

0.20

0.25

m/(mol kg ) Fig. 1. Plot of apparent molal volume (Vϕ ) against molality (m) of potassium fluoride at () T = 303.15 K, () T = 308.15 K, () T = 313.15 K, (䊉) T = 318.15 K of solution with 0.9879 mole fraction of water + 0.0121 mole fraction of DMSO.

an average of all the data points [16,20,21]. The values of Vϕ 0 are given in Table 2. The partial molal volumes of transfer Vϕ 0 for potassium fluoride from pure water to dimethyl sulfoxide water mixtures, presented in Table 2 are calculated as follows: Vϕ 0 = Vϕ 0 (in aqueous DMSO solution) − Vϕ 0 (in water)

(3)

Hepler [22] proposed a method by which quantitative information on hydration of a solute can be obtained. Accordingly, (∂2 Vϕ 0 /∂T2 )p values should be negative for structure breaking and positive for structure making solutes. In order to obtain the hydrophobic or hydrophilic character of potassium fluoride in aqueous DMSO solutions, the variation of Vϕ 0 with temperature is expressed as Vϕ 0 = a + bT + cT 2

(4)

The coefficients a, b and c are determined and are given in Table 2. The adiabatic compressibility ˇs of the solute is determined from the experimental values of the ultrasonic speed and density using the Newton–Laplace equation

(1)

(2)

0.05

-1

ˇs =

where M is the molar mass of the solute, m is the solution molality and  and 0 are the densities of the solution and solvent, respectively and are included in Table 1. Values of Vϕ calculated with Eq. (1) can be fitted to the following equation [20]:

11

0

Potassium fluoride (GR grade 99% assay Merck Ltd., Mumbai) was used as such without any pre-treatment. Dimethyl sulfoxide (GR grade 99.5% assay Merck Ltd., Mumbai) was stored over molecular sieves (Type 0.4 nm Merck Ltd., Mumbai) and used without further purification. Double distilled deionised water with a conductivity of 1.5 × 10−4 −1 m−1 was used to prepare aqueous DMSO solutions (0–20%) and were used as solvents to prepare 0.05, 0.1, 0.15 and 0.2 M potassium fluoride solutions. The densities of the solutions were measured using a single stem pycnometer (pyrex glass) of bulb capacity of 12 × 10−3 dm3 having a graduated stem with 5 × 10−7 dm3 division. All density measurements were performed in triplicate or quadruplicate with the pycnometer. The reproducibility of density measurements was ±2.8 × 10−4 g cm−3 . The mass measurements were made using a high precision AND electronic balance (Model HR 300, Japan) with a precision of ±0.1 mg. The ultrasonic speed was determined using a multifrequency ultrasonic interferometer (M-84, Mittal make, India) at a frequency of 2 MHz and the reproducibility of the speed values were within ±0.03%. Viscosity was measured by means of a suspended level Ubbelohde viscometer with a flow time of 204 s at 303.15 K. The time of flow was measured with a stop watch capable of recording ±0.01 s. The overall experimental reproducibility was estimated to be within ±2 × 10−3 mPa s. The temperatures of the solutions were maintained to an uncertainty of ±0.01 K in an electronically controlled thermostatic water bath (Eurotherm, Mittal enterprises, New Delhi). The viscometer filled with test solutions was allowed to stand for about 30 min in the thermostatic water bath so as to minimize thermal fluctuations. The values of measured densities , velocities u and viscosities  of pure DMSO at different temperatures have been compared with the corresponding literature values given within parenthesis. The values  = 1.0859 g cm−3 (1.0854 g cm−3 ), u = 1457.9 m s−1 (1456.0 m s−1 ),  = 1.655 mPa s (1.6552 mPa s) at 308.15 K and  = 1.0756 g cm−3 (1.0755 g cm−3 ), u = 1423.4 m s−1 (1422.0 m s−1 ),  = 1.392 mPa s (1.3940 mPa s) at 318.15 K are found to be in good agreement with the literature values [17]. Further, viscosity value  = 1.789 mPa s at 303.15 K is close to the reported literature values  = 1.700 mPa s [18] and  = 1.7900 mPa s [19].

Vφ / (10 m mol )

2. Experimental

1 u2

(5)

The ˇs values as functions of concentration and temperature have been listed in Table 3. The change and relative change in compressibility values have been obtained using following equations [23] ˇs = ˇ0 − ˇs = A + Bm

(6)

ˇs = ˇ0 − ˛ˇ0

(7)

˛=

ˇ0 − ˇs ˇs = ˇ0 ˇ0

ˇs = A1 + B1 m ˇ0

(8) (9)

K. Rajagopal, S. Edwin Gladson / Thermochimica Acta 525 (2011) 197–205

199

Table 1 Density, , and apparent molal volume, Vϕ , of potassium fluoride in aqueous DMSO solution at different temperatures. m (mol kg−1 )

T = 303.15 K  (g cm−3 )

x1 = 1, x2 = 0 0 0.05 0.1 0.15 0.2

T = 308.15 K 106 Vϕ (m3 mol−1 )

 (g cm−3 )

T = 313.15 K 106 Vϕ (m3 mol−1 )

 (g cm−3 )

T = 318.15 K 106 Vϕ (m3 mol−1 )

 (g cm−3 )

106 Vϕ (m3 mol−1 )

0.9956 0.9982 5.88(0.11) 1.0004 9.88(0.10) 1.0026 11.20(0.09) 1.0047 12.34(0.09) ı = 1.43 × 10−3

0.9940 0.9966 5.81(0.11) 0.9988 9.82(0.10) 1.0010 11.14(0.09) 1.0032 11.78(0.09) ı = 1.44 × 10−3

0.9922 0.9947 7.75(0.11) 0.997 9.75(0.10) 0.9991 11.75(0.09) 1.0012 12.73(0.09) ı = 1.42 × 10−3

0.9902 0.9927 7.66(0.11) 0.9948 11.71(0.10) 0.9970 12.36(0.09) 0.9992 12.66(0.09) ı = 1.41 × 10−3

x1 = 0.9879, x2 = 0.0121 1.0020 0 1.0046 6.18(0.11) 0.05 0.1 1.0068 10.13(0.10) 0.15 1.0091 10.76(0.09) 1.0112 12.06(0.09) 0.2 ı = 1.45 × 10−3

1.0003 1.0028 8.09(0.11) 1.0052 9.07(0.10) 1.0075 10.04(0.09) 1.0095 12.00(0.09) ı = 1.46 × 10−3

0.9985 1.0010 8.02(0.11) 1.0032 10.99(0.09) 1.0054 11.97(0.09) 1.0075 12.94(0.09) ı = 1.42 × 10−3

0.9962 0.9986 9.93(0.11) 1.0010 9.91(0.10) 1.0031 11.89(0.09) 1.0053 12.36(0.09) ı = 1.44 × 10−3

x1 = 0.9745, x2 = 0.0255 1.0080 0 1.0106 6.44(0.11) 0.05 1.0128 10.35(0.10) 0.1 1.0151 10.98(0.09) 0.15 1.0174 11.28(0.09) 0.2 −3 ı = 1.47 × 10

1.0064 1.0089 8.34(0.11) 1.0113 9.31(0.10) 1.0136 10.27(0.09) 1.0157 11.71(0.09) ı = 1.47 × 10−3

1.0044 1.0069 8.26(0.11) 1.0092 10.22(0.10) 1.0115 10.85(0.09) 1.0136 12.14(0.09) −3 ı = 1.45 × 10

1.0023 1.0047 10.16(0.11) 1.0070 11.13(0.10) 1.0092 12.09(0.09) 1.0115 12.07(0.09) −3 ı = 1.45 × 10

x1 = 0.9576, x2 = 0.0424 1.0153 0 1.0178 8.70(0.11) 0.05 1.0202 9.64(0.10) 0.1 0.15 1.0226 9.94(0.09) 1.0248 11.04(0.09) 0.2 ı = 1.51 × 10−3

1.0136 1.0161 8.63(0.11) 1.0185 9.58(0.10) 1.0208 10.53(0.09) 1.0232 10.50(0.09) ı = 1.51 × 10−3

1.0114 1.0139 8.54(0.11) 1.0162 10.47(0.10) 1.0186 10.45(0.09) 1.0210 10.42(0.09) ı = 1.51 × 10−3

1.0093 1.0117 10.42(0.11) 1.0140 11.37(0.10) 1.0163 11.67(0.09) 1.0186 11.81(0.09) ı = 1.47 × 10−3

x1 = 0.9417, x2 = 0.0583 1.0214 0 1.0240 0.05 0.1 1.0266 1.0294 0.15 0.2 1.0322 ı = 1.71 × 10−3

1.0193 1.0219 1.0245 1.0274 1.0302 ı = 1.73 × 10−3

1.0176 1.0202 1.0228 1.0257 1.0286 ı = 1.74 × 10−3

1.0153 1.0179 1.0205 1.0235 1.0265 ı = 1.77 × 10−3

7.02(0.13) 7.00(0.11) 5.72(0.10) 5.07(0.10)

6.93(0.13) 6.92(0.11) 4.99(0.11) 4.50(0.10)

6.86(0.13) 6.84(0.11) 4.91(0.11) 3.94(0.10)

6.76(0.13) 6.75(0.11) 4.16(0.11) 2.87(0.11)

x1 , mole fraction of water in the solvent; x2 , mole fraction of DMSO in the solvent; m, molality of potassium fluoride in water + DMSO. ı indicates the uncertainties in density. Values within parenthesis indicate standard error in Vϕ .

where ˇ0 and ˇs are the compressibilities of solvent and solution, respectively. A and B are the intercept and slope values of ˇs versus m plot, respectively (see representative plot in Fig. 2), ˛ represents the relative change in the compressibility values. Furthermore, A1 and B1 stand for the intercept and slope values of (ˇs /ˇ0 ) versus m plot, respectively (see representative plot in Fig. 3). The calculated values of ˇs /ˇ0 are given in Table 4. Apparent molal compressibility (Kϕ ) has been calculated using Eq. (10) Kϕ =

Mˇs ˇ0  − ˇs 0 − 1000  m0

(10)

The symbols represent the same parameters as mentioned earlier. The values of Kϕ are given in Table 5. It is observed that, the values of Kϕ have a linear dependence on m and using the least square fit method (shown in Fig. 4) the values of partial molal adiabatic compressibilities (Kϕ 0 ) are evaluated by the following equation Kϕ = Kϕ 0 + Sk m

(11)

where Sk is the experimental slope. The calculated values of Kϕ 0 and Sk are given in Table 6. Partial molal adiabatic compressibilities of transfer (Kϕ 0 ) from water to aqueous DMSO solutions are listed in Table 6 and are calculated as follows: Kϕ 0 = Kϕ 0 (in aqueous DMSO solution) − Kϕ 0 (in water)

(12)

The A and B coefficients of viscosity are obtained by the analysis of viscosity data (Table 7) using the Jones–Dole equation [24] r =

 = 1 + Am1/2 + Bm, 0

(13)

where m is the molality of potassium fluoride,  and 0 are the viscosities of the solution and solvent (DMSO + water), respectively and A is the Falkenhagen coefficient and B is the Jones–Dole coefficient. The values of viscosity coefficients A and B were obtained from the intercept and slope of the plot r − 1/m1/2 against m1/2 (Fig. 5). A determines the solute–solute interactions whereas, B is a measure of structural modification due to solute–solvent interactions [25,26]. The values of A and B are summarized in Table 8. The viscosity B coefficient data in aqueous and in mixed aqueous solutions have been used to calculate the transfer function B as follows: B = B (in aqueous DMSO solution) − B (in water)

(14)

The dB/dT values, which give the important information regarding the structure making and structure breaking role of the solute in solvent media, are better criterion [27] than B coefficient. The values of dB/dT are recorded in Table 8. 4. Discussion From Table 1 it is seen that density of ternary system increases with an increase in concentration of potassium fluoride. This may

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3.0

1.4

1.2 2.5

2.0 -2

Δβs / β0 / (10 )

0.8

Δβ s / (10

-12

2

-1

m N )

1.0

0.6

1.5

0.4 1.0 0.2

0.0

0.5 0.00

0.05

0.10

0.15

0.20

0.25

0.00

0.05

0.10

0.15

0.20

0.25

m/(mol kg -1)

m/( mol kg-1) Fig. 2. Plot of change in adiabatic compressibility (ˇs ) against molality (m) of potassium fluoride at () T = 303.15 K, () T = 308.15 K, () T = 313.15 K, (䊉) T = 318.15 K of solution with 0.9879 mole fraction of water + 0.0121 mole fraction of DMSO.

Fig. 3. Plot of relative change in adiabatic compressibility (ˇs /ˇ0 ) against molality (m) of potassium fluoride at () T = 303.15 K, () T = 308.15 K, () T = 313.15 K, (䊉) T = 318.15 K of solution with 0.9879 mole fraction of water + 0.0121 mole fraction of DMSO.

be attributed to the shrinkage in the volume which in turn is due to the presence of the solute. In other words, the increase in density may be interpreted due to the enhanced structure of the solvent mixture due to the added solute [28]. It is seen from Table 2, that the Vϕ 0 values are positive for all salt concentrations.

The positive values of Vϕ 0 and increase with temperature shows that solute–solvent interactions are rendered stronger with the rise of temperature, which may be attributed to increased solvation of potassium fluoride molecules at higher temperatures [29]. It is found that the values of Sv are also positive which indicates the

Table 2 Partial molal volume Vϕ 0 , experimental slope Sv , transfer molal volume Vϕ 0 and Hepler’s coefficients a, b and c of potassium fluoride in aqueous DMSO solution at different temperatures. T (K)

106 Vϕ 0 (m3 mol−1 )

106 Sv (m3 kg mol−2 )

106 Vϕ 0 (m3 mol−1 )

x1 = 1, x2 = 0 303.15 308.15 313.15 318.15

4.65(1.22) 4.82(1.16) 6.26(0.96) 7.18(1.01)

41.38 38.51 33.89 31.32

– – – –

x1 = 0.9879, x2 = 0.0121 5.21(1.10) 303.15 308.15 6.63(0.72) 7.05(0.92) 313.15 8.70(0.56) 318.15

36.56 25.38 31.45 18.54

0.56 1.81 0.79 1.52

x1 = 0.9745, x2 = 0.0255 5.98(0.97) 303.15 308.15 7.14(0.62) 7.3(0.70) 313.15 9.69(0.40) 318.15

30.25 22.12 24.51 13.35

1.33 2.32 1.04 2.51

x1 = 0.9576, x2 = 0.0424 303.15 8.00(0.42) 308.15 8.17(0.39) 8.57(0.41) 313.15 10.2(0.27) 318.15

14.65 13.10 11.21 8.93

3.35 3.35 2.31 3.02

x1 = 0.9417, x2 = 0.0583 303.15 7.99(0.42) 308.15 8.14(0.55) 8.31(0.63) 313.15 8.7(0.84) 318.15

−14.29 −18.47 −21.40 −28.54

3.34 3.32 2.05 1.52

b coefficient (m3 mol−1 K−1 )

c coefficient (m6 mol−2 K−2 )

673.1

−4.479

0.007

161.1

−1.211

0.002

1124

−7.416

0.012

1373

−8.931

0.014

−1.445

0.002

a coefficient

225.5

x1 , mole fraction of water in the solvent; x2 , mole fraction of dimethyl sulfoxide in the solvent. Values within parenthesis indicate standard error.

K. Rajagopal, S. Edwin Gladson / Thermochimica Acta 525 (2011) 197–205

201

Table 3 Ultrasonic speed, u, adiabatic compressibility, ˇs , of potassium fluoride in aqueous DMSO solution at different temperatures. m (mol kg−1 )

T = 303.15 K

T = 308.15 K

T = 313.15 K

T = 318.15 K

u (m s−1 )

1010 ˇs (m2 N−1 )

u (m s−1 )

1010 ˇs (m2 N−1 )

u (m s−1 )

1010 ˇs (m2 N−1 )

u (m s−1 )

1010 ˇs (m2 N−1 )

1512.0 1515.5 1518.9 1522.1 1525.8 ıu = 2.16

4.39(0.01) 4.36(0.01) 4.33(0.01) 4.30(0.01) 4.27(0.01)

1520.4 1524.0 1526.9 1530.5 1534.0 ıu = 2.13

4.35(0.01) 4.32(0.01) 4.29(0.01) 4.26(0.01) 4.24(0.01)

1528.0 1531.4 1536.1 1538.6 1542.4 ıu = 2.28

4.32(0.01) 4.29(0.01) 4.25(0.01) 4.23(0.01) 4.20(0.01)

1535.2 1538.6 1543.4 1546.2 1549.4 ıu = 2.28

4.28(0.01) 4.25(0.01) 4.22(0.01) 4.19(0.01) 4.17(0.01)

x1 = 0.9879, x2 = 0.0121 0 1534.6 0.05 1537.9 0.1 1541.4 0.15 1544.9 0.2 1548.6 ıu = 2.21

4.24(0.01) 4.21(0.01) 4.18(0.01) 4.15(0.01) 4.12(0.01)

1541.3 1544.6 1548.0 1551.5 1555.0 ıu = 2.17

4.21(0.01) 4.18(0.01) 4.15(0.01) 4.12(0.01) 4.10(0.01)

1546.2 1549.5 1553.3 1557.0 1560.6 ıu = 2.30

4.19(0.01) 4.16(0.01) 4.13(0.01) 4.10(0.01) 4.07(0.01)

1552.4 1555.9 1559.4 1563.4 1567.1 ıu = 2.33

4.16(0.01) 4.14(0.01) 4.11(0.01) 4.08(0.01) 4.05(0.01)

x1 = 0.9745, x2 = 0.0255 1556.6 0 1560.0 0.05 1563.9 0.1 1567.5 0.15 0.2 1570.7 ıu = 2.26

4.09(0.01) 4.07(0.01) 4.04(0.01) 4.01(0.01) 3.98(0.01)

1561.7 1565.1 1568.5 1572.1 1575.7 ıu = 2.21

4.07(0.01) 4.05(0.01) 4.02(0.01) 3.99(0.01) 3.96(0.01)

1566.0 1569.4 1572.9 1576.5 1580.1 ıu = 2.23

4.06(0.01) 4.03(0.01) 4.00(0.01) 3.98(0.01) 3.95(0.01)

1569.7 1573.1 1576.7 1580.2 1583.1 ıu = 2.14

4.05(0.01) 4.02(0.01) 3.99(0.01) 3.97(0.01) 3.94(0.01)

x1 = 0.9576, x2 = 0.0424 1580.0 0 1583.8 0.05 1586.9 0.1 0.15 1590.4 1594.1 0.2 ıu = 2.20

3.94(0.01) 3.92(0.01) 3.89(0.01) 3.87(0.01) 3.84(0.01)

1583.1 1586.7 1590.5 1594.1 1597.1 ıu = 2.24

3.94(0.01) 3.91(0.01) 3.88(0.01) 3.85(0.01) 3.83(0.01)

1586.1 1589.6 1592.7 1596.0 1599.3 ıu = 2.07

3.93(0.01) 3.90(0.01) 3.88(0.01) 3.85(0.01) 3.83(0.01)

1587.2 1590.5 1594.0 1597.4 1600.3 ıu = 2.09

3.93(0.01) 3.91(0.01) 3.88(0.01) 3.86(0.01) 3.83(0.01)

x1 = 0.9417, x2 = 0.0583 1602.7 0 1606.8 0.05 0.1 1610.4 1614.5 0.15 0.2 1618.7 ıu = 2.51

3.81(0.01) 3.78(0.01) 3.76(0.01) 3.73(0.01) 3.70(0.01)

1603.5 1607.7 1610.6 1615.7 1619.8 ıu = 2.57

3.81(0.01) 3.79(0.01) 3.76(0.01) 3.73(0.01) 3.70(0.01)

1604.9 1608.7 1612.2 1616.0 1619.9 ıu = 2.36

3.81(0.01) 3.79(0.01) 3.76(0.01) 3.73(0.01) 3.70(0.01)

1603.3 1606.7 1610.2 1613.2 1616.5 ıu = 2.08

3.83(0.01) 3.80(0.01) 3.78(0.01) 3.75(0.01) 3.73(0.01)

x1 = 1, x2 = 0 0 0.05 0.1 0.15 0.2

x1 , mole fraction of water in the solvent; x2 , mole fraction of dimethyl sulfoxide in the solvent; m, molality of potassium fluoride in water + DMSO. ıu indicates the uncertainties in ultrasonic speed. Values within parenthesis indicate standard error.

presence of solute–solvent interactions. But these values decrease with the increase of DMSO content in the solution, which suggests that solute–solute interactions of the solution become weaker in the presence of DMSO. The lowering of Vϕ 0 values at 20% DMSO is probably due to the increased steric hindrance of the bulkier solvent molecules to the ion–solvent interaction [30]. The partial molar volume may also be explained based on scaled particle theory (SP) [31] as follows:

-51.0

Vϕ 0 = Vcavity + Vinteraction + ˇ0 RT

-1

m mol Pa

-1

)

-50.0

K φ / (10

-15

3

-52.0

-53.0

-54.0

-55.0 0.00

0.05

0.10

0.15

0.20

0.25

m/(mol kg -1) Fig. 4. Plot of apparent molal compressibility (Kϕ ) against molality (m) of potassium fluoride at () T = 303.15 K, () T = 308.15 K, () T = 313.15 K, (䊉) T = 318.15 K of solution with 0.9879 mole fraction of water + 0.0121 mole fraction of DMSO.

(15)

where Vcavity is related to the contribution of the formation of a cavity while Vinteraction is the term corresponding to the intermolecular interactions, respectively. The ˇ0 is the adiabatic compressibility of the solvent, R is the gas constant and T is the absolute temperature. The creation of the cavity is by definition a positive contribution to the partial molar volume of a solute, whereas the attractive intermolecular solute–solvent interactions cause a negative contribution by shrinking the cavity. The results are also viewed in terms of the geometrical fit of the potassium fluoride molecules in an ordered solvent. It is difficult to accommodate potassium fluoride in an ordered solvent environment like aqueous DMSO solution. As the temperature of the solution is increased, cavities are produced in the ordered solution environment, resulting in the better fit of the complex structured solutes in the solvent. With increasing temperature, the contribution from the salt–solvent binding is weakened and the partial molal volume of the salt compounds increases significantly with temperature [32] (as in Table 2).

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Table 4 Change in adiabatic compressibility, ˇs , and relative change in adiabatic compressibility, ˇs /ˇ0 , of potassium fluoride in aqueous DMSO solution at different temperatures. m (mol kg−1 )

T = 303.15 K

T = 308.15 K

T = = 313.15 K

T = 318.15 K

1011 ˇs (m2 N−1 )

102 ˇs /ˇ0

1011 ˇs (m2 N−1 )

102 ˇs /ˇ0

1011 ˇs (m2 N−1 )

102 ˇs /ˇ0

1011 ˇs (m2 N−1 )

102 ˇs /ˇ0

0.32 0.61 0.88 1.18

0. 72 1.38 2.01 2.69

0.32 0.58 0.87 1.16

0.73 1.33 2.01 2.67

0.30 0.66 0.89 1.18

0.69 1.53 2.05 2.74

0.30 0.65 0.89 1.16

0.69 1.52 2.09 2.71

x1 = 0.9879, x2 = 0.0121 0.29 0.05 0.57 0.1 0.86 0.15 0.2 1.14

0.69 1.35 2.02 2.69

0.28 0.57 0.85 1.11

0.67 1.35 2.01 2.65

0.28 0.58 0.86 1.14

0.67 1.38 2.06 2.71

0.29 0.57 0.87 1.15

0.69 1.37 2.08 2.75

x1 = 0.9745, x2 = 0.0255 0.28 0.05 0.57 0.1 0.85 0.15 0.2 1.10

0.69 1.40 2.07 2.69

0.27 0.55 0.82 1.09

0.68 1.34 2.02 2.67

0.28 0.55 0.82 1.08

0.68 1.35 2.02 2.67

0.27 0.55 0.81 1.04

0.67 1.35 2.00 2.58

x1 = 0.9576, x2 = 0.0424 0.28 0.05 0.53 0.1 0.79 0.15 1.05 0.2

0.72 1.34 2.01 2.67

0.27 0.55 0.81 1.05

0.70 1.40 2.07 2.67

0.27 0.51 0.76 1.01

0.68 1.29 1.93 2.57

0.25 0.51 0.77 0.99

0.65 1.31 1.95 2.53

x1 = 0.9417, x2 = 0.0583 0.29 0.05 0.55 0.1 0.85 0.15 0.2 1.14

0.76 1.45 2.22 2.99

0.29 0.53 0.87 1.16

0.77 1.38 2.28 3.04

0.28 0.53 0.82 1.10

0.72 1.41 2.15 2.89

0.26 0.52 0.77 1.03

0.68 1.36 2.01 2.70

x1 = 1, x2 = 0 0.05 0.1 0.15 0.2

x1 , mole fraction of water in the solvent; x2 , mole fraction of dimethyl sulfoxide in the solvent; m, molality of potassium fluoride in water + DMSO.

As seen from Table 2, Vϕ 0 values from water to aqueous DMSO are positive and increase with increasing DMSO content. This suggests that potassium fluoride at higher concentration has a larger dehydration effect. It is observed from Table 2 that values of Hepler’s constant (∂2 Vϕ 0 /∂T2 ) are positive indicating that potassium fluoride acts as structure maker in aqueous DMSO solutions [33].

In the studied system (Table 3), the values of ultrasonic speed increase with increase in molal concentration of potassium fluoride as well as temperature. An increase in the ultrasonic velocity in any solution with the addition of a solute is indicative of greater association of molecules due to effective solute–solvent interactions [34]. The decrease in adiabatic compressibility, in DMSO + water

Table 5 Apparent molal compressibility, Kϕ , of potassium fluoride in aqueous DMSO solution at different temperatures. m (mol kg−1 )

1015 Kϕ (m3 mol−1 Pa−1 ) T = 303.15 K

T = 308.15 K

T = 313.15 K

x1 = 1, x2 = 0 0.05 0.1 0.15 0.2

−61.04 −56.70 −54.36 −54.08

−61.55 −53.84 −53.79 −53.37

−57.05 −62.34 −54.62 −54.27

−56.65 −60.72 −55.12 −53.33

x1 = 0.9879, x2 = 0.0121 0.05 0.1 0.15 0.2

−55.46 −52.99 −52.58 −51.98

−53.42 −52.90 −52.40 −50.82

−53.23 −53.20 −52.69 −51.66

−53.48 −53.25 −53.14 −52.60

x1 = 0.9745, x2 = 0.0255 0.05 0.1 0.15 0.2

−53.56 −52.73 −51.81 −50.24

−51.74 −50.73 −50.41 −49.37

−51.64 −50.35 −50.12 −49.13

−50.02 −50.03 −49.04 −47.35

x1 = 0.9576, x2 = 0.0424 0.05 0.1 0.15 0.2

−52.84 −48.47 −48.18 −47.67

−50.86 −50.85 −49.56 −47.77

−49.93 −46.28 −46.10 −45.92

−46.65 −46.67 −46.23 −44.74

x1 = 0.9417, x2 = 0.0583 0.05 0.1 0.15 0.2

−54.24 −51.69 −53.15 −53.97

−55.39 −49.16 −55.06 −55.22

−51.81 −50.19 −51.86 −52.78

−48.53 −48.79 −49.13 −49.87

x1 , mole fraction of water in the solvent; x2 , mole fraction of dimethyl sulfoxide in the solvent; m, molality of potassium fluoride in water + DMSO.

T = 318.15 K

K. Rajagopal, S. Edwin Gladson / Thermochimica Acta 525 (2011) 197–205 Table 6 Partial molal compressibility, Kϕ 0 , experimental slope, Sk , and transfer partial molal compressibility, Kϕ 0 of potassium fluoride in aqueous DMSO solution at different temperatures. 1015 Kϕ 0 (m3 mol−1 Pa−1 )

T (K)

1018 Sk (kg m3 mol−2 Pa−1 )

203

Table 7 Viscosity, , of potassium fluoride in aqueous DMSO solution at different temperatures. m (mol kg−1 )

1015 Kϕ 0 (m3 mol−1 Pa−1 )

 (mPa s) T = 303.15 K

T = 308.15 K

T = 313.15 K

T = 318.15 K

0.797 0.805 0.811 0.819 0.827 ı = 0.005

0.719 0.726 0.734 0.741 0.745 ı = 0.004

0.653 0.660 0.668 0.672 0.679 ı = 0.004

0.597 0.604 0.612 0.615 0.622 ı = 0.004

x1 = 0.9879, x2 = 0.0121 0 0.900 0.05 0.908 0.1 0.916 0.15 0.925 0.2 0.934 ı = 0.005

0.805 0.814 0.822 0.830 0.838 ı = 0.005

0.729 0.736 0.745 0.750 0.756 ı = 0.004

0.667 0.673 0.680 0.684 0.691 ı = 0.004

x1 = 0.9745, x2 = 0.0255 0.979 0 0.986 0.05 0.994 0.1 1.005 0.15 1.016 0.2 ı = 0.006

0.888 0.898 0.908 0.918 0.927 ı = 0.006

0.806 0.814 0.820 0.828 0.836 ı = 0.005

0.735 0.742 0.748 0.756 0.761 ı = 0.004

x1 , mole fraction of water in the solvent; x2 , mole fraction of dimethyl sulfoxide in the solvent. Values within parenthesis indicate standard error.

x1 = 0.9576, x2 = 0.0424 1.089 0 1.100 0.05 0.1 1.111 0.15 1.128 0.2 1.136 ı = 0.008

0.988 1.000 1.016 1.026 1.036 ı = 0.008

0.887 0.898 0.912 0.920 0.930 ı = 0.007

0.808 0.818 0.827 0.835 0.845 ı = 0.006

mixtures with amino acids in the present study generally confirms the conclusions drawn from the velocity data. The larger adiabatic compressibility ˇs values indicate that the molecular association/interaction is greater [35]. Similar conclusions are drawn for

x1 = 0.9417, x2 = 0.0583 0 1.224 1.233 0.05 1.244 0.1 0.15 1.259 1.270 0.2 ı = 0.007

1.102 1.115 1.126 1.141 1.152 ı = 0.008

1.002 1.008 1.015 1.026 1.035 ı = 0.005

0.903 0.911 0.919 0.927 0.937 ı = 0.005

x1 = 1, x2 = 0 303.15 308.15 313.15 318.15

−62.35(0.17) −61.78(0.35) −61.08(0.46) −60.34(0.36)

4.64 4.92 3.21 3.11

– – – –

x1 = 0.9879, x2 = 0.0121 303.15 −55.96(0.09) 308.15 −54.26(0.05) 313.15 −54.01(0.04) 318.15 −53.81(0.02)

2.17 1.64 1.05 0.55

6.39 7.52 7.07 6.53

x1 = 0.9745, x2 = 0.0255 303.15 −54.81(0.03) 308.15 −52.42(0.03) 313.15 −52.25(0.04) −51.36(0.07) 318.15

2.18 1.48 1.55 1.80

7.54 9.36 8.83 8.98

x1 = 0.9576, x2 = 0.0424 −53.24(0.19) 303.15 −52.39(0.08) 308.15 −50.11(0.16) 313.15 318.15 −47.61(0.07)

3.16 2.11 2.44 1.23

9.11 9.39 10.97 12.73

x1 = 0.9417, x2 = 0.0583 −53.10(0.17) 303.15 308.15 −52.36(0.44) −50.51(0.13) 313.15 −47.99(0.02) 318.15

−0.13 −1.08 −0.91 −0.87

9.25 9.42 10.57 12.35

x1 , mole fraction of water in the solvent; x2 , mole fraction of dimethyl sulfoxide in the solvent; m, molality of potassium fluoride in water + DMSO. ı indicates the uncertainties in viscosity.

0.10

0.08

η r-1/√m

x1 = 1, x2 = 0 0 0.05 0.1 0.15 0.2

0.06

0.04

0.02 0.20

0.30

0.40

0.50

√m √ √ Fig. 5. Plot of (r − 1/ m) against square root of molality ( m) of potassium fluoride at () T = 303.15 K, () T = 308.15 K, () T = 313.15 K, (䊉) T = 318.15 K of solution with 0.9879 mole fraction of water + 0.0121 mole fraction of DMSO.

several aqueous mono hydrochlorides [36], salbutamol sulphate [37] and sodium fluoride [38]. From Table 4, it is seen that the values of ˇs and ˇs /ˇ0 increase with increase in drug concentration. This may be attributed to an increase in the incompressible part in the solution. The variation of the change and relative change in adiabatic compressibility values with temperature may be attributed to thermal rupture of water structure. A close observation of plots of ˇs and ˇs /ˇ0 versus potassium fluoride concentration (see Figs. 3 and 4) indicate that the intercept values for all the systems (% of DMSO) are zero or close to zero and such a behaviour supports the strong solute–solvent intermolecular/interionic interactions in these systems. Similar trends were reported in electrolyte systems [23]. It can be seen from Tables 5 and 6 that the apparent molal compressibility (Kϕ ) and the partial molal adiabatic compressibility (Kϕ 0 ) of the potassium fluoride in aqueous DMSO solutions are negative. The bulk water has an open structure compared with electrostricted water and is therefore more compressible. The electrostricted water becomes like bulk water on addition of DMSO and this accounts for the apparent molal compressibilities for the potassium fluoride in mixed solvents being larger than the corresponding ones in water. An increase in temperature also causes an increase in Kϕ 0 thus complimenting volumetric results.

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Table 8 Viscosity A coefficient, B coefficient, transfer B coefficient, B, and dB/dT of potassium fluoride in aqueous DMSO solution at different temperatures. T (K)

103 A (m3/2 mol−1/2 )

103 B (m3 mol−1 )

103 B (m3 mol−1 )

dB/dT (m3 mol−1 K−1 )

x1 = 1, x2 = 0 303.15 308.15 313.15 318.15

0.002(0.006) 0.007(0.010) 0.012(0.010) 0.018(0.010)

0.179(0.02) 0.174(0.03) 0.173(0.03) 0.169(0.04)

– – – –

−0.0006

x1 = 0.9879, x2 = 0.0121 303.15 308.15 313.15 318.15

−0.006(0.002) 0.008(0.001) 0.008(0.010) 0.003(0.009)

0.201(0.01) 0.187(0.00) 0.173(0.03) 0.170(0.02)

0.022 0.013 0.000 0.001

−0.0021

x1 = 0.9745, x2 = 0.0255 303.15 308.15 313.15 318.15

−0.023(0.006) 0.002(0.002) 0.002(0.007) 0.003(0.006)

0.236(0.02) 0.215(0.01) 0.175(0.02) 0.172(0.02)

0.057 0.041 0.002 0.003

−0.0046

x1 = 0.9576, x2 = 0.0424 303.15 308.15 313.15 318.15

−0.010(0.010) 0.005(0.010) 0.008(0.010) 0.008(0.004)

0.244(0.04) 0.236(0.04) 0.226(0.04) 0.204(0.01)

0.065 0.062 0.053 0.035

−0.0026

x1 = 0.9417, x2 = 0.0583 303.15 308.15 313.15 318.15

−0.020(0.005) 0.000(0.007) −0.023(0.007) −0.005(0.004)

0.232(0.02) 0.222(0.02) 0.212(0.02) 0.192(0.01)

0.053 0.048 0.039 0.023

−0.002

x1 , mole fraction of water in the solvent; x2 , mole fraction of dimethyl sulfoxide in the solvent. Values within parenthesis indicate standard error.

It is seen further that Kϕ 0 increases with increasing DMSO content as a result of more interactions between the solute and solvent. From Table 7, it is observed that the values of viscosity increase with increase in solute concentration as well as DMSO content. This increasing trend indicates the existence of molecular interaction occurring in these systems. In order to shed more light on this, the role of viscosity B coefficient has also been obtained. The values of A (Table 8) are positive and also negative in some cases. Since A is a measure of ionic interaction [39], it is evident that there is a weak ion–ion interaction in the system studied, which is indicated by the smaller magnitude of A values. The viscosity B-coefficients provide information about the solvation of the solutes and their effects on the structure of the solvent in the near environment of the solute molecule. The values of B-coefficient for potassium fluoride in aqueous DMSO solutions are positive in all the concentration ranges at the measured temperatures. Moreover, the B-coefficient values decrease with temperature, thus dB/dT is negative. This may be the effect of decrease in solvation and disruption of liquid structure at higher temperature. The negative value of dB/dT shows that potassium fluoride acts as a structure maker in these solutions thereby complimenting the volumetric conclusions.

5. Conclusions In the present work, the volumetric, acoustic and viscometric properties of potassium fluoride in aqueous DMSO solutions are reported for different temperatures. The values of partial molar volumes, partial molar compressibility and viscosity B-coefficients indicate the presence of solute–solvent interactions in the DMSO solution. Further, the volumetric, acoustic and viscometric studies conclude that potassium fluoride acts as structure maker in aqueous DMSO solutions.

Acknowledgements The authors express their sincere gratitude to reviewers and the editor for making critical suggestions which helped us to improve the quality of the manuscript.

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