Speed of Sound and Excess Isentropic Compressibility of 1,3

Ind. Eng. Chem. Res. 2010, 49, 8365–8368

8365

Speed of Sound and Excess Isentropic Compressibility of 1,3-Dioxolane or 1,4-Dioxane + Butan-1-ol or + Butan-2-ol Binary Mixtures at 308.15 K and Atmospheric Pressure Satish Kumar,† V. K. Sharma,‡ and Il Moon*,† Department of Chemical and Bimolecular Engineering, Yonsei UniVersity 262-Seongsanoo, Seodaemun-gu, Seoul 120-749, Republic of Korea, and Department of Chemistry, Maharshi Dayanand UniVersity, Rohtak-124001, India

Speed of sound (u12) of 1,3-dioxolane or 1,4-dioxane (1) + butan-1-ol or + butan-2-ol (2) binary mixtures were measured over entire composition range at 308.15 K and atmospheric pressure. The experimental data have been used to evaluate isentropic and excess isentropic compressibilities (κsE)12. Two methods, Redlich-Kister and Graph theory, were used to compute and correlate (κsE)12 values. Hence, (κsE)12 values were fitted to Redlich-Kister polynomial equation to derive binary coefficients and the standard errors between experimental and calculated quantities. (κsE)12 values were also analyzed by Graph theory, which involves the topology of the components of the mixture, to extract information about the state of components in pure and mixture states. It has been observed that (κsE)12 values analyzed by Graph theory compare well with their corresponding experimental values. 1. Introduction Thermodynamic investigation of molecular interactions in oxygenated compounds such as ethers and alcohols have attracted the attention of researchers as they are used as gasoline additives owing to their octane enhancing and pollution reducing properties.1,2 The use of ethers as oxygenated agents in gasoline technology3 has resulted in an increased interest in thermodynamic properties of ether + alcohol mixtures. Moreover, cyclic ethers have attracted interest as model substances for biosystems, separation techniques, and chemical analysis. Further, alcohols are heavily used in pharmaceutical and aroma industries as a solvent and extracting agent. Therefore, the molecular interactions between ethers and alcohols have been a subject of many investigators. Alcohols are known to be associated molecular entities, thus the addition of cyclic ethers like 1,3-dioxolane or 1,4-dioxane to alcohols may rupture or enhance the association of alcohols, which would reflect change in their respective topology. Recent studies4-6 have shown that the graph theoretical approach, which is based upon the topology of the constituents of the mixture, can be utilized to extract the information about (1) the state of component in pure and mixture state and (2) the nature and extent of molecular interactions operating between the components. In our earlier publications6,7 we have reported the excess molar volumes and excess molar enthalpies of 1,3-dioxolane or 1,4-dioxane (1) + butan-1-ol or butan-2-ol (2) binary mixtures. 2. Experimental Section 2.1. Materials. 1,3-Dioxolane (Fluka 99%), 1,4-dioxane (Fluka 99%), butan-1-ol, and butan-2-ol, (Merck) were purified by standard methods.8,9 The purities of the purified liquids were checked by measuring their densities by a glass pycnometer at 298.15 ( 0.01 K, and these agreed to ((5 × * To whom correspondence should be addressed. E-mail: ilmoon@ yonsei.ac.kr; [email protected]. † Yonsei University. ‡ Maharshi Dayanand University.

10-5) g · cm-3 with their corresponding literature values10-12 reported in Table 1. 2.2. Apparatus and Procedure. Each binary system was prepared by mass using a Mettler mass balance (Switzerland, model AE-200) with an accuracy of (0.0001 g. The first component, which was the least volatile, was filled directly in to the airtight stoppered 5 cm3 glass vial, and then weighed. Then the second component was injected in to the vial through the stopper by means of a syringe and it is also weighed. The possible error in mole fraction using this procedure is estimated to be lower than 0.0001. The speed of sound of pure liquids as well as for all the binary mixtures was determined by using a quartz crystal ultrasonic interferometer (Mittal Enterprises, New Delhi, India) at 2 MHz. The measuring cell was a specially designed double-walled cell in which water was circulated to maintain the temperature at 308.15 ( 0.01 K. The speeds of sound values for the purified liquids are recorded in Table 1 and are compared with their corresponding literature values.13-15 The uncertainties in the measured speeds of sound values are (1 ms-1. 3. Results and Discussion Speed-of-sound, (u12) data of 1,3-dioxolane or 1,4-dioxane (1) + butan-1-ol or + butan-2-ol (2) binary mixtures have been measured as a function of composition at 308.15 K and are reported in Table 2. The isentropic compressibilities, (κs)12 Table 1. Comparison of Densities (G), and Speeds of Sound, (u), of Pure Liquids along with Their Literature Values at 298.15 and 308.15 K u (m · s-1)

F (g · cm3) pure liquids 1,3-dioxolane 1,4-dioxane butan-1-ol butan-2-ol

T (K) 298.15 308.15 298.15 308.15 298.15 308.15 298.15 308.15

10.1021/ie101286f  2010 American Chemical Society Published on Web 08/17/2010

exptl

lit.

exptl

lit.

1338

1338.813

1324

132514

1234

123215

1210

1211.517

10

1.05885

1.05881

1.02792

1.0279710

0.80975

0.8097911

0.80254

0.8025012

8366

Ind. Eng. Chem. Res., Vol. 49, No. 18, 2010

Table 2. Speed of Sound u12, Isentropic Compressibility (Ks)12, and (KsE)12 Excess Isentropic Compressibility for Various (1 + 2) Mixtures As a Function of x1 the Mole Fraction of Component 1 x1

u12 (m · s-1)

(κs)12

(κsE)12 (T · Pa-1)

1,3-Dioxolane (1) + Butan-1-ol (2) 0.1119 0.1764 0.2251 0.2911 0.3570 0.4180 0.4628 0.5010 0.5416 0.6552 0.7250 0.7778 0.8386 0.9410

1234 1236 1238 1239 1240 1243 1233 1249 1253 1257 1268 1276 1282 1293

800.9 786.7 775.8 765.9 760.9 745.0 800.6 717.9 707.6 695.5 642.5 642.6 626.8 606.4

-3.2 -4.0 -4.7 -5.0 -5.6 -6.0 -6.1 -6.5 -6.2 -5.1 -4.1 -4.0 -3.2 -2.2

Figure 1. Excess isentropic compressibilities (κsE)12 of 1,3-dioxolane (1) + butan-1-ol (2) (4); 1,3-dioxolane (1) + butan-2-ol (2) (O); 1,4-dioxane (1) + butan-1-ol (2) (9); 1,4-dioxane (1) + butan-2-ol (2) ([) at 308.15 K. Table 3. Values of the Various Parameters of eq 4 along with Standard Deviations, σ(KsE) at 308.15 Ka


1235 1237 1239 1241 1243 1246 1248 1251 1253 1254 1261 1273 1285 1293

800.4 791.4 781.6 730.3 763.4 755.5 742.9 723.3 713.0 703.7 675.3 639.9 614.4 599.4

3.8 3.9 2.9 2.0 1.1 -0.7 -4.6 -6.7 -8.3 -11.9 -12.6 -10.8 -8.9 -7.9

1233 1233 1234 1235 1236 1237 1238 1239 1241 1244 1254 1258 1280 1291 1307 1309

808.2 801.3 798.2 795.1 784.0 772.0 768.0 758.0 749.4 733.2 724.8 692.3 679.7 629.5 607.5 578.0

1232 1233 1234 1235 1236 1239 1243 1245 1250 1255 1260 1265 1273 1290

804.0 793.1 781.0 770.2 760.0 743.2 725.0 719.1 702.1 688.5 674.6 662.0 643.4 610.2

(κs(2))

σ(κsE)

1,3-dioxolane (1) + butan-1-ol (2) 1,3-dioxolane (1) + butan-2-ol (2) 1,4-dioxane (1) + butan-1-ol (2) 1,4-dioxane (1) + butan-2-ol (2)

-25.6 -30.2 -30.2 -30.2

3.5 -80.5 -80.5 -80.5

15.3 10.3 10.3 10.3

0.1 0.1 0.1 0.1

(κs(o)) and σ(κsE) are in T · Pa-1.

2

VE12 )

2

∑ x M (F 1

1

-1 12)

-

i)1

∑ (x M )(F )

-1

1

1

1

(2)

i)1

where x1, M1, F1, etc. are the mole fraction, molecular mass, and density of pure component (1) of the binary mixtures. Excess isentropic compressibilities, (κs)12 for binary mixtures were determined using

-3.8 -5.0 -5.5 -6.0 -7.6 -9.2 -9.5 -10.5 -11.2 -12.0 -12.1 -11.2 -10.5 -7.0 -4.6 -2.2

2

(κsE)12 ) κs -

∑ φ (κ ) 1

s 1

(3)

i)1

where φ1 and (κs)1 are the volume fraction and isentropic compressibility of the 1st component of binary mixtures. Such (κsE)12 values for binary mixtures are recorded in Table 2 and are shown graphically in Figure 1. (κsE)12 values for (1 + 2) binary mixtures were fitted to the Redlich-Kister16 equation: 2

(κsE)12 ) x1x2[

-3.7 -5.2 -7.0 -8.7 -9.5 -11.0 -11.2 -11.3 -10.5 -10.1 -9.0 -8.2 -6.5 -3.3

∑κ

(n) s (2x1

- 1)n]

(4)

n)0

κs(n) (n ) 0-2) etc. are the adjustable parameters and were calculated using the least-squares method. These parameters are recorded in Table 3 along with standard deviation, defined by σ(κsE)12 ) [

values were evaluated from the experimentally measured speed of sound, (u12) values of binary mixtures (1 + 2) using (κs)12 ) (F12u212)-1

(κs(1))

The density F12 of binary mixtures were determined from their E data reported in experimental molar excess volumes, V12 literature6,7 via


(κs(o))

a

1,4-Dioxolane (1) + Butan-1-ol (2) 0.1010 0.1328 0.1520 0.1617 0.2180 0.2764 0.2912 0.3340 0.3716 0.4364 0.4681 0.5843 0.6263 0.7824 0.8461 0.9268

mixture

(1)

∑ (κ

E s(exptl)

E 2 0.5 - κs(calcd eq4)) /(m - n)]

(5)

where m is the number of data points and n is the adjustable parameter. (κsE)12 values for 1,3-dioxolane or 1,4-dioxane (1) + butan1-ol or + butan-2-ol (2) binary mixtures are negative over the entire composition range. However, for 1,3-dioxolane (1) + butan-2-ol (2) mixture (κsE)12 values vary from positive to negative with an increase in mole fraction of 1,3-dioxolane. These negative values represent strong molecular interactions in mixtures as compared to pure liquids. These negative values are due to strong interactions between ethereal oxygen atoms


of cyclic ethers and hydrogen atoms of alcohols thus representing strong hydrogen bonding. However less negative values of 1,3-dioxolane (1) + butan1-ol (2) binary mixtures than those for corresponding 1,4dioxane (1) + butan-1-ol or + butan-2-ol (2) binary mixtures may be due to stronger dipole-dipole interactions in pure 1,3dioxolane17 than for 1,4-dioxane. Further, more negative (κsE)12values of 1,4-dioxane (1) + butan-2-ol (2) binary mixture than those for 1,3-dioxolane + butan-2-ol binary mixture suggest that the addition of butan-2-ol gives relatively more packed structure in 1,4-dioxane as compared to 1,3-dioxolane. (κsE)12 has also been analyzed in terms of Graph theory.

4

(κsE)12 )

∑ ∆X

1

) [x1x2V2 /

i)1

∑ x V ][χ 1 1

12

8367

+ x1χ11 + x1χ22 + x2χ12 ′ ]

(11)

Since V2/V1 ) 3ξ1/3ξ221 consequently eq 11 reduces to eq 12 (κsE)12 ) [x1x2(3ξ1 / 3ξ2)/x1 + x2(3ξ1 / 3ξ2)][χ12 + x1χ11 + x1χ22 + x2χ12 ′ ]

(12)

′ and χ11 For the studied mixtures, if it is assumed that χ12 = χ12 = χ22 ) χ* then eq 12 would be expressed by (κsE)12 ) [x1x2(3ξ1 / 3ξ2)/x1 + x2(3ξ1 / 3ξ2)][(1 + x2)χ12 ′ + 2x1χ*] (13)

4. Graph Theory Thermodynamical studies of VE and HE data of 1,3-dioxolane or 1,4-dioxane (1) + butan-1-ol or butan-2-ol (2) binary mixtures revealed that6,7 butan-1-ol exists as an associated molecular entity and butan-2-ol exists as monomer. Also 1 + 2 mixtures formation involves (a) the establishment of unlike contacts between (1) and (2); (b) unlike contact formation between 1n-2n then causes depolymerization of 1n or 2n to yield their respective monomers; and (c) the monomers (1) and (2) then undergo ′ interaction to form 1:2 molecular entities. If χ11, χ22, and χ12 are molar compressibility interactions parameter for 1-2 contact, 1-1 and 2-2 contact formation, and specific interactions between the monomers of precesses (a) and (b), then the change in molar isentropic compressibility due to processes (a-c) is given by18-21

∑x V ]

(7)

∆X2(X ) ks) ) x21x2V2χ11 /

∑x V

(8)

∆X3(X ) ks) ) x21x2V2χ22 /

∑x V

(9)

∑x V

(10)

∆X1(X ) ks) ) [x1x2χ12V2 /

∆X4(X ) ks) )

x1x22V2χ12 ′ /

1 1

1 1

1 1

Further analysis of VE and HE at 308.15 K for 1,3-dioxolane or 1,4-dioxane (1) + butan-1-ol (2) binary mixture by graph theoretical approach have revealed6,7 that 1,3-dioxolane or 1,4dioxane exists as monomers, and butan-1-ol exists as an associated molecular entity. Thus χ11 ) 0 and consequently eq 12 for these binary mixtures would reduce to (κsE)12 ) [x1x2(3ξ1 / 3ξ2)/x1 + x2(3ξ1 / 3ξ2)][χ12 + x1χ22 + x2χ12] (14) if it would be assumed that χ12 = χ22 ) χ12 ′ so eq 14 reduces to eq 15 (κsE)12 ) [x1x2(3ξ1 / 3ξ2)/x1 + x2(3ξ1 / 3ξ2)][(1 + x1)χ12 ′ + x2χ12] (15) For D or D′ (i) + butan-2-ol mixture, the over all change in isentropic compressibility would be due to processes (a) and (c). Consequently, (κsE)12 for these mixtures can be expressed by (κsE) ) [x1x2(3ξ1 / 3ξ2)/x1 + x2(3ξ1 / 3ξ2)][χ12 ′ + x2χ12]

(16)

1 1

where V1 is the molar volume of component 1. The overall changes in thermodynamic property, (κsE)12 for (1 + 2) mixture formation would then be expressed by

Equations 13, 15, and 16 contain two unknown parameters (χ12′, χ12 or χ*). For the present analysis of binary mixtures we have evaluated these parameters by employing (κsE)12 data of binary mixtures at two compositions (x1 ) 0.4 and 0.5). The calculated parameters were then utilized to predict (κsE)12 data as functions

Table 4. Comparison of Excess Isentropic Compressibilities, (KsE)12 Values for Various (1 + 2) Mixtures as a Function of x1, Mole Fraction of Component 1, at 308.15 K along with Values Evaluated from Graph Theorya 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

-2.9 -3.9

-2.2 -2.2

-11.9 -11.8

-7.9 -7.8

-6.5 -6.2

-3.2 -3.1

-4.4 -7.1

-2.0 -3.9

1,3-Dioxolane (1) + Butan-1-ol (2) (κsE)12 (exptl) (κsE)12 (graph)

-1.7 -2.3

-3.5 -5.1 -5.8 -4.5 -4.2 -5.4 -6.0 -5.2 (3ξ1) ) (3ξ1)m ) 0.650, (3ξ2) ) (3ξ2)m ) 0.901, χ12′ ) -17.0, χ* ) -9.8

(κsE)12 (exptl) (κsE)12 (graph)

3.6 3.9

3.4 0.8 -11.0 -12.7 3.7 0.9 -10.9 -12.6 (3ξ1) ) (3ξ1)m ) 0.601, (3ξ2) ) (3ξ2)m ) 0.952, χ12 ) -68.8, χ12′ ) 135.1


-3.6 -3.5

-7.3 -10.1 -11.4 - 9.4 -7.2 -10.0 -11.5 -9.2 (3ξ1)m ) (3ξ1)m ) 0.744, (3ξ2) ) (3ξ2)m ) 0.901, χ12 ) -27.2, χ* ) -20.3


-4.1 -2.6

-7.3 -9.6 -10.1 -9.4 -6.0 -9.0 -10.7 -9.4 (3ξ1)m ) (3ξ1)m ) 0.801, (ξ2)m ) (ξ2)m ) 1.110, χ12 ) -26.2, χ12′ ) -20.0

1,3-Dioxolane (1) + Butan-2-ol (2)



a

Also included are the interaction energy parameters, χ′12, χ12, etc., in units of T · Pa-1.

8368


of x1. Such (κsE)12 values along with calculated parameters are recorded in Table 4 and are also compared with corresponding experimental values. Examination of data in Table 4 reveals that (κsE)12 values compare well with their corresponding experimental values which lend additional support to the assumptions made in deriving eqs 13, 15, and 16 and also to the validity of assumption V2/V1 ) 3ξ1/3ξ2. 5. Conclusions The speed of sound (u12) of 1,3-dioxolane or 1,4-dioxane (1) + butan-1-ol or + butan-2-ol (2) binary mixtures were determined as a function of composition at 308.15 K and were fitted to the Redlich-Kister equation. Results were analyzed taking into account molecular interactions and structural effects in the mixtures. The values calculated by Graph theory are very close to the experimental values. This shows the validity of this theory for the studied mixtures. Further, all binary mixtures show negative deviations except 1,3-dioxolane (1) + butan-2-ol (2) mixture in which the (κEs )12 values vary from positive to negative with an increase in mole fraction of 1,3-dioxolane. Acknowledgment This research was supported by a grant from the Ministry of Education (MOE) of Korea through its BK 21 Program and also respectfully supported by the GAS Plant R&D Center funded by the Ministry of Land, Transportation and Maritime Affairs (MLTM) of the Korean government. Literature Cited (1) Reynolds, R. W.; Smith, J. S.; Steinmetz, T. Methyl ethers as motor fuel components. Abstr. Pap. Am. Chem. Soc. 1974, 11. (2) Csikos, R.; Pallay, J.; Laky, J.; Radchenko, E. D.; Englin, B. A.; Robert, J. A. Low lead fuel with MTBE and C4 alcohols. Hydrocarbon Processes Int. Ed. 1976, 55, 121. (3) Marsh, K. N.; Niamskul, P.; Gmehling, J.; Bolts, R. Review of thermophysical property measurements on mixtures containing MTBE, TAME, and other ethers with non-polar solvents. Fluid Phase Equlib. 1999, 156, 207. (4) Kumar, S.; Sharma, V. K.; Yadav, J. S.; Moon, Il. Thermodynamic investigation of molecular interactions in 1,3-dioxolane or 1,4-dioxane + benzene or toluene + formamide or N,N-dimethylformamide ternary mixtures at 308.15 K and atmospheric pressure. J. Solution Chem. 2010, 39, 680. (5) Kumar, S.; Lim, W.; Lee, Y.; Yadav, J. S.; Sharma, D.; Sharma, V. K. Thermodynamic and acoustic properties for binary and ternary

mixtures of cyclic ethers with industrially important solvents at 308.15 K. J. Mol. Liq. 2010, 155, 8. (6) Sharma, V. K.; Kumar, S. Topological investigations of molecular interactions in mixtures containing alkanols: Molar excess volumes and molar excess enthalpies. Thermochim. Acta 2004, 413, 255. (7) Sharma, V. K.; Kumar, S. Topological investigations of molecular interactions in mixtures containing 1,4-dioxane and alkanols. Thermochim. Acta 2005, 428, 83. (8) Vogel, A. I. A Textbook of Practical Organic Chemistry, 5th ed.; English Language Book Society: London, 2003; p 402, 407. (9) Riddick, J. A.; Bunger, W. B.; Sakana, T. K. Organic SolVents: Physical Properties and Methods of Purification; Wiley: New York, 1986. (10) Franscesconi, R.; Castellari, C.; Comelli, F. Excess molar enthalpies and excess molar volumes of binary mixtures Containing 1,3-dioxolane or 1,4-dioxane + pine resins at (298.15 and 313.15) K and at atmospheric pressure. J. Chem. Eng. Data 2001, 46, 577. (11) Ilaukhani, H.; Zarei, H. A. Excess molar enthalpies of N,Ndimethylformamide + alkan-1-ols (C1-C6). J. Chem. Eng. Data 2002, 47, 195. (12) Tu, C. H.; Lee, S. L.; Peng, I. H. Excess volumes and viscosities of binary mixtures of aliphatic alcohols (C1-C4) with nitromethane. J. Chem. Eng. Data 2001, 46, 151. (13) Gascon, I.; Martin, S.; Cea, P.; Lopez, M. C.; Royo, F. M. Density and speed of sound for binary mixtures of a cyclic ether with a butanol isomer. J. Solution Chem. 2002, 31, 905. (14) Rodriquez, S.; Lafuente, C.; Artigas, H.; Royo, F. M.; Urieta, J. S. Densities, speeds of sound, and isentropic compressibilities of a cyclic ether with chlorocyclohexane, or bromocyclohexane at the temperatures 298.15 and 313.15 K. J. Chem. Themodyn. 1999, 31, 139. (15) Rao, T. S.; Veeraih, N.; Rambabu, C. Excess volumes, viscosities and compressibilities of binary mixtures consisting of propan-1-ol, butan1-ol and pentan-1-ol with 1,2-dibromoethane at different temperatures. Ind. J. Chem. 2002, 41A, 2268. (16) Redlich, O.; Kister, A. T. Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 1948, 40, 345. (17) Lafuente, C.; Gascon, I.; Artigas, H.; Martin, S.; Cea, P. Excess molar enthalpies of 1,3-dioxolane, or 1,4-dioxane with isomeric butanols. J.Chem. Thermodyn. 2002, 34, 1351. (18) Huggins, M. L. Properties of liquids, including solutions. Part I. Intermolecular energies in monotonic liquids and their mixtures. J. Phys. Chem. 1970, 34, 371. (19) Huggins, M. L. The thermodynamic properties of liquids, including solutions. Part 2. Polymer solutions considered as diatonic systems. Polymer 1971, 12 (6), 389. (20) Singh, P. P.; Bhatia, M. Energetic of molecular interactions in binary mixtures of non-electrolytes containing a salt. Chem. Soc., Faraday Trans. 1989, I 85, 3807. (21) Singh, P. P.; Nigam, R. K.; Sharma, V. K.; Sharma, S. P.; Singh, K. C. Topological aspect of the excess enthalpies of binary mixtures of non-electrolytes. Thermochim. Acta 1982, 52, 87.

ReceiVed for reView June 15, 2010 ReVised manuscript receiVed August 2, 2010 Accepted August 4, 2010 IE101286F

Speed of Sound and Excess Isentropic Compressibility of 1,3

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