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Research ArticleThermophysical Properties of BinaryMixtures of Dimethylsulfoxide with 1-Phenylethanone and14-Dimethylbenzene at Various Temperatures
Harmandeep Singh Gill and V K Rattan
Dr SSB University Institute of Chemical Engineering and Technology Panjab University Chandigarh 160014 India
Correspondence should be addressed to Harmandeep Singh Gill harman gilloutlookcom
Received 18 September 2013 Revised 10 December 2013 Accepted 1 January 2014 Published 24 February 2014
Academic Editor K A Antonopoulos
Copyright copy 2014 H S Gill and V K Rattan This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This research article reports the experimental results of the density viscosity refractive index and speed of sound analysis of binarymixtures of dimethylsulfoxide (DMSO) + 1-phenylethanone (acetophenone) and + 14-dimethylbenzene (para-xylene) over thewhole composition range at 31315 31815 32315 and 32815 K and at atmospheric pressureThe excessmolar volumes (119881119864) viscositydeviations (Δ120578) excess Gibbs energy of activation (119866119864) deviations in isentropic compressibility (119870119864
119878) deviations in speed of sound
(119906119864) and deviations in the molar refraction (Δ119877) were calculated from the experimental data The computed quantities were fittedto the Redlich-Kister equation to derive the coefficients and estimate the standard error values The viscosities have also beencorrelated with two and three-parameter models that is Heric correlation McAllister model and Grunberg-Nissan correlationrespectively
1 Introduction
This paper is a continuation of our ongoing research on thesolution properties Studies of the thermodynamic propertiesof binary mixtures play an important role in the fundamentalunderstanding of different molecules and the interactionsprevalent in them In the present study data on densityviscosity refractive index and speed of sound of binarymixtures of dimethylsulfoxide (DMSO) + 1-phenylethanone(acetophenone) and 14-Dimethylbenzene (119901119886119903119886-xylene) at31315 31815 32315 and 32815 K has been measured exper-imentally From these results the excess molar volumesviscosity deviations deviations in molar refraction devia-tions in speed of sound and isentropic compressibility havebeen derived Dimethylsulfoxide is a versatile nonaqueousdipolar aprotic solvent having wide range of applications likein veterinary medicine dermatology microbiology exper-imental immunology and enzyme catalyzed reactions Itcan easily pass through membranes a quality which hasbeen verified by numerous researchers It has the abilityto penetrate through living tissues without damaging them
Therefore an anesthetic or penicillin can be carried throughthe skin without using a needle which makes it paramountin medicinal field Acetophenone is the simplest aromaticketone organic compound It can easily dissolve in water butsince it is denser than water it tends to sink Its vapor isheavier than air and when inhaled in high concentrations itcan be narcotic and also mild irritant to the eyes and skinIt is mostly used to create fragrances that smell like cherryalmond strawberry or other fruits Acetophenone can alsobe found naturally occurring in fruits such as apple andbanana 119875119886119903119886-xylene is an aromatic hydrocarbon based onbenzene with twomethyl substituents opposite to each otherIt is a colorless flammable liquid and is insoluble in waterIt is used as a thinner for paint and in paints and varnishesThe study of the thermodynamic properties of DMSO + 1-phenylethanone (acetophenone) and + 14-dimethylbenzene(119901119886119903119886-xylene) mixtures is of interest mainly in industrialfields where solvent mixtures could be used as selectivesolvents for numerous reactions In principle interactionsbetween the molecules can be established from the studyof the deviations from ideal behavior of physical properties
Hindawi Publishing CorporationJournal of ermodynamicsVolume 2014 Article ID 607052 9 pageshttpdxdoiorg1011552014607052
2 Journal of Thermodynamics
Table 1 Physical properties of the components at 29815 K
such as molar volume and isentropic compressibility Thenegative or positive deviations from the ideal value dependon the type and the extent of the interactions between theunlike molecules as well as on the composition and thetemperature The variation of the isentropic compressibilityis analogous of that of the excess molar volume whereas thechange of the deviation in speed of sound tends to becomethe inverse [1] Physical and transport properties of liquidmixtures also affect most separation procedures such asliquid-liquid extraction gas absorption and distillation [2]Themixture DMSO-119901-xylene has been earlier reported twicein literature at different temperatures [1 3]
2 Experimental Section
21 Materials The chemicals used are of analytical reagentgrade Dimethylsulfoxide (DMSO) is from Riedel Germany1-phenylethanone (acetophenone) and 14-dimethylbenzene(119901119886119903119886-xylene) are from S-D Fine Chemicals Mumbai Thechemicals were purified using standard procedure [4] andwere stored overmolecular sievesThe purity of the chemicalswas verified by comparing density viscosity and refractiveindex with the known values reported in the literature asshown in Table 1 All the compositions were prepared byusing SARTORIUS balance The possible uncertainty in themole fraction is estimated to be less than plusmn1 times 10minus4
22 Viscosity Kinematic viscosities were measured by usinga calibrated modified Ubbelohde viscometer [5]The calibra-tion of viscometer was done at each temperature in order todetermine the constants 119860 and 119861 of the following equation
] =120578
120588= 119860119905 +
119861
119905 (1)
The viscometer was kept vertically in a transparent-walledwater bath with a thermal stability of plusmn005K for about30 minutes to attain thermal equilibrium Flow time wasmeasured with an electronic stop watch with precision ofplusmn001 s The corresponding uncertainty in the kinematicviscosity is plusmn0001 times 10minus6m2 sminus1 The efflux time was repeatedat least three times for each composition and the averageof these readings was taken The temperature of the bathwas maintained constant with the help of a circulatingtype cryostat (type MK70 MLW Germany) The dynamicviscosities were found out after the DSA analysis that isby dividing the above found kinematic viscosity by densityThe uncertainty in the values of dynamic viscosity is withinplusmn0003mPasdots
23 Density and Speed of Sound Density and speed ofsound were measured with the help of an ANTON PAARdensity meter (DSA 5000)The accuracy in the measurementof density and speed of sound is plusmn0000005 g cmminus3 andplusmn05msminus1 respectively The density meter was calibrated byusing triply distilled degassed water
24 Refractive Index Refractive indices were measured forsodiumD-line by ABBE-3L refractometer having Bausch andLomb lenses The temperature was maintained constant withthe help of water bath used for the viscosity measurementA minimum of three independent readings were taken foreach composition and the average value was considered inall the calculations Refractive index values are accurate up toplusmn00001 units
3 Experimental Results and Correlations
At least three independent readings of all the physicalpropertymeasurements of density (120588) viscosity (120578) refractiveindex (119899
119863) and speed of sound (119906) were taken for each
composition and the averages of these experimental valuesare presented in Tables 2 and 3 for both systems The experi-mentally determined values are used for the deviation calcu-lations
31 Excess Molar Volume Density values are used to evaluateexcess molar volume by the equation
119881119864=11990911198721+ 11990921198722
120588minus11990911198721
1205881
minus11990921198722
1205882
(2)
where 1205881 1205882are the densities of pure components and 120588 is the
density of the mixture11987211198722are the molar mass of the two
components and 1199091 1199092are the mole fraction of DMSO
Excess Gibbsrsquo free energy of activation has been alsocalculated using the viscosity and density of the mixture bythe equation
Δ119866119864= 119877119879[ln (120578119881) minus
2
sum
119894=1
119909119894ln (120578119894119881119894)] (3)
where 119877 is a universal gas constant 119879 is the temperature ofthemixture and 120578 and 120578
119894are the viscosities of themixture and
pure compound respectively119881119881119894refer to the molar volume
of the mixture and pure components respectively
32 Viscosity Calculations The deviation in viscosity isobtained by the following equation
Δ120578 = 120578 minus 12057811199091minus 12057821199092 (4)
Journal of Thermodynamics 3
Table 2 Refractive indices 119899119863 density 120588 speed of sound 119906 and viscosity 120578 for DMSO(1) + acetophenone(2) system at different tem-
Table 3 Refractive indices 119899119863 density 120588 speed of sound 119906 and viscosity 120578 for DMSO(1) + p-xylene(2) system at different temperatures
have been fitted to viscosity data and it was found that bothhave the same standard errors at each temperature
33 Isentropic Compressibility The experimental results forthe speed of sound of binary mixtures are listed in Tables 2and 3 The isentropic compressibility was evaluated by using119870119878= 119906minus2120588minus1 and the deviation in isentropic compressibility
is calculated using the following equation
119870119864
119878= 119870119878minus 119870
id119878 (8)
where 119870id119878stands for isentropic compressibility for an ideal
mixture calculated using Benson-Kiyohara model [8 9]
119870id119878=
2
sum
119894=1
Φ119894[119870119878119894+
119879119881119894(1205722
119894)
119862119901119894
]
minus
119879(sum2
119894=1119909119894119881119894) (sum2
119894=1Φ119894119886119894)2
sum2
119894=1119909119894119862119901119894
(9)
where 119886119894and 119862
119901are the thermal expansion coefficient and
molar heat capacity of the 119894th components respectivelyThe deviation in speed of sound is given by
Δ119906 = 119906 minus 11990911199061minus 11990921199062 (10)
34 Molar Refraction Refractive indices have been used forthe calculation of molar refraction (119877
119898) that is obtained by
using Lorentz-Lorenz equation [8]Deviation in molar refraction (Δ119877) is calculated by the
following equation
119877 = 119877119898minussumΦ
119894119877119894
Φ119894=
119909119894
sum119909119895119881119895
(11)
00
05
00 01 02 03 04 05 06 07 08 09 10
minus05
minus10
minus15
minus20
minus25
minus30
minus35
x1
VE(cm3middotm
olminus1)
Figure 1 Experimental and calculated excess molar volume for(i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-Xylene(2)at 31315 K Q 31815 K ◼ 32315 K 998771 32815 K e symbols rep-resent the experimental values dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-119901-Xylenemixture both optimised by Redlich-Kister parameters
where 119899119863refers to the refractive index119877
119898is molar refraction
of the mixture 119877119894is molar refraction of the 119894th component
and Φ is ideal state volume fractionAll the deviations (119881119864 Δ119877 Δ120578 Δ119906 and 119870
119864
119878) have been
fitted to Redlich-Kister polynomial regression of the type
Δ119884 = 11990911199092
119898
sum
119894=1
119860119894(1 minus 2119909
1)119894minus1 (12)
to derive the constant119860119894using themethod of the least square
Standard deviation for each case is calculated by
120590 = [
sum (Δ119884exptl minus Δ119884calcd)2
119898 minus 119899]
05
(13)
where 119898 is the number of data points and 119899 is the numberof coefficients Derived parameters of the Redlich-Kisterequation (12) and standard deviations (13) are presented inTables 4 and 5
4 Discussions
The excess molar volume from 31315 to 32815 K versusthe mole fraction of both mixtures with respect to DMSOis shown in Figure 1 The molar volume of the mixturesand the viscosity data have been used for the calculationof Gibbsrsquo free energy presented in Figure 5 The 119881119864 valuesdecrease with increasing temperatures for the systems butare positive in case of DMSO-acetophenone mixture andnegative for DMSO-119901-xylene mixture Treszczanowicz et al
6 Journal of Thermodynamics
Table 4 Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures atdifferent temperatures (DMSO-acetophenone)
[10] and Roux and Desnoyers [11] suggested that 119881119864 is theresultant contribution from several opposing effects Theseeffects can be primarily divided into three types namelychemical physical and structural A physical contributionthat is specific interactions between the real species presentin the mixture contribute in negative terms to 119881
119864 Thechemical or specific intermolecular interactions result ina volume decrease and these include charge transfer typeforces and other complex forming interactions This effectalso contributes in negative values to 119881
119864 The structuralcontributions are mostly negative and can arise from severaleffects especially from changes of free volume and interstitialaccommodation In other words structural contributionsarising from geometrical fitting of one component into theother due to the differences in the free volume and molarvolume between components lead to a negative contributionto 119881119864 The viscosity and deviations are presented in Table 2and plotted in Figure 2 respectively for both systems Theviscosity deviations decreasewith the increase in temperaturefor both systems The negative Δ120578 values are generallyobserved for systems where dispersion or weak dipole-dipoleforces are primarily responsible for interaction between the
component molecules The viscosity data is also fitted tothe two and the three-parameter models that is Herriccorrelation the McAllister model and Grunberg-Nissancorrelation and the evaluated parameters are presented inTables 6 and 7 The deviations in molar refraction for bothsystems are shown in Figure 3 The Δ119877 values are positivefor acetophenone system for the whole composition rangewhich goes on increasing as the temperature of the solutionincreasesThe Δ119877 values are negative for 119901119886119903119886-xylene systemfor the whole composition range which goes on decreasingas the temperature of the solution increases In general thenegative values of Δ119877 suggest that we have weak interactionsbetween the componentmolecules in themixtureThe resultsof excess isentropic compressibility (119870119864
119878) are also plotted in
Figure 4The deviations for DMSO-acetophenone system areinitially negative and then become positive when mole frac-tion is around 05 whereas for DMSO-119901-xylene system theyare negative over the entire composition range Deviation inGibbs free energy forDMSO-acetophenone system follows anarbitrary path going from negative to positive and vice versatwice while for DMSO-119901119886119903119886-xylene system the deviationsare negative and increase with increasing temperature
Journal of Thermodynamics 7
Table 5 Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures atdifferent temperatures (DMSO-119901-xylene)
Table 6 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-acetophenone)
Table 7 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-119901-xylene)
Figure 2 Experimental and calculated deviations in viscosityfor (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 KQ 31815 K ◼ 32315 K998771 32815 Ke symbolsrepresent the experimental values dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-119901-xylenemixture both optimised by Redlich-Kister parameters
Symbols Used
1198601 1198602 1198603 1198604 Parameters of Redlich-Kister equation
11986012 11986021 Interaction coefficients of McAllister
model12057212 12 Coefficients of Herricrsquos correlation
] Kinematic viscosity (m2sminus1)120588 Density (g cmminus3)
005
00 01 02 03 04 05 06 07 08 09 10
minus015
minus035
minus055
minus075
minus095
minus115
x1
ΔR
Figure 3 Experimental and calculated deviations in molar refrac-tion for (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 998771 32815 K e andsymbols represent the experimental values dotted lines representDMSO-acetophenone mixture and solid lines represent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
120590 Standard deviation120572 Thermal expansion coefficient (Kminus1)120578 Dynamic viscosity (mPasdots)Δ119866119864 Excess Gibbs free energy (Jmolminus1)
Figure 4 Experimental and calculated deviations in isentropiccompressibility for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values dottedlines represent DMSO-Acetophenone mixture and solid lines rep-resent DMSO-119901-xylene mixture both optimised by Redlich-Kisterparameters
0
50
00 01 02 03 04 05 06 07 08 09 10minus50
minus100
minus150
minus200
minus250
minus300
minus350
minus400
x1
ΔGE(Jmiddotm
olminus1)
Figure 5 Experimental and calculated deviations in Gibbs freeenergy of activation for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values solidlines represent DMSO-Acetophenone mixture and dotted linesrepresent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
119877 Universal gas constant(8314 Jmolminus1Kminus1)
119879 Absolute temperature (K)11988912 Grunberg-nissan parameter
Φ119894 Volume fraction (dimensionless)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] M M Palaiologou G K Arianas and N G Tsierkezos ldquoTher-modynamic investigation of dimethyl sulfoxide binarymixturesat 29315 and 31315 Krdquo Journal of Solution Chemistry vol 35 no11 pp 1551ndash1565 2006
[2] K Zhang J Yang X Yu J Zhang and X Wei ldquoDensities andviscosities for binary mixtures of poly(ethylene glycol) 400 +dimethyl sulfoxide and poly(ethylene glycol) 600 + water atdifferent temperaturesrdquo Journal of Chemical and EngineeringData vol 56 no 7 pp 3083ndash3088 2011
[3] A Ali A K Nain D Chand and R Ahmad ldquoViscosities andrefractive indices of binary mixtures of dimethylsulphoxidewith some aromatic hydrocarbons at different temperaturesan experimental and theoretical studyrdquo Journal of the ChineseChemical Society vol 53 no 3 pp 531ndash543 2006
[4] J A Riddick W B Bunger and T K Sakano Organic SolventsPhysical Properties and Methods of Purifications vol 2 ofTechniques of Chemistry John Wiley amp Sons New York NYUSA 1986
[5] V K Rattan S Kapoor and K Tochigi ldquoViscosities anddensities of binary mixtures of toluene with acetic acid andpropionic acid at (29315 30315 31315 and 32315) Krdquo Journalof Chemical and Engineering Data vol 47 no 5 pp 1182ndash11842002
[6] R A McAllister ldquoThe viscosity of liquid mixturesrdquo AIChEJournal vol 6 pp 427ndash431 1960
[7] L Grunberg and A H Nissan ldquoThe energies of vaporisationviscosity and cohesion and the structure of liquidsrdquo Transac-tions of the Faraday Society vol 45 pp 125ndash137 1949
[8] G C Benson and O Kiyohara ldquoEvaluation of excess isentropiccompressibilities and isochoric heat capacitiesrdquo The Journal ofChemical Thermodynamics vol 11 no 11 pp 1061ndash1064 1979
[9] GDouheretM I Davis I J Fjellanger andHHoslashiland ldquoUltra-sonic speeds and volumetric properties of binary mixtures ofwater with poly(ethylene glycol)s at 29815 Krdquo Journal of theChemical Society - Faraday Transactions vol 93 no 10 pp1943ndash1949 1997
[10] A J Treszczanowicz O Kiyohara and G C Benson ldquoExcessvolumes for n-alkanols +n-alkanes IV Binary mixtures ofdecan-1-ol +n-pentane +n-hexane +n-octane +n-decane and+n-hexadecanerdquoThe Journal of ChemicalThermodynamics vol13 no 3 pp 253ndash260 1981
[11] A H Roux and J E Desnoyers ldquoAssociation models for alco-hol-water mixturesrdquo Journal of Proceedings of the Indian Acad-emy of Sciences Chemical Sciences vol 98 no 5-6 pp 435ndash451
such as molar volume and isentropic compressibility Thenegative or positive deviations from the ideal value dependon the type and the extent of the interactions between theunlike molecules as well as on the composition and thetemperature The variation of the isentropic compressibilityis analogous of that of the excess molar volume whereas thechange of the deviation in speed of sound tends to becomethe inverse [1] Physical and transport properties of liquidmixtures also affect most separation procedures such asliquid-liquid extraction gas absorption and distillation [2]Themixture DMSO-119901-xylene has been earlier reported twicein literature at different temperatures [1 3]
2 Experimental Section
21 Materials The chemicals used are of analytical reagentgrade Dimethylsulfoxide (DMSO) is from Riedel Germany1-phenylethanone (acetophenone) and 14-dimethylbenzene(119901119886119903119886-xylene) are from S-D Fine Chemicals Mumbai Thechemicals were purified using standard procedure [4] andwere stored overmolecular sievesThe purity of the chemicalswas verified by comparing density viscosity and refractiveindex with the known values reported in the literature asshown in Table 1 All the compositions were prepared byusing SARTORIUS balance The possible uncertainty in themole fraction is estimated to be less than plusmn1 times 10minus4
22 Viscosity Kinematic viscosities were measured by usinga calibrated modified Ubbelohde viscometer [5]The calibra-tion of viscometer was done at each temperature in order todetermine the constants 119860 and 119861 of the following equation
] =120578
120588= 119860119905 +
119861
119905 (1)
The viscometer was kept vertically in a transparent-walledwater bath with a thermal stability of plusmn005K for about30 minutes to attain thermal equilibrium Flow time wasmeasured with an electronic stop watch with precision ofplusmn001 s The corresponding uncertainty in the kinematicviscosity is plusmn0001 times 10minus6m2 sminus1 The efflux time was repeatedat least three times for each composition and the averageof these readings was taken The temperature of the bathwas maintained constant with the help of a circulatingtype cryostat (type MK70 MLW Germany) The dynamicviscosities were found out after the DSA analysis that isby dividing the above found kinematic viscosity by densityThe uncertainty in the values of dynamic viscosity is withinplusmn0003mPasdots
23 Density and Speed of Sound Density and speed ofsound were measured with the help of an ANTON PAARdensity meter (DSA 5000)The accuracy in the measurementof density and speed of sound is plusmn0000005 g cmminus3 andplusmn05msminus1 respectively The density meter was calibrated byusing triply distilled degassed water
24 Refractive Index Refractive indices were measured forsodiumD-line by ABBE-3L refractometer having Bausch andLomb lenses The temperature was maintained constant withthe help of water bath used for the viscosity measurementA minimum of three independent readings were taken foreach composition and the average value was considered inall the calculations Refractive index values are accurate up toplusmn00001 units
3 Experimental Results and Correlations
At least three independent readings of all the physicalpropertymeasurements of density (120588) viscosity (120578) refractiveindex (119899
119863) and speed of sound (119906) were taken for each
composition and the averages of these experimental valuesare presented in Tables 2 and 3 for both systems The experi-mentally determined values are used for the deviation calcu-lations
31 Excess Molar Volume Density values are used to evaluateexcess molar volume by the equation
119881119864=11990911198721+ 11990921198722
120588minus11990911198721
1205881
minus11990921198722
1205882
(2)
where 1205881 1205882are the densities of pure components and 120588 is the
density of the mixture11987211198722are the molar mass of the two
components and 1199091 1199092are the mole fraction of DMSO
Excess Gibbsrsquo free energy of activation has been alsocalculated using the viscosity and density of the mixture bythe equation
Δ119866119864= 119877119879[ln (120578119881) minus
2
sum
119894=1
119909119894ln (120578119894119881119894)] (3)
where 119877 is a universal gas constant 119879 is the temperature ofthemixture and 120578 and 120578
119894are the viscosities of themixture and
pure compound respectively119881119881119894refer to the molar volume
of the mixture and pure components respectively
32 Viscosity Calculations The deviation in viscosity isobtained by the following equation
Δ120578 = 120578 minus 12057811199091minus 12057821199092 (4)
Journal of Thermodynamics 3
Table 2 Refractive indices 119899119863 density 120588 speed of sound 119906 and viscosity 120578 for DMSO(1) + acetophenone(2) system at different tem-
Table 3 Refractive indices 119899119863 density 120588 speed of sound 119906 and viscosity 120578 for DMSO(1) + p-xylene(2) system at different temperatures
have been fitted to viscosity data and it was found that bothhave the same standard errors at each temperature
33 Isentropic Compressibility The experimental results forthe speed of sound of binary mixtures are listed in Tables 2and 3 The isentropic compressibility was evaluated by using119870119878= 119906minus2120588minus1 and the deviation in isentropic compressibility
is calculated using the following equation
119870119864
119878= 119870119878minus 119870
id119878 (8)
where 119870id119878stands for isentropic compressibility for an ideal
mixture calculated using Benson-Kiyohara model [8 9]
119870id119878=
2
sum
119894=1
Φ119894[119870119878119894+
119879119881119894(1205722
119894)
119862119901119894
]
minus
119879(sum2
119894=1119909119894119881119894) (sum2
119894=1Φ119894119886119894)2
sum2
119894=1119909119894119862119901119894
(9)
where 119886119894and 119862
119901are the thermal expansion coefficient and
molar heat capacity of the 119894th components respectivelyThe deviation in speed of sound is given by
Δ119906 = 119906 minus 11990911199061minus 11990921199062 (10)
34 Molar Refraction Refractive indices have been used forthe calculation of molar refraction (119877
119898) that is obtained by
using Lorentz-Lorenz equation [8]Deviation in molar refraction (Δ119877) is calculated by the
following equation
119877 = 119877119898minussumΦ
119894119877119894
Φ119894=
119909119894
sum119909119895119881119895
(11)
00
05
00 01 02 03 04 05 06 07 08 09 10
minus05
minus10
minus15
minus20
minus25
minus30
minus35
x1
VE(cm3middotm
olminus1)
Figure 1 Experimental and calculated excess molar volume for(i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-Xylene(2)at 31315 K Q 31815 K ◼ 32315 K 998771 32815 K e symbols rep-resent the experimental values dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-119901-Xylenemixture both optimised by Redlich-Kister parameters
where 119899119863refers to the refractive index119877
119898is molar refraction
of the mixture 119877119894is molar refraction of the 119894th component
and Φ is ideal state volume fractionAll the deviations (119881119864 Δ119877 Δ120578 Δ119906 and 119870
119864
119878) have been
fitted to Redlich-Kister polynomial regression of the type
Δ119884 = 11990911199092
119898
sum
119894=1
119860119894(1 minus 2119909
1)119894minus1 (12)
to derive the constant119860119894using themethod of the least square
Standard deviation for each case is calculated by
120590 = [
sum (Δ119884exptl minus Δ119884calcd)2
119898 minus 119899]
05
(13)
where 119898 is the number of data points and 119899 is the numberof coefficients Derived parameters of the Redlich-Kisterequation (12) and standard deviations (13) are presented inTables 4 and 5
4 Discussions
The excess molar volume from 31315 to 32815 K versusthe mole fraction of both mixtures with respect to DMSOis shown in Figure 1 The molar volume of the mixturesand the viscosity data have been used for the calculationof Gibbsrsquo free energy presented in Figure 5 The 119881119864 valuesdecrease with increasing temperatures for the systems butare positive in case of DMSO-acetophenone mixture andnegative for DMSO-119901-xylene mixture Treszczanowicz et al
6 Journal of Thermodynamics
Table 4 Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures atdifferent temperatures (DMSO-acetophenone)
[10] and Roux and Desnoyers [11] suggested that 119881119864 is theresultant contribution from several opposing effects Theseeffects can be primarily divided into three types namelychemical physical and structural A physical contributionthat is specific interactions between the real species presentin the mixture contribute in negative terms to 119881
119864 Thechemical or specific intermolecular interactions result ina volume decrease and these include charge transfer typeforces and other complex forming interactions This effectalso contributes in negative values to 119881
119864 The structuralcontributions are mostly negative and can arise from severaleffects especially from changes of free volume and interstitialaccommodation In other words structural contributionsarising from geometrical fitting of one component into theother due to the differences in the free volume and molarvolume between components lead to a negative contributionto 119881119864 The viscosity and deviations are presented in Table 2and plotted in Figure 2 respectively for both systems Theviscosity deviations decreasewith the increase in temperaturefor both systems The negative Δ120578 values are generallyobserved for systems where dispersion or weak dipole-dipoleforces are primarily responsible for interaction between the
component molecules The viscosity data is also fitted tothe two and the three-parameter models that is Herriccorrelation the McAllister model and Grunberg-Nissancorrelation and the evaluated parameters are presented inTables 6 and 7 The deviations in molar refraction for bothsystems are shown in Figure 3 The Δ119877 values are positivefor acetophenone system for the whole composition rangewhich goes on increasing as the temperature of the solutionincreasesThe Δ119877 values are negative for 119901119886119903119886-xylene systemfor the whole composition range which goes on decreasingas the temperature of the solution increases In general thenegative values of Δ119877 suggest that we have weak interactionsbetween the componentmolecules in themixtureThe resultsof excess isentropic compressibility (119870119864
119878) are also plotted in
Figure 4The deviations for DMSO-acetophenone system areinitially negative and then become positive when mole frac-tion is around 05 whereas for DMSO-119901-xylene system theyare negative over the entire composition range Deviation inGibbs free energy forDMSO-acetophenone system follows anarbitrary path going from negative to positive and vice versatwice while for DMSO-119901119886119903119886-xylene system the deviationsare negative and increase with increasing temperature
Journal of Thermodynamics 7
Table 5 Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures atdifferent temperatures (DMSO-119901-xylene)
Table 6 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-acetophenone)
Table 7 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-119901-xylene)
Figure 2 Experimental and calculated deviations in viscosityfor (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 KQ 31815 K ◼ 32315 K998771 32815 Ke symbolsrepresent the experimental values dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-119901-xylenemixture both optimised by Redlich-Kister parameters
Symbols Used
1198601 1198602 1198603 1198604 Parameters of Redlich-Kister equation
11986012 11986021 Interaction coefficients of McAllister
model12057212 12 Coefficients of Herricrsquos correlation
] Kinematic viscosity (m2sminus1)120588 Density (g cmminus3)
005
00 01 02 03 04 05 06 07 08 09 10
minus015
minus035
minus055
minus075
minus095
minus115
x1
ΔR
Figure 3 Experimental and calculated deviations in molar refrac-tion for (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 998771 32815 K e andsymbols represent the experimental values dotted lines representDMSO-acetophenone mixture and solid lines represent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
120590 Standard deviation120572 Thermal expansion coefficient (Kminus1)120578 Dynamic viscosity (mPasdots)Δ119866119864 Excess Gibbs free energy (Jmolminus1)
Figure 4 Experimental and calculated deviations in isentropiccompressibility for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values dottedlines represent DMSO-Acetophenone mixture and solid lines rep-resent DMSO-119901-xylene mixture both optimised by Redlich-Kisterparameters
0
50
00 01 02 03 04 05 06 07 08 09 10minus50
minus100
minus150
minus200
minus250
minus300
minus350
minus400
x1
ΔGE(Jmiddotm
olminus1)
Figure 5 Experimental and calculated deviations in Gibbs freeenergy of activation for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values solidlines represent DMSO-Acetophenone mixture and dotted linesrepresent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
119877 Universal gas constant(8314 Jmolminus1Kminus1)
119879 Absolute temperature (K)11988912 Grunberg-nissan parameter
Φ119894 Volume fraction (dimensionless)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] M M Palaiologou G K Arianas and N G Tsierkezos ldquoTher-modynamic investigation of dimethyl sulfoxide binarymixturesat 29315 and 31315 Krdquo Journal of Solution Chemistry vol 35 no11 pp 1551ndash1565 2006
[2] K Zhang J Yang X Yu J Zhang and X Wei ldquoDensities andviscosities for binary mixtures of poly(ethylene glycol) 400 +dimethyl sulfoxide and poly(ethylene glycol) 600 + water atdifferent temperaturesrdquo Journal of Chemical and EngineeringData vol 56 no 7 pp 3083ndash3088 2011
[3] A Ali A K Nain D Chand and R Ahmad ldquoViscosities andrefractive indices of binary mixtures of dimethylsulphoxidewith some aromatic hydrocarbons at different temperaturesan experimental and theoretical studyrdquo Journal of the ChineseChemical Society vol 53 no 3 pp 531ndash543 2006
[4] J A Riddick W B Bunger and T K Sakano Organic SolventsPhysical Properties and Methods of Purifications vol 2 ofTechniques of Chemistry John Wiley amp Sons New York NYUSA 1986
[5] V K Rattan S Kapoor and K Tochigi ldquoViscosities anddensities of binary mixtures of toluene with acetic acid andpropionic acid at (29315 30315 31315 and 32315) Krdquo Journalof Chemical and Engineering Data vol 47 no 5 pp 1182ndash11842002
[6] R A McAllister ldquoThe viscosity of liquid mixturesrdquo AIChEJournal vol 6 pp 427ndash431 1960
[7] L Grunberg and A H Nissan ldquoThe energies of vaporisationviscosity and cohesion and the structure of liquidsrdquo Transac-tions of the Faraday Society vol 45 pp 125ndash137 1949
[8] G C Benson and O Kiyohara ldquoEvaluation of excess isentropiccompressibilities and isochoric heat capacitiesrdquo The Journal ofChemical Thermodynamics vol 11 no 11 pp 1061ndash1064 1979
[9] GDouheretM I Davis I J Fjellanger andHHoslashiland ldquoUltra-sonic speeds and volumetric properties of binary mixtures ofwater with poly(ethylene glycol)s at 29815 Krdquo Journal of theChemical Society - Faraday Transactions vol 93 no 10 pp1943ndash1949 1997
[10] A J Treszczanowicz O Kiyohara and G C Benson ldquoExcessvolumes for n-alkanols +n-alkanes IV Binary mixtures ofdecan-1-ol +n-pentane +n-hexane +n-octane +n-decane and+n-hexadecanerdquoThe Journal of ChemicalThermodynamics vol13 no 3 pp 253ndash260 1981
[11] A H Roux and J E Desnoyers ldquoAssociation models for alco-hol-water mixturesrdquo Journal of Proceedings of the Indian Acad-emy of Sciences Chemical Sciences vol 98 no 5-6 pp 435ndash451
Table 2 Refractive indices 119899119863 density 120588 speed of sound 119906 and viscosity 120578 for DMSO(1) + acetophenone(2) system at different tem-
Table 3 Refractive indices 119899119863 density 120588 speed of sound 119906 and viscosity 120578 for DMSO(1) + p-xylene(2) system at different temperatures
have been fitted to viscosity data and it was found that bothhave the same standard errors at each temperature
33 Isentropic Compressibility The experimental results forthe speed of sound of binary mixtures are listed in Tables 2and 3 The isentropic compressibility was evaluated by using119870119878= 119906minus2120588minus1 and the deviation in isentropic compressibility
is calculated using the following equation
119870119864
119878= 119870119878minus 119870
id119878 (8)
where 119870id119878stands for isentropic compressibility for an ideal
mixture calculated using Benson-Kiyohara model [8 9]
119870id119878=
2
sum
119894=1
Φ119894[119870119878119894+
119879119881119894(1205722
119894)
119862119901119894
]
minus
119879(sum2
119894=1119909119894119881119894) (sum2
119894=1Φ119894119886119894)2
sum2
119894=1119909119894119862119901119894
(9)
where 119886119894and 119862
119901are the thermal expansion coefficient and
molar heat capacity of the 119894th components respectivelyThe deviation in speed of sound is given by
Δ119906 = 119906 minus 11990911199061minus 11990921199062 (10)
34 Molar Refraction Refractive indices have been used forthe calculation of molar refraction (119877
119898) that is obtained by
using Lorentz-Lorenz equation [8]Deviation in molar refraction (Δ119877) is calculated by the
following equation
119877 = 119877119898minussumΦ
119894119877119894
Φ119894=
119909119894
sum119909119895119881119895
(11)
00
05
00 01 02 03 04 05 06 07 08 09 10
minus05
minus10
minus15
minus20
minus25
minus30
minus35
x1
VE(cm3middotm
olminus1)
Figure 1 Experimental and calculated excess molar volume for(i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-Xylene(2)at 31315 K Q 31815 K ◼ 32315 K 998771 32815 K e symbols rep-resent the experimental values dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-119901-Xylenemixture both optimised by Redlich-Kister parameters
where 119899119863refers to the refractive index119877
119898is molar refraction
of the mixture 119877119894is molar refraction of the 119894th component
and Φ is ideal state volume fractionAll the deviations (119881119864 Δ119877 Δ120578 Δ119906 and 119870
119864
119878) have been
fitted to Redlich-Kister polynomial regression of the type
Δ119884 = 11990911199092
119898
sum
119894=1
119860119894(1 minus 2119909
1)119894minus1 (12)
to derive the constant119860119894using themethod of the least square
Standard deviation for each case is calculated by
120590 = [
sum (Δ119884exptl minus Δ119884calcd)2
119898 minus 119899]
05
(13)
where 119898 is the number of data points and 119899 is the numberof coefficients Derived parameters of the Redlich-Kisterequation (12) and standard deviations (13) are presented inTables 4 and 5
4 Discussions
The excess molar volume from 31315 to 32815 K versusthe mole fraction of both mixtures with respect to DMSOis shown in Figure 1 The molar volume of the mixturesand the viscosity data have been used for the calculationof Gibbsrsquo free energy presented in Figure 5 The 119881119864 valuesdecrease with increasing temperatures for the systems butare positive in case of DMSO-acetophenone mixture andnegative for DMSO-119901-xylene mixture Treszczanowicz et al
6 Journal of Thermodynamics
Table 4 Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures atdifferent temperatures (DMSO-acetophenone)
[10] and Roux and Desnoyers [11] suggested that 119881119864 is theresultant contribution from several opposing effects Theseeffects can be primarily divided into three types namelychemical physical and structural A physical contributionthat is specific interactions between the real species presentin the mixture contribute in negative terms to 119881
119864 Thechemical or specific intermolecular interactions result ina volume decrease and these include charge transfer typeforces and other complex forming interactions This effectalso contributes in negative values to 119881
119864 The structuralcontributions are mostly negative and can arise from severaleffects especially from changes of free volume and interstitialaccommodation In other words structural contributionsarising from geometrical fitting of one component into theother due to the differences in the free volume and molarvolume between components lead to a negative contributionto 119881119864 The viscosity and deviations are presented in Table 2and plotted in Figure 2 respectively for both systems Theviscosity deviations decreasewith the increase in temperaturefor both systems The negative Δ120578 values are generallyobserved for systems where dispersion or weak dipole-dipoleforces are primarily responsible for interaction between the
component molecules The viscosity data is also fitted tothe two and the three-parameter models that is Herriccorrelation the McAllister model and Grunberg-Nissancorrelation and the evaluated parameters are presented inTables 6 and 7 The deviations in molar refraction for bothsystems are shown in Figure 3 The Δ119877 values are positivefor acetophenone system for the whole composition rangewhich goes on increasing as the temperature of the solutionincreasesThe Δ119877 values are negative for 119901119886119903119886-xylene systemfor the whole composition range which goes on decreasingas the temperature of the solution increases In general thenegative values of Δ119877 suggest that we have weak interactionsbetween the componentmolecules in themixtureThe resultsof excess isentropic compressibility (119870119864
119878) are also plotted in
Figure 4The deviations for DMSO-acetophenone system areinitially negative and then become positive when mole frac-tion is around 05 whereas for DMSO-119901-xylene system theyare negative over the entire composition range Deviation inGibbs free energy forDMSO-acetophenone system follows anarbitrary path going from negative to positive and vice versatwice while for DMSO-119901119886119903119886-xylene system the deviationsare negative and increase with increasing temperature
Journal of Thermodynamics 7
Table 5 Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures atdifferent temperatures (DMSO-119901-xylene)
Table 6 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-acetophenone)
Table 7 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-119901-xylene)
Figure 2 Experimental and calculated deviations in viscosityfor (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 KQ 31815 K ◼ 32315 K998771 32815 Ke symbolsrepresent the experimental values dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-119901-xylenemixture both optimised by Redlich-Kister parameters
Symbols Used
1198601 1198602 1198603 1198604 Parameters of Redlich-Kister equation
11986012 11986021 Interaction coefficients of McAllister
model12057212 12 Coefficients of Herricrsquos correlation
] Kinematic viscosity (m2sminus1)120588 Density (g cmminus3)
005
00 01 02 03 04 05 06 07 08 09 10
minus015
minus035
minus055
minus075
minus095
minus115
x1
ΔR
Figure 3 Experimental and calculated deviations in molar refrac-tion for (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 998771 32815 K e andsymbols represent the experimental values dotted lines representDMSO-acetophenone mixture and solid lines represent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
120590 Standard deviation120572 Thermal expansion coefficient (Kminus1)120578 Dynamic viscosity (mPasdots)Δ119866119864 Excess Gibbs free energy (Jmolminus1)
Figure 4 Experimental and calculated deviations in isentropiccompressibility for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values dottedlines represent DMSO-Acetophenone mixture and solid lines rep-resent DMSO-119901-xylene mixture both optimised by Redlich-Kisterparameters
0
50
00 01 02 03 04 05 06 07 08 09 10minus50
minus100
minus150
minus200
minus250
minus300
minus350
minus400
x1
ΔGE(Jmiddotm
olminus1)
Figure 5 Experimental and calculated deviations in Gibbs freeenergy of activation for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values solidlines represent DMSO-Acetophenone mixture and dotted linesrepresent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
119877 Universal gas constant(8314 Jmolminus1Kminus1)
119879 Absolute temperature (K)11988912 Grunberg-nissan parameter
Φ119894 Volume fraction (dimensionless)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] M M Palaiologou G K Arianas and N G Tsierkezos ldquoTher-modynamic investigation of dimethyl sulfoxide binarymixturesat 29315 and 31315 Krdquo Journal of Solution Chemistry vol 35 no11 pp 1551ndash1565 2006
[2] K Zhang J Yang X Yu J Zhang and X Wei ldquoDensities andviscosities for binary mixtures of poly(ethylene glycol) 400 +dimethyl sulfoxide and poly(ethylene glycol) 600 + water atdifferent temperaturesrdquo Journal of Chemical and EngineeringData vol 56 no 7 pp 3083ndash3088 2011
[3] A Ali A K Nain D Chand and R Ahmad ldquoViscosities andrefractive indices of binary mixtures of dimethylsulphoxidewith some aromatic hydrocarbons at different temperaturesan experimental and theoretical studyrdquo Journal of the ChineseChemical Society vol 53 no 3 pp 531ndash543 2006
[4] J A Riddick W B Bunger and T K Sakano Organic SolventsPhysical Properties and Methods of Purifications vol 2 ofTechniques of Chemistry John Wiley amp Sons New York NYUSA 1986
[5] V K Rattan S Kapoor and K Tochigi ldquoViscosities anddensities of binary mixtures of toluene with acetic acid andpropionic acid at (29315 30315 31315 and 32315) Krdquo Journalof Chemical and Engineering Data vol 47 no 5 pp 1182ndash11842002
[6] R A McAllister ldquoThe viscosity of liquid mixturesrdquo AIChEJournal vol 6 pp 427ndash431 1960
[7] L Grunberg and A H Nissan ldquoThe energies of vaporisationviscosity and cohesion and the structure of liquidsrdquo Transac-tions of the Faraday Society vol 45 pp 125ndash137 1949
[8] G C Benson and O Kiyohara ldquoEvaluation of excess isentropiccompressibilities and isochoric heat capacitiesrdquo The Journal ofChemical Thermodynamics vol 11 no 11 pp 1061ndash1064 1979
[9] GDouheretM I Davis I J Fjellanger andHHoslashiland ldquoUltra-sonic speeds and volumetric properties of binary mixtures ofwater with poly(ethylene glycol)s at 29815 Krdquo Journal of theChemical Society - Faraday Transactions vol 93 no 10 pp1943ndash1949 1997
[10] A J Treszczanowicz O Kiyohara and G C Benson ldquoExcessvolumes for n-alkanols +n-alkanes IV Binary mixtures ofdecan-1-ol +n-pentane +n-hexane +n-octane +n-decane and+n-hexadecanerdquoThe Journal of ChemicalThermodynamics vol13 no 3 pp 253ndash260 1981
[11] A H Roux and J E Desnoyers ldquoAssociation models for alco-hol-water mixturesrdquo Journal of Proceedings of the Indian Acad-emy of Sciences Chemical Sciences vol 98 no 5-6 pp 435ndash451
Table 3 Refractive indices 119899119863 density 120588 speed of sound 119906 and viscosity 120578 for DMSO(1) + p-xylene(2) system at different temperatures
have been fitted to viscosity data and it was found that bothhave the same standard errors at each temperature
33 Isentropic Compressibility The experimental results forthe speed of sound of binary mixtures are listed in Tables 2and 3 The isentropic compressibility was evaluated by using119870119878= 119906minus2120588minus1 and the deviation in isentropic compressibility
is calculated using the following equation
119870119864
119878= 119870119878minus 119870
id119878 (8)
where 119870id119878stands for isentropic compressibility for an ideal
mixture calculated using Benson-Kiyohara model [8 9]
119870id119878=
2
sum
119894=1
Φ119894[119870119878119894+
119879119881119894(1205722
119894)
119862119901119894
]
minus
119879(sum2
119894=1119909119894119881119894) (sum2
119894=1Φ119894119886119894)2
sum2
119894=1119909119894119862119901119894
(9)
where 119886119894and 119862
119901are the thermal expansion coefficient and
molar heat capacity of the 119894th components respectivelyThe deviation in speed of sound is given by
Δ119906 = 119906 minus 11990911199061minus 11990921199062 (10)
34 Molar Refraction Refractive indices have been used forthe calculation of molar refraction (119877
119898) that is obtained by
using Lorentz-Lorenz equation [8]Deviation in molar refraction (Δ119877) is calculated by the
following equation
119877 = 119877119898minussumΦ
119894119877119894
Φ119894=
119909119894
sum119909119895119881119895
(11)
00
05
00 01 02 03 04 05 06 07 08 09 10
minus05
minus10
minus15
minus20
minus25
minus30
minus35
x1
VE(cm3middotm
olminus1)
Figure 1 Experimental and calculated excess molar volume for(i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-Xylene(2)at 31315 K Q 31815 K ◼ 32315 K 998771 32815 K e symbols rep-resent the experimental values dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-119901-Xylenemixture both optimised by Redlich-Kister parameters
where 119899119863refers to the refractive index119877
119898is molar refraction
of the mixture 119877119894is molar refraction of the 119894th component
and Φ is ideal state volume fractionAll the deviations (119881119864 Δ119877 Δ120578 Δ119906 and 119870
119864
119878) have been
fitted to Redlich-Kister polynomial regression of the type
Δ119884 = 11990911199092
119898
sum
119894=1
119860119894(1 minus 2119909
1)119894minus1 (12)
to derive the constant119860119894using themethod of the least square
Standard deviation for each case is calculated by
120590 = [
sum (Δ119884exptl minus Δ119884calcd)2
119898 minus 119899]
05
(13)
where 119898 is the number of data points and 119899 is the numberof coefficients Derived parameters of the Redlich-Kisterequation (12) and standard deviations (13) are presented inTables 4 and 5
4 Discussions
The excess molar volume from 31315 to 32815 K versusthe mole fraction of both mixtures with respect to DMSOis shown in Figure 1 The molar volume of the mixturesand the viscosity data have been used for the calculationof Gibbsrsquo free energy presented in Figure 5 The 119881119864 valuesdecrease with increasing temperatures for the systems butare positive in case of DMSO-acetophenone mixture andnegative for DMSO-119901-xylene mixture Treszczanowicz et al
6 Journal of Thermodynamics
Table 4 Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures atdifferent temperatures (DMSO-acetophenone)
[10] and Roux and Desnoyers [11] suggested that 119881119864 is theresultant contribution from several opposing effects Theseeffects can be primarily divided into three types namelychemical physical and structural A physical contributionthat is specific interactions between the real species presentin the mixture contribute in negative terms to 119881
119864 Thechemical or specific intermolecular interactions result ina volume decrease and these include charge transfer typeforces and other complex forming interactions This effectalso contributes in negative values to 119881
119864 The structuralcontributions are mostly negative and can arise from severaleffects especially from changes of free volume and interstitialaccommodation In other words structural contributionsarising from geometrical fitting of one component into theother due to the differences in the free volume and molarvolume between components lead to a negative contributionto 119881119864 The viscosity and deviations are presented in Table 2and plotted in Figure 2 respectively for both systems Theviscosity deviations decreasewith the increase in temperaturefor both systems The negative Δ120578 values are generallyobserved for systems where dispersion or weak dipole-dipoleforces are primarily responsible for interaction between the
component molecules The viscosity data is also fitted tothe two and the three-parameter models that is Herriccorrelation the McAllister model and Grunberg-Nissancorrelation and the evaluated parameters are presented inTables 6 and 7 The deviations in molar refraction for bothsystems are shown in Figure 3 The Δ119877 values are positivefor acetophenone system for the whole composition rangewhich goes on increasing as the temperature of the solutionincreasesThe Δ119877 values are negative for 119901119886119903119886-xylene systemfor the whole composition range which goes on decreasingas the temperature of the solution increases In general thenegative values of Δ119877 suggest that we have weak interactionsbetween the componentmolecules in themixtureThe resultsof excess isentropic compressibility (119870119864
119878) are also plotted in
Figure 4The deviations for DMSO-acetophenone system areinitially negative and then become positive when mole frac-tion is around 05 whereas for DMSO-119901-xylene system theyare negative over the entire composition range Deviation inGibbs free energy forDMSO-acetophenone system follows anarbitrary path going from negative to positive and vice versatwice while for DMSO-119901119886119903119886-xylene system the deviationsare negative and increase with increasing temperature
Journal of Thermodynamics 7
Table 5 Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures atdifferent temperatures (DMSO-119901-xylene)
Table 6 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-acetophenone)
Table 7 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-119901-xylene)
Figure 2 Experimental and calculated deviations in viscosityfor (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 KQ 31815 K ◼ 32315 K998771 32815 Ke symbolsrepresent the experimental values dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-119901-xylenemixture both optimised by Redlich-Kister parameters
Symbols Used
1198601 1198602 1198603 1198604 Parameters of Redlich-Kister equation
11986012 11986021 Interaction coefficients of McAllister
model12057212 12 Coefficients of Herricrsquos correlation
] Kinematic viscosity (m2sminus1)120588 Density (g cmminus3)
005
00 01 02 03 04 05 06 07 08 09 10
minus015
minus035
minus055
minus075
minus095
minus115
x1
ΔR
Figure 3 Experimental and calculated deviations in molar refrac-tion for (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 998771 32815 K e andsymbols represent the experimental values dotted lines representDMSO-acetophenone mixture and solid lines represent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
120590 Standard deviation120572 Thermal expansion coefficient (Kminus1)120578 Dynamic viscosity (mPasdots)Δ119866119864 Excess Gibbs free energy (Jmolminus1)
Figure 4 Experimental and calculated deviations in isentropiccompressibility for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values dottedlines represent DMSO-Acetophenone mixture and solid lines rep-resent DMSO-119901-xylene mixture both optimised by Redlich-Kisterparameters
0
50
00 01 02 03 04 05 06 07 08 09 10minus50
minus100
minus150
minus200
minus250
minus300
minus350
minus400
x1
ΔGE(Jmiddotm
olminus1)
Figure 5 Experimental and calculated deviations in Gibbs freeenergy of activation for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values solidlines represent DMSO-Acetophenone mixture and dotted linesrepresent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
119877 Universal gas constant(8314 Jmolminus1Kminus1)
119879 Absolute temperature (K)11988912 Grunberg-nissan parameter
Φ119894 Volume fraction (dimensionless)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] M M Palaiologou G K Arianas and N G Tsierkezos ldquoTher-modynamic investigation of dimethyl sulfoxide binarymixturesat 29315 and 31315 Krdquo Journal of Solution Chemistry vol 35 no11 pp 1551ndash1565 2006
[2] K Zhang J Yang X Yu J Zhang and X Wei ldquoDensities andviscosities for binary mixtures of poly(ethylene glycol) 400 +dimethyl sulfoxide and poly(ethylene glycol) 600 + water atdifferent temperaturesrdquo Journal of Chemical and EngineeringData vol 56 no 7 pp 3083ndash3088 2011
[3] A Ali A K Nain D Chand and R Ahmad ldquoViscosities andrefractive indices of binary mixtures of dimethylsulphoxidewith some aromatic hydrocarbons at different temperaturesan experimental and theoretical studyrdquo Journal of the ChineseChemical Society vol 53 no 3 pp 531ndash543 2006
[4] J A Riddick W B Bunger and T K Sakano Organic SolventsPhysical Properties and Methods of Purifications vol 2 ofTechniques of Chemistry John Wiley amp Sons New York NYUSA 1986
[5] V K Rattan S Kapoor and K Tochigi ldquoViscosities anddensities of binary mixtures of toluene with acetic acid andpropionic acid at (29315 30315 31315 and 32315) Krdquo Journalof Chemical and Engineering Data vol 47 no 5 pp 1182ndash11842002
[6] R A McAllister ldquoThe viscosity of liquid mixturesrdquo AIChEJournal vol 6 pp 427ndash431 1960
[7] L Grunberg and A H Nissan ldquoThe energies of vaporisationviscosity and cohesion and the structure of liquidsrdquo Transac-tions of the Faraday Society vol 45 pp 125ndash137 1949
[8] G C Benson and O Kiyohara ldquoEvaluation of excess isentropiccompressibilities and isochoric heat capacitiesrdquo The Journal ofChemical Thermodynamics vol 11 no 11 pp 1061ndash1064 1979
[9] GDouheretM I Davis I J Fjellanger andHHoslashiland ldquoUltra-sonic speeds and volumetric properties of binary mixtures ofwater with poly(ethylene glycol)s at 29815 Krdquo Journal of theChemical Society - Faraday Transactions vol 93 no 10 pp1943ndash1949 1997
[10] A J Treszczanowicz O Kiyohara and G C Benson ldquoExcessvolumes for n-alkanols +n-alkanes IV Binary mixtures ofdecan-1-ol +n-pentane +n-hexane +n-octane +n-decane and+n-hexadecanerdquoThe Journal of ChemicalThermodynamics vol13 no 3 pp 253ndash260 1981
[11] A H Roux and J E Desnoyers ldquoAssociation models for alco-hol-water mixturesrdquo Journal of Proceedings of the Indian Acad-emy of Sciences Chemical Sciences vol 98 no 5-6 pp 435ndash451
have been fitted to viscosity data and it was found that bothhave the same standard errors at each temperature
33 Isentropic Compressibility The experimental results forthe speed of sound of binary mixtures are listed in Tables 2and 3 The isentropic compressibility was evaluated by using119870119878= 119906minus2120588minus1 and the deviation in isentropic compressibility
is calculated using the following equation
119870119864
119878= 119870119878minus 119870
id119878 (8)
where 119870id119878stands for isentropic compressibility for an ideal
mixture calculated using Benson-Kiyohara model [8 9]
119870id119878=
2
sum
119894=1
Φ119894[119870119878119894+
119879119881119894(1205722
119894)
119862119901119894
]
minus
119879(sum2
119894=1119909119894119881119894) (sum2
119894=1Φ119894119886119894)2
sum2
119894=1119909119894119862119901119894
(9)
where 119886119894and 119862
119901are the thermal expansion coefficient and
molar heat capacity of the 119894th components respectivelyThe deviation in speed of sound is given by
Δ119906 = 119906 minus 11990911199061minus 11990921199062 (10)
34 Molar Refraction Refractive indices have been used forthe calculation of molar refraction (119877
119898) that is obtained by
using Lorentz-Lorenz equation [8]Deviation in molar refraction (Δ119877) is calculated by the
following equation
119877 = 119877119898minussumΦ
119894119877119894
Φ119894=
119909119894
sum119909119895119881119895
(11)
00
05
00 01 02 03 04 05 06 07 08 09 10
minus05
minus10
minus15
minus20
minus25
minus30
minus35
x1
VE(cm3middotm
olminus1)
Figure 1 Experimental and calculated excess molar volume for(i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-Xylene(2)at 31315 K Q 31815 K ◼ 32315 K 998771 32815 K e symbols rep-resent the experimental values dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-119901-Xylenemixture both optimised by Redlich-Kister parameters
where 119899119863refers to the refractive index119877
119898is molar refraction
of the mixture 119877119894is molar refraction of the 119894th component
and Φ is ideal state volume fractionAll the deviations (119881119864 Δ119877 Δ120578 Δ119906 and 119870
119864
119878) have been
fitted to Redlich-Kister polynomial regression of the type
Δ119884 = 11990911199092
119898
sum
119894=1
119860119894(1 minus 2119909
1)119894minus1 (12)
to derive the constant119860119894using themethod of the least square
Standard deviation for each case is calculated by
120590 = [
sum (Δ119884exptl minus Δ119884calcd)2
119898 minus 119899]
05
(13)
where 119898 is the number of data points and 119899 is the numberof coefficients Derived parameters of the Redlich-Kisterequation (12) and standard deviations (13) are presented inTables 4 and 5
4 Discussions
The excess molar volume from 31315 to 32815 K versusthe mole fraction of both mixtures with respect to DMSOis shown in Figure 1 The molar volume of the mixturesand the viscosity data have been used for the calculationof Gibbsrsquo free energy presented in Figure 5 The 119881119864 valuesdecrease with increasing temperatures for the systems butare positive in case of DMSO-acetophenone mixture andnegative for DMSO-119901-xylene mixture Treszczanowicz et al
6 Journal of Thermodynamics
Table 4 Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures atdifferent temperatures (DMSO-acetophenone)
[10] and Roux and Desnoyers [11] suggested that 119881119864 is theresultant contribution from several opposing effects Theseeffects can be primarily divided into three types namelychemical physical and structural A physical contributionthat is specific interactions between the real species presentin the mixture contribute in negative terms to 119881
119864 Thechemical or specific intermolecular interactions result ina volume decrease and these include charge transfer typeforces and other complex forming interactions This effectalso contributes in negative values to 119881
119864 The structuralcontributions are mostly negative and can arise from severaleffects especially from changes of free volume and interstitialaccommodation In other words structural contributionsarising from geometrical fitting of one component into theother due to the differences in the free volume and molarvolume between components lead to a negative contributionto 119881119864 The viscosity and deviations are presented in Table 2and plotted in Figure 2 respectively for both systems Theviscosity deviations decreasewith the increase in temperaturefor both systems The negative Δ120578 values are generallyobserved for systems where dispersion or weak dipole-dipoleforces are primarily responsible for interaction between the
component molecules The viscosity data is also fitted tothe two and the three-parameter models that is Herriccorrelation the McAllister model and Grunberg-Nissancorrelation and the evaluated parameters are presented inTables 6 and 7 The deviations in molar refraction for bothsystems are shown in Figure 3 The Δ119877 values are positivefor acetophenone system for the whole composition rangewhich goes on increasing as the temperature of the solutionincreasesThe Δ119877 values are negative for 119901119886119903119886-xylene systemfor the whole composition range which goes on decreasingas the temperature of the solution increases In general thenegative values of Δ119877 suggest that we have weak interactionsbetween the componentmolecules in themixtureThe resultsof excess isentropic compressibility (119870119864
119878) are also plotted in
Figure 4The deviations for DMSO-acetophenone system areinitially negative and then become positive when mole frac-tion is around 05 whereas for DMSO-119901-xylene system theyare negative over the entire composition range Deviation inGibbs free energy forDMSO-acetophenone system follows anarbitrary path going from negative to positive and vice versatwice while for DMSO-119901119886119903119886-xylene system the deviationsare negative and increase with increasing temperature
Journal of Thermodynamics 7
Table 5 Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures atdifferent temperatures (DMSO-119901-xylene)
Table 6 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-acetophenone)
Table 7 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-119901-xylene)
Figure 2 Experimental and calculated deviations in viscosityfor (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 KQ 31815 K ◼ 32315 K998771 32815 Ke symbolsrepresent the experimental values dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-119901-xylenemixture both optimised by Redlich-Kister parameters
Symbols Used
1198601 1198602 1198603 1198604 Parameters of Redlich-Kister equation
11986012 11986021 Interaction coefficients of McAllister
model12057212 12 Coefficients of Herricrsquos correlation
] Kinematic viscosity (m2sminus1)120588 Density (g cmminus3)
005
00 01 02 03 04 05 06 07 08 09 10
minus015
minus035
minus055
minus075
minus095
minus115
x1
ΔR
Figure 3 Experimental and calculated deviations in molar refrac-tion for (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 998771 32815 K e andsymbols represent the experimental values dotted lines representDMSO-acetophenone mixture and solid lines represent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
120590 Standard deviation120572 Thermal expansion coefficient (Kminus1)120578 Dynamic viscosity (mPasdots)Δ119866119864 Excess Gibbs free energy (Jmolminus1)
Figure 4 Experimental and calculated deviations in isentropiccompressibility for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values dottedlines represent DMSO-Acetophenone mixture and solid lines rep-resent DMSO-119901-xylene mixture both optimised by Redlich-Kisterparameters
0
50
00 01 02 03 04 05 06 07 08 09 10minus50
minus100
minus150
minus200
minus250
minus300
minus350
minus400
x1
ΔGE(Jmiddotm
olminus1)
Figure 5 Experimental and calculated deviations in Gibbs freeenergy of activation for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values solidlines represent DMSO-Acetophenone mixture and dotted linesrepresent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
119877 Universal gas constant(8314 Jmolminus1Kminus1)
119879 Absolute temperature (K)11988912 Grunberg-nissan parameter
Φ119894 Volume fraction (dimensionless)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] M M Palaiologou G K Arianas and N G Tsierkezos ldquoTher-modynamic investigation of dimethyl sulfoxide binarymixturesat 29315 and 31315 Krdquo Journal of Solution Chemistry vol 35 no11 pp 1551ndash1565 2006
[2] K Zhang J Yang X Yu J Zhang and X Wei ldquoDensities andviscosities for binary mixtures of poly(ethylene glycol) 400 +dimethyl sulfoxide and poly(ethylene glycol) 600 + water atdifferent temperaturesrdquo Journal of Chemical and EngineeringData vol 56 no 7 pp 3083ndash3088 2011
[3] A Ali A K Nain D Chand and R Ahmad ldquoViscosities andrefractive indices of binary mixtures of dimethylsulphoxidewith some aromatic hydrocarbons at different temperaturesan experimental and theoretical studyrdquo Journal of the ChineseChemical Society vol 53 no 3 pp 531ndash543 2006
[4] J A Riddick W B Bunger and T K Sakano Organic SolventsPhysical Properties and Methods of Purifications vol 2 ofTechniques of Chemistry John Wiley amp Sons New York NYUSA 1986
[5] V K Rattan S Kapoor and K Tochigi ldquoViscosities anddensities of binary mixtures of toluene with acetic acid andpropionic acid at (29315 30315 31315 and 32315) Krdquo Journalof Chemical and Engineering Data vol 47 no 5 pp 1182ndash11842002
[6] R A McAllister ldquoThe viscosity of liquid mixturesrdquo AIChEJournal vol 6 pp 427ndash431 1960
[7] L Grunberg and A H Nissan ldquoThe energies of vaporisationviscosity and cohesion and the structure of liquidsrdquo Transac-tions of the Faraday Society vol 45 pp 125ndash137 1949
[8] G C Benson and O Kiyohara ldquoEvaluation of excess isentropiccompressibilities and isochoric heat capacitiesrdquo The Journal ofChemical Thermodynamics vol 11 no 11 pp 1061ndash1064 1979
[9] GDouheretM I Davis I J Fjellanger andHHoslashiland ldquoUltra-sonic speeds and volumetric properties of binary mixtures ofwater with poly(ethylene glycol)s at 29815 Krdquo Journal of theChemical Society - Faraday Transactions vol 93 no 10 pp1943ndash1949 1997
[10] A J Treszczanowicz O Kiyohara and G C Benson ldquoExcessvolumes for n-alkanols +n-alkanes IV Binary mixtures ofdecan-1-ol +n-pentane +n-hexane +n-octane +n-decane and+n-hexadecanerdquoThe Journal of ChemicalThermodynamics vol13 no 3 pp 253ndash260 1981
[11] A H Roux and J E Desnoyers ldquoAssociation models for alco-hol-water mixturesrdquo Journal of Proceedings of the Indian Acad-emy of Sciences Chemical Sciences vol 98 no 5-6 pp 435ndash451
Table 4 Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures atdifferent temperatures (DMSO-acetophenone)
[10] and Roux and Desnoyers [11] suggested that 119881119864 is theresultant contribution from several opposing effects Theseeffects can be primarily divided into three types namelychemical physical and structural A physical contributionthat is specific interactions between the real species presentin the mixture contribute in negative terms to 119881
119864 Thechemical or specific intermolecular interactions result ina volume decrease and these include charge transfer typeforces and other complex forming interactions This effectalso contributes in negative values to 119881
119864 The structuralcontributions are mostly negative and can arise from severaleffects especially from changes of free volume and interstitialaccommodation In other words structural contributionsarising from geometrical fitting of one component into theother due to the differences in the free volume and molarvolume between components lead to a negative contributionto 119881119864 The viscosity and deviations are presented in Table 2and plotted in Figure 2 respectively for both systems Theviscosity deviations decreasewith the increase in temperaturefor both systems The negative Δ120578 values are generallyobserved for systems where dispersion or weak dipole-dipoleforces are primarily responsible for interaction between the
component molecules The viscosity data is also fitted tothe two and the three-parameter models that is Herriccorrelation the McAllister model and Grunberg-Nissancorrelation and the evaluated parameters are presented inTables 6 and 7 The deviations in molar refraction for bothsystems are shown in Figure 3 The Δ119877 values are positivefor acetophenone system for the whole composition rangewhich goes on increasing as the temperature of the solutionincreasesThe Δ119877 values are negative for 119901119886119903119886-xylene systemfor the whole composition range which goes on decreasingas the temperature of the solution increases In general thenegative values of Δ119877 suggest that we have weak interactionsbetween the componentmolecules in themixtureThe resultsof excess isentropic compressibility (119870119864
119878) are also plotted in
Figure 4The deviations for DMSO-acetophenone system areinitially negative and then become positive when mole frac-tion is around 05 whereas for DMSO-119901-xylene system theyare negative over the entire composition range Deviation inGibbs free energy forDMSO-acetophenone system follows anarbitrary path going from negative to positive and vice versatwice while for DMSO-119901119886119903119886-xylene system the deviationsare negative and increase with increasing temperature
Journal of Thermodynamics 7
Table 5 Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures atdifferent temperatures (DMSO-119901-xylene)
Table 6 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-acetophenone)
Table 7 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-119901-xylene)
Figure 2 Experimental and calculated deviations in viscosityfor (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 KQ 31815 K ◼ 32315 K998771 32815 Ke symbolsrepresent the experimental values dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-119901-xylenemixture both optimised by Redlich-Kister parameters
Symbols Used
1198601 1198602 1198603 1198604 Parameters of Redlich-Kister equation
11986012 11986021 Interaction coefficients of McAllister
model12057212 12 Coefficients of Herricrsquos correlation
] Kinematic viscosity (m2sminus1)120588 Density (g cmminus3)
005
00 01 02 03 04 05 06 07 08 09 10
minus015
minus035
minus055
minus075
minus095
minus115
x1
ΔR
Figure 3 Experimental and calculated deviations in molar refrac-tion for (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 998771 32815 K e andsymbols represent the experimental values dotted lines representDMSO-acetophenone mixture and solid lines represent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
120590 Standard deviation120572 Thermal expansion coefficient (Kminus1)120578 Dynamic viscosity (mPasdots)Δ119866119864 Excess Gibbs free energy (Jmolminus1)
Figure 4 Experimental and calculated deviations in isentropiccompressibility for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values dottedlines represent DMSO-Acetophenone mixture and solid lines rep-resent DMSO-119901-xylene mixture both optimised by Redlich-Kisterparameters
0
50
00 01 02 03 04 05 06 07 08 09 10minus50
minus100
minus150
minus200
minus250
minus300
minus350
minus400
x1
ΔGE(Jmiddotm
olminus1)
Figure 5 Experimental and calculated deviations in Gibbs freeenergy of activation for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values solidlines represent DMSO-Acetophenone mixture and dotted linesrepresent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
119877 Universal gas constant(8314 Jmolminus1Kminus1)
119879 Absolute temperature (K)11988912 Grunberg-nissan parameter
Φ119894 Volume fraction (dimensionless)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] M M Palaiologou G K Arianas and N G Tsierkezos ldquoTher-modynamic investigation of dimethyl sulfoxide binarymixturesat 29315 and 31315 Krdquo Journal of Solution Chemistry vol 35 no11 pp 1551ndash1565 2006
[2] K Zhang J Yang X Yu J Zhang and X Wei ldquoDensities andviscosities for binary mixtures of poly(ethylene glycol) 400 +dimethyl sulfoxide and poly(ethylene glycol) 600 + water atdifferent temperaturesrdquo Journal of Chemical and EngineeringData vol 56 no 7 pp 3083ndash3088 2011
[3] A Ali A K Nain D Chand and R Ahmad ldquoViscosities andrefractive indices of binary mixtures of dimethylsulphoxidewith some aromatic hydrocarbons at different temperaturesan experimental and theoretical studyrdquo Journal of the ChineseChemical Society vol 53 no 3 pp 531ndash543 2006
[4] J A Riddick W B Bunger and T K Sakano Organic SolventsPhysical Properties and Methods of Purifications vol 2 ofTechniques of Chemistry John Wiley amp Sons New York NYUSA 1986
[5] V K Rattan S Kapoor and K Tochigi ldquoViscosities anddensities of binary mixtures of toluene with acetic acid andpropionic acid at (29315 30315 31315 and 32315) Krdquo Journalof Chemical and Engineering Data vol 47 no 5 pp 1182ndash11842002
[6] R A McAllister ldquoThe viscosity of liquid mixturesrdquo AIChEJournal vol 6 pp 427ndash431 1960
[7] L Grunberg and A H Nissan ldquoThe energies of vaporisationviscosity and cohesion and the structure of liquidsrdquo Transac-tions of the Faraday Society vol 45 pp 125ndash137 1949
[8] G C Benson and O Kiyohara ldquoEvaluation of excess isentropiccompressibilities and isochoric heat capacitiesrdquo The Journal ofChemical Thermodynamics vol 11 no 11 pp 1061ndash1064 1979
[9] GDouheretM I Davis I J Fjellanger andHHoslashiland ldquoUltra-sonic speeds and volumetric properties of binary mixtures ofwater with poly(ethylene glycol)s at 29815 Krdquo Journal of theChemical Society - Faraday Transactions vol 93 no 10 pp1943ndash1949 1997
[10] A J Treszczanowicz O Kiyohara and G C Benson ldquoExcessvolumes for n-alkanols +n-alkanes IV Binary mixtures ofdecan-1-ol +n-pentane +n-hexane +n-octane +n-decane and+n-hexadecanerdquoThe Journal of ChemicalThermodynamics vol13 no 3 pp 253ndash260 1981
[11] A H Roux and J E Desnoyers ldquoAssociation models for alco-hol-water mixturesrdquo Journal of Proceedings of the Indian Acad-emy of Sciences Chemical Sciences vol 98 no 5-6 pp 435ndash451
Table 5 Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures atdifferent temperatures (DMSO-119901-xylene)
Table 6 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-acetophenone)
Table 7 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-119901-xylene)
Figure 2 Experimental and calculated deviations in viscosityfor (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 KQ 31815 K ◼ 32315 K998771 32815 Ke symbolsrepresent the experimental values dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-119901-xylenemixture both optimised by Redlich-Kister parameters
Symbols Used
1198601 1198602 1198603 1198604 Parameters of Redlich-Kister equation
11986012 11986021 Interaction coefficients of McAllister
model12057212 12 Coefficients of Herricrsquos correlation
] Kinematic viscosity (m2sminus1)120588 Density (g cmminus3)
005
00 01 02 03 04 05 06 07 08 09 10
minus015
minus035
minus055
minus075
minus095
minus115
x1
ΔR
Figure 3 Experimental and calculated deviations in molar refrac-tion for (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 998771 32815 K e andsymbols represent the experimental values dotted lines representDMSO-acetophenone mixture and solid lines represent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
120590 Standard deviation120572 Thermal expansion coefficient (Kminus1)120578 Dynamic viscosity (mPasdots)Δ119866119864 Excess Gibbs free energy (Jmolminus1)
Figure 4 Experimental and calculated deviations in isentropiccompressibility for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values dottedlines represent DMSO-Acetophenone mixture and solid lines rep-resent DMSO-119901-xylene mixture both optimised by Redlich-Kisterparameters
0
50
00 01 02 03 04 05 06 07 08 09 10minus50
minus100
minus150
minus200
minus250
minus300
minus350
minus400
x1
ΔGE(Jmiddotm
olminus1)
Figure 5 Experimental and calculated deviations in Gibbs freeenergy of activation for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values solidlines represent DMSO-Acetophenone mixture and dotted linesrepresent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
119877 Universal gas constant(8314 Jmolminus1Kminus1)
119879 Absolute temperature (K)11988912 Grunberg-nissan parameter
Φ119894 Volume fraction (dimensionless)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] M M Palaiologou G K Arianas and N G Tsierkezos ldquoTher-modynamic investigation of dimethyl sulfoxide binarymixturesat 29315 and 31315 Krdquo Journal of Solution Chemistry vol 35 no11 pp 1551ndash1565 2006
[2] K Zhang J Yang X Yu J Zhang and X Wei ldquoDensities andviscosities for binary mixtures of poly(ethylene glycol) 400 +dimethyl sulfoxide and poly(ethylene glycol) 600 + water atdifferent temperaturesrdquo Journal of Chemical and EngineeringData vol 56 no 7 pp 3083ndash3088 2011
[3] A Ali A K Nain D Chand and R Ahmad ldquoViscosities andrefractive indices of binary mixtures of dimethylsulphoxidewith some aromatic hydrocarbons at different temperaturesan experimental and theoretical studyrdquo Journal of the ChineseChemical Society vol 53 no 3 pp 531ndash543 2006
[4] J A Riddick W B Bunger and T K Sakano Organic SolventsPhysical Properties and Methods of Purifications vol 2 ofTechniques of Chemistry John Wiley amp Sons New York NYUSA 1986
[5] V K Rattan S Kapoor and K Tochigi ldquoViscosities anddensities of binary mixtures of toluene with acetic acid andpropionic acid at (29315 30315 31315 and 32315) Krdquo Journalof Chemical and Engineering Data vol 47 no 5 pp 1182ndash11842002
[6] R A McAllister ldquoThe viscosity of liquid mixturesrdquo AIChEJournal vol 6 pp 427ndash431 1960
[7] L Grunberg and A H Nissan ldquoThe energies of vaporisationviscosity and cohesion and the structure of liquidsrdquo Transac-tions of the Faraday Society vol 45 pp 125ndash137 1949
[8] G C Benson and O Kiyohara ldquoEvaluation of excess isentropiccompressibilities and isochoric heat capacitiesrdquo The Journal ofChemical Thermodynamics vol 11 no 11 pp 1061ndash1064 1979
[9] GDouheretM I Davis I J Fjellanger andHHoslashiland ldquoUltra-sonic speeds and volumetric properties of binary mixtures ofwater with poly(ethylene glycol)s at 29815 Krdquo Journal of theChemical Society - Faraday Transactions vol 93 no 10 pp1943ndash1949 1997
[10] A J Treszczanowicz O Kiyohara and G C Benson ldquoExcessvolumes for n-alkanols +n-alkanes IV Binary mixtures ofdecan-1-ol +n-pentane +n-hexane +n-octane +n-decane and+n-hexadecanerdquoThe Journal of ChemicalThermodynamics vol13 no 3 pp 253ndash260 1981
[11] A H Roux and J E Desnoyers ldquoAssociation models for alco-hol-water mixturesrdquo Journal of Proceedings of the Indian Acad-emy of Sciences Chemical Sciences vol 98 no 5-6 pp 435ndash451
Table 7 Interaction parameters for the McAllister model (5) Herric correlation (6) and Grunberg-Nissan correlation (7) for viscosity atdifferent temperatures (DMSO-119901-xylene)
Figure 2 Experimental and calculated deviations in viscosityfor (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 KQ 31815 K ◼ 32315 K998771 32815 Ke symbolsrepresent the experimental values dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-119901-xylenemixture both optimised by Redlich-Kister parameters
Symbols Used
1198601 1198602 1198603 1198604 Parameters of Redlich-Kister equation
11986012 11986021 Interaction coefficients of McAllister
model12057212 12 Coefficients of Herricrsquos correlation
] Kinematic viscosity (m2sminus1)120588 Density (g cmminus3)
005
00 01 02 03 04 05 06 07 08 09 10
minus015
minus035
minus055
minus075
minus095
minus115
x1
ΔR
Figure 3 Experimental and calculated deviations in molar refrac-tion for (i) DMSO(1) + acetophenone(2) and (ii) DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 998771 32815 K e andsymbols represent the experimental values dotted lines representDMSO-acetophenone mixture and solid lines represent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
120590 Standard deviation120572 Thermal expansion coefficient (Kminus1)120578 Dynamic viscosity (mPasdots)Δ119866119864 Excess Gibbs free energy (Jmolminus1)
Figure 4 Experimental and calculated deviations in isentropiccompressibility for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values dottedlines represent DMSO-Acetophenone mixture and solid lines rep-resent DMSO-119901-xylene mixture both optimised by Redlich-Kisterparameters
0
50
00 01 02 03 04 05 06 07 08 09 10minus50
minus100
minus150
minus200
minus250
minus300
minus350
minus400
x1
ΔGE(Jmiddotm
olminus1)
Figure 5 Experimental and calculated deviations in Gibbs freeenergy of activation for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values solidlines represent DMSO-Acetophenone mixture and dotted linesrepresent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
119877 Universal gas constant(8314 Jmolminus1Kminus1)
119879 Absolute temperature (K)11988912 Grunberg-nissan parameter
Φ119894 Volume fraction (dimensionless)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] M M Palaiologou G K Arianas and N G Tsierkezos ldquoTher-modynamic investigation of dimethyl sulfoxide binarymixturesat 29315 and 31315 Krdquo Journal of Solution Chemistry vol 35 no11 pp 1551ndash1565 2006
[2] K Zhang J Yang X Yu J Zhang and X Wei ldquoDensities andviscosities for binary mixtures of poly(ethylene glycol) 400 +dimethyl sulfoxide and poly(ethylene glycol) 600 + water atdifferent temperaturesrdquo Journal of Chemical and EngineeringData vol 56 no 7 pp 3083ndash3088 2011
[3] A Ali A K Nain D Chand and R Ahmad ldquoViscosities andrefractive indices of binary mixtures of dimethylsulphoxidewith some aromatic hydrocarbons at different temperaturesan experimental and theoretical studyrdquo Journal of the ChineseChemical Society vol 53 no 3 pp 531ndash543 2006
[4] J A Riddick W B Bunger and T K Sakano Organic SolventsPhysical Properties and Methods of Purifications vol 2 ofTechniques of Chemistry John Wiley amp Sons New York NYUSA 1986
[5] V K Rattan S Kapoor and K Tochigi ldquoViscosities anddensities of binary mixtures of toluene with acetic acid andpropionic acid at (29315 30315 31315 and 32315) Krdquo Journalof Chemical and Engineering Data vol 47 no 5 pp 1182ndash11842002
[6] R A McAllister ldquoThe viscosity of liquid mixturesrdquo AIChEJournal vol 6 pp 427ndash431 1960
[7] L Grunberg and A H Nissan ldquoThe energies of vaporisationviscosity and cohesion and the structure of liquidsrdquo Transac-tions of the Faraday Society vol 45 pp 125ndash137 1949
[8] G C Benson and O Kiyohara ldquoEvaluation of excess isentropiccompressibilities and isochoric heat capacitiesrdquo The Journal ofChemical Thermodynamics vol 11 no 11 pp 1061ndash1064 1979
[9] GDouheretM I Davis I J Fjellanger andHHoslashiland ldquoUltra-sonic speeds and volumetric properties of binary mixtures ofwater with poly(ethylene glycol)s at 29815 Krdquo Journal of theChemical Society - Faraday Transactions vol 93 no 10 pp1943ndash1949 1997
[10] A J Treszczanowicz O Kiyohara and G C Benson ldquoExcessvolumes for n-alkanols +n-alkanes IV Binary mixtures ofdecan-1-ol +n-pentane +n-hexane +n-octane +n-decane and+n-hexadecanerdquoThe Journal of ChemicalThermodynamics vol13 no 3 pp 253ndash260 1981
[11] A H Roux and J E Desnoyers ldquoAssociation models for alco-hol-water mixturesrdquo Journal of Proceedings of the Indian Acad-emy of Sciences Chemical Sciences vol 98 no 5-6 pp 435ndash451
Figure 4 Experimental and calculated deviations in isentropiccompressibility for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values dottedlines represent DMSO-Acetophenone mixture and solid lines rep-resent DMSO-119901-xylene mixture both optimised by Redlich-Kisterparameters
0
50
00 01 02 03 04 05 06 07 08 09 10minus50
minus100
minus150
minus200
minus250
minus300
minus350
minus400
x1
ΔGE(Jmiddotm
olminus1)
Figure 5 Experimental and calculated deviations in Gibbs freeenergy of activation for (i) DMSO(1) + acetophenone(2) and (ii)DMSO(1) + p-xylene(2) at 31315 K Q 31815 K ◼ 32315 K 99877132815 K e and symbols represent the experimental values solidlines represent DMSO-Acetophenone mixture and dotted linesrepresent DMSO-119901-xylene mixture both optimised by Redlich-Kister parameters
119877 Universal gas constant(8314 Jmolminus1Kminus1)
119879 Absolute temperature (K)11988912 Grunberg-nissan parameter
Φ119894 Volume fraction (dimensionless)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] M M Palaiologou G K Arianas and N G Tsierkezos ldquoTher-modynamic investigation of dimethyl sulfoxide binarymixturesat 29315 and 31315 Krdquo Journal of Solution Chemistry vol 35 no11 pp 1551ndash1565 2006
[2] K Zhang J Yang X Yu J Zhang and X Wei ldquoDensities andviscosities for binary mixtures of poly(ethylene glycol) 400 +dimethyl sulfoxide and poly(ethylene glycol) 600 + water atdifferent temperaturesrdquo Journal of Chemical and EngineeringData vol 56 no 7 pp 3083ndash3088 2011
[3] A Ali A K Nain D Chand and R Ahmad ldquoViscosities andrefractive indices of binary mixtures of dimethylsulphoxidewith some aromatic hydrocarbons at different temperaturesan experimental and theoretical studyrdquo Journal of the ChineseChemical Society vol 53 no 3 pp 531ndash543 2006
[4] J A Riddick W B Bunger and T K Sakano Organic SolventsPhysical Properties and Methods of Purifications vol 2 ofTechniques of Chemistry John Wiley amp Sons New York NYUSA 1986
[5] V K Rattan S Kapoor and K Tochigi ldquoViscosities anddensities of binary mixtures of toluene with acetic acid andpropionic acid at (29315 30315 31315 and 32315) Krdquo Journalof Chemical and Engineering Data vol 47 no 5 pp 1182ndash11842002
[6] R A McAllister ldquoThe viscosity of liquid mixturesrdquo AIChEJournal vol 6 pp 427ndash431 1960
[7] L Grunberg and A H Nissan ldquoThe energies of vaporisationviscosity and cohesion and the structure of liquidsrdquo Transac-tions of the Faraday Society vol 45 pp 125ndash137 1949
[8] G C Benson and O Kiyohara ldquoEvaluation of excess isentropiccompressibilities and isochoric heat capacitiesrdquo The Journal ofChemical Thermodynamics vol 11 no 11 pp 1061ndash1064 1979
[9] GDouheretM I Davis I J Fjellanger andHHoslashiland ldquoUltra-sonic speeds and volumetric properties of binary mixtures ofwater with poly(ethylene glycol)s at 29815 Krdquo Journal of theChemical Society - Faraday Transactions vol 93 no 10 pp1943ndash1949 1997
[10] A J Treszczanowicz O Kiyohara and G C Benson ldquoExcessvolumes for n-alkanols +n-alkanes IV Binary mixtures ofdecan-1-ol +n-pentane +n-hexane +n-octane +n-decane and+n-hexadecanerdquoThe Journal of ChemicalThermodynamics vol13 no 3 pp 253ndash260 1981
[11] A H Roux and J E Desnoyers ldquoAssociation models for alco-hol-water mixturesrdquo Journal of Proceedings of the Indian Acad-emy of Sciences Chemical Sciences vol 98 no 5-6 pp 435ndash451