Densities,ApparentMolarVolume,Expansivities,Hepler’s Constant ...downloads.hindawi.com/journals/ijce/2018/8689534.pdf · 2019-07-30 · V ϕ V 0 +S v m √ +B v ·m, (2) where V0

Research ArticleDensities Apparent Molar Volume Expansivities HeplerrsquosConstant and Isobaric Thermal Expansion Coefficients of theBinary Mixtures of Piperazine with Water Methanol andAcetone at T= 29315 to 32815K

Qazi Mohammed Omar 1 Jean-Noel Jaubert 2 and Javeed A Awan 1

1Institute of Chemical Engineering and Technology Faculty of Engineering and Technology University of the PunjabLahore Pakistan2Universite de Lorraine Ecole Nationale Superieure des Industries Chimiques Laboratoire Reactions et Genie des Procedes (UMRCNRS 7274) 1 rue Grandville 54000 Nancy France

Correspondence should be addressed to Jean-Noel Jaubert jean-noeljaubertuniv-lorrainefr and JaveedA Awan javeedawanyahoocom

Received 11 May 2018 Revised 26 July 2018 Accepted 2 September 2018 Published 14 November 2018

Academic Editor Gianluca Di Profio

Copyright copy 2018 Qazi Mohammed Omar et al 2is 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 properly cited

2e properties of 3 binary mixtures containing piperazine were investigated in this work In a first step the densities for the twobinary mixtures (piperazine +methanol) and (piperazine + acetone) were measured in the temperature range of 29315 to 32815Kand 29315 to 32315K respectively at atmospheric pressure by using a Rudolph research analytical density meter (DDM 2911)2e concentration of piperazine in the (piperazine +methanol) mixture was varied from 06978 to 14007molkg and theconcentration of piperazine in the (piperazine + acetone) mixture was varied from 03478 to 18834molkg On the other hand thedensity data for the (piperazine +water) mixture were taken from the literature in the temperature range of 29815 to 32815K Ina second step for the 3 investigated systems the apparent molar volume (Vϕ) and the limiting apparent molar volume (V0

ϕ) atinfinite dilution were calculated using the RedlichndashMayer equation2e limiting apparent molar volumes (V0

ϕ) were used to studythe influence of the solute-solvent and solute-solute interactions2e temperature dependency of the apparent molar volumes wasused to estimate the apparent molar expansibility Heplerrsquos constant (z2V0

ϕzT2)P and isobaric thermal expansion coefficients αP

1 Introduction

Information about the physical properties of solutions in thevast range of solute concentrations at different temperaturesis greatly important for physicochemical processes (sepa-ration process crystallization vaporization desalinationwaste aqua treatment environment protection oil retrievaletc) and the natural environment [1 2]

2e apparent molar volumes are particularly relevant todetermine the molecular interactions (solute to solute soluteto solvent and solvent to solvent) happening in solutions[3] Also the apparent molar volumes of solutions at infinitedilution are useful to obtain information regarding solute tosolvent and solvent to solvent interactions However theapparent molal volumes depend on strength of solution that

can be used for the determination of solute to solute in-teractions [4ndash6]

2e thermophysical properties of piperazine +water isimportant for the design of gas processing technology [7]like in the treatment of natural gas having significantamount of H2S and in processing of refinery waste gases aswell as synthesis gas for manufacturing of NH3 where so-lution of piperazine +water is used as a solvent for the re-moval of acidic gases (carbon dioxide and hydrogen sulfide)2e highly effective removal of CO2 from industrial gasescan also be performed by mixing piperazine with an alcoholsuch as the 2-amino-2-methyl-1-propanol [7 8] whichsuggests that the alcoholic solutions of piperazine are alsoimportant in many separation processes As another ex-ample the separation of o- and p-chlorobenzoic acids from

HindawiInternational Journal of Chemical EngineeringVolume 2018 Article ID 8689534 10 pageshttpsdoiorg10115520188689534

their eutectic blend usually uses a mixture of (piperazine+methanol) [9] as the solvent In chemical processes pi-perazine is present with crude products and has to beseparated In such a case acetone is classically used due to itsstronger molecular interaction with piperazine as comparedto the higher molecular weight ketone [10]

In conclusion the thermophysical properties of the 3 bi-nary systems (piperazine+water) (piperazine+ acetone) and(piperazine+methanol) are involved in many separationprocesses and thus need to be known Consequently it wasdecided to measure the densities of the (piperazine+ acetone)and (piperazine+methanol) systems in the temperature rangeof 29315 to 3281K and 29315 to 32315K respectively sincethey are not available in the open literature 2e concentrationof piperazine was varied from 06978 to 14007molkg andfrom 03478 to 18834molkg for methanol and acetone re-spectively2e density data for (piperazine+water) were takenfrom literature in the temperature range of 29815 to 32815K[11] For the 3 investigated binary systems the density datawere used for the calculation of the apparent molar volumelimiting apparent molar volume apparent molar expansivitiesHeplerrsquos constant and isobaric thermal expansion coefficient

2 Experimental Work

21Materials 2e chemicals used in this work are piperazine(purityge 99) methanol (ge994) and acetone (ge998)2ey were provided by Sigma-Aldrich (Germany) and wereused without any further purification or treatment2e purityof these chemicals used along with their source and CASnumber are tabulated in Table 12e deionized water has beenprepared in lab through alfa-pore machine (WAP-4)

22 Measurement of the Density An analytical digital vi-brating glass U-tube densitometer (DDM-2911 Rudolph)with an accuracy of 005 kgm3 was used to measure thedensity of the 2 mixtures piperazine +methanol andpiperazine + acetone A schematic diagram of the useddensitometer is illustrated in Figure 1 2e binary mixtureswere prepared by weight using a Sartorius analytical weightbalance with an uncertainty of plusmn000029 g (the corre-sponding uncertainty in molality was plusmn00004molkg) 2edensities of the pure solvents and their blends with piper-azine were measured in a temperature range varying from29815 to 33315K 2e calibration of the apparatus wasconducted by comparing the density of air and water at29315K and the barometric pressure Air was providedthrough a suction tube filled with silica balls to ensurea provision of dry air and double-distilled water was injectedthrough a syringe into the density meter Silica balls wereregularly heated to remove the moisture content absorbedfrom the atmospheric air Once calibrated the U-tubedensitometer was washed with distilled water and dried withacetone and air 2e density data reported in this study arean average of at least three runs To remove the air bubblesfrom the samples all the solutions were sonicated by usinga universal ultrasonic cleaner for 30min Later the sampleswere stored in vials and placed into a desiccator for 10minutes for proper mixing and settling For each

measurement the tube was washed with water and driedwith acetone During the measurements the air pump wasalways turned off to avoid irregularities due to vibrations

Table 2 shows the densities of the pure solvents(methanol and acetone) measured in this study in thetemperature range of 2931ndash32815K along with values re-ported in the literature An average deviation of approxi-mately 003 is observed between both sets of data whichsuggests that our data are consistent with previously mea-sured densities and that our equipment is reliable

3 Results and Discussion

2e densities of all three binary mixtures (piperazine +water)(piperazine +methanol) and (piperazine + acetone) asa function of the molality of piperazine and temperature arepresented in Table 3 and plotted in Figures 2ndash4 2e ex-periments cover the commercially significant concentrationrange of piperazine with water methanol and acetone that isconcentrations that are important for industrial applicationslike the design of gas processing technology liquid-liquidextraction and leaching More specifically the mixtures ofpiperazine +methanol were prepared in a concentrationrange of 2187wt to 30978wt (06978molkg to14007molkg) Similarly mixtures of piperazine + acetonewere prepared in concentration range from 198wt to 986wt (03478molkg to 18834molkg) It is observed that thedensity of the mixture increases with an increase in theconcentration of piperazine However the density decreaseswith an increase in the temperature

2e apparent molar volumes [26] (Vϕ) (in m3mol) ofpiperazine were calculated from the densities of the solutionsby using the equation given below

Vϕ M

ρ+

ρ0 minus ρm middot ρ middot ρ0

(1)

where m is the molality of piperazine (molkg) ρ and ρ0 aredensities (in kgm3) of the solution and pure solvent re-spectively andM is the molar mass of piperazine (in kgmol)2e apparent molar volume (Vϕ) of all three binary mixtures(piperazine +water) (piperazine +methanol) and (piperazine+ acetone) calculated from Equation (1) as a function ofmolality of piperazine and temperature is tabulated in Table 4and plotted in Figures 5ndash7 (denoted by markers) Figures 5ndash7show thatVϕ values rise with rise in temperature for each binarymixture highlighting that the overall order of the structure isimproved or increased in solution with rising temperature [27]2e influence of the molality depends on the studied systemthat is the apparent molar volumes may rise decrease orprogress through a maximum Our data were correlated withthe RedlichndashMayer equation [28]

Table 1 List of chemicals used in this work

Chemicals Purity Source CAS numberPiperazine ge99 Merck 110-85-0Methanol ge994 Merck 67-56-1Acetone ge998 Merck 67-64-1

2 International Journal of Chemical Engineering

Vϕ V0ϕ + Sv

m

radic+ Bv middot m (2)

where V0ϕ is the limiting apparent molar volume of the

piperazine mixtures and Sv and Bv are two regression pa-rameters Figures 6 and 7 highlight that our data are ac-curately correlated with such a simple model 2ecorresponding values of V0

ϕ Sv and Bv are tabulated inTable 5 From this table notably the V0

ϕ values rise with rise intemperature for each binary mixture As highlighted by [29]this behavior characterizes the presence of strong solute tosolvent interactions that are strengthened with the rise intemperature It is worth noting that this behavior was alsoobserved formany systemsWe can cite the (methanol+methylacetate) system reviewed by [30] the (methanol+ ethyl acetate)the (ethanol+methyl acetate) and (ethanol + ethyl acetate)systems studied by [29] the (methanol+ isopropyl alcohol) the(methyl salicylate+DMSO) and (hydroxamic acid+DMSO)examined by [31] 2e V0

ϕ values of the mixtures rise in the

following order (piperazine+methanol)lt (piperazine+water)lt (piperazine+ acetone) which could be duemdashas explained by[29]mdashto an enhancement in the strengths of the solute tosolvent interactions 2is enhancement results in an increase ofcontraction in the volume

2e values of SV and BV are also tabulated in Table 5 2e SVvalues are negative for (piperazine+acetone) and positive for the(piperazine+water) and (piperazine+methanol) systems at eachtemperature 2e SV value decreases with rise in temperature foreach binary system2e strength of the solute to solute interactionsof each system increases in the following order (piperazine+methanol)gt (piperazine+water)gt (piperazine+acetone) 2esolute to solute interaction decreases with an increase in temper-ature for each binary system 2e BV values are negative for the(piperazine+methanol) and (piperazine+water) mixtures andpositive for the (piperazine+acetone)mixture at each temperature2e BV values rise with rise in temperature for each binary system2e negative BV values show rise in solute to solute interactions for

Table 2 Comparison of the densities of the pure solvents measured in this study with those reported previously at various temperatures andat atmospheric pressure with standard uncertainties u (T)plusmn001K u (ρ)plusmn01 kgm3 u (m)plusmn00004molkg and u (P)plusmn0002 atm

Density (ρ0) kgm3

Methanol AcetoneTK 2is work Lit value (Reference) TK 2is work Lit value (Reference)29315 7916 7919 (Papanastasiou and Ziogas [12]) 29315 7899 79002 (Kinart et al [13])

79165 (Gonfa et al [14]) 790355 (Janz and Tomkins [15])29815 7869 786884 (Anwar and Yasmeen [16]) 29815 7842 78445 (Kinart et al [13])

78668 (Tu et al [17]) 784638 (Janz and Tomkins [15])30315 7822 782158 (Anwar and Yasmeen [16]) 30315 7785 7787 (Fan et al [18])

7819 (Tu et al [19]) 77857 (Enders et al [20])30815 7772 7772 (Tu et al [17]) 30815 7730 7730 (Hafez and Hartland [21])

777414 (Anwar and Yasmeen [16]) 773065 (Janz and Tomkins [15])31315 7724 7723 (Tu et al [19]) 31315 7673 76703 (Fan et al [18])

77264 (Anwar and Yasmeen [16]) 76721 (Estrada-Baltazar et al [22])31815 7675 7676 (Tu et al [17]) 31815 7616 761288 (Janz and Tomkins [15])

767844 (Anwar and Yasmeen [16]) 7613 (Hafez and Hartland [21])32315 7627 7627 (Bhuiyan and Uddin [23]) 32315 7557 75514 (Fan et al [18])

763028 (Anwar and Yasmeen [16]) 75531 (Estrada-Baltazar et al [22])32815 7577 7592 (Cai et al [24]) 75554 (Wu et al [25])

Vials

Dry air pipe

Oahus pioneer analyticalbalance

Waste container

Syringe

Burette with silica balls

Drain pipeMouse

Glass U-tubeU-tube window

Display screen

M

Analytical density meter (DDM 2911)

Specific gravity

Air

Water

10474 kgm3

Figure 1 Schematic diagram of the experimental setup (analytical density meter (DDM 2911))

International Journal of Chemical Engineering 3

mixtures that is (piperazine+water) and (piperazine+methanol)2e positive BV values indicate strong solute to solute interactionsfor the (piperazine+acetone) system

2e temperature dependence of the limiting apparentmolar volume (V0

ϕ) can be expressed in terms of the fol-lowing equation [26]

Table 3 Densities (kgm3) of the binary mixtures (piperazine +water) (piperazine +methanol) and (piperazine + acetone) as a function ofthe molality and temperature at atmospheric pressure A global uncertainty calculation was performed on each point and the correspondingvalues are given in parentheses

Temperature (K) 29315 29815 30315 30815 31315 31815 32315 32815Molality (molkg)of piperazine Binary system densities (kgm3) with global uncertainty (kgm3) in parentheses

System (piperazine +water) (Muhammad et al [11])09838 mdash 9983 9969 9952 9934 9914 9892 986830226 mdash 9994 9979 9963 9944 9924 9901 987864138 mdash 10013 9998 9980 9961 9940 9917 9893

System (piperazine +methanol) (this work)06978 8058 (002) 8012 (001) 7964 (002) 7913 (0007) 7865 (002) 7817 (001) 7766 (001) 7713 (001)14000 8174 (004) 8129 (002) 8082 (003) 8035 (001) 7986 (002) 7936 (001) 7884 (002) 7832 (001)22148 8296 (003) 8252 (002) 8205 (003) 8157 (002) 8109 (002) 8059 (002) 8008 (002) 7956 (002)30544 8407 (004) 8363 (002) 8317 (004) 8270 (004) 8221 (003) 8172 (003) 8121 (003) 8069 (002)37151 8490 (004) 8446 (002) 8400 (004) 8353 (004) 8305 (004) 8256 (003) 8205 (004) 8154 (002)51007 8626 (005) 8582 (003) 8537 (004) 8490 (005) 8445 (004) 8396 (004) 8346 (004) 8295 (003)59003 8703 (005) 8660 (003) 8615 (005) 8569 (005) 8521 (005) 8472 (004) 8422 (005) 8371 (004)74725 8814 (006) 8771 (003) 8726 (005) 8680 (006) 8632 (006) 8584 (005) 8534 (006) 8483 (004)92198 8939 (006) 8896 (004) 8852 (005) 8806 (006) 8758 (006) 8710 (005) 8661 (007) 8611 (005)14007 9126 (006) 9084 (005) 9039 (006) 8993 (006) 8946 (007) 8896 (005) 8842 (007) 8793 (006)

System (piperazine + acetone) (this work)03478 7924 (001) 7865 (0005) 7808 (001) 7749 (0006) 7688 (0002) 7627 (0002) 7563 (0002) mdash08416 7967 (002) 7910 (002) 7852 (002) 7793 (002) 7733 (0008) 7672 (001) 7609 (001) mdash10951 7993 (003) 7935 (002) 7877 (003) 7816 (002) 7755 (001) 7691 (002) 7627 (002) mdash13359 8023 (003) 7970 (003) 7907 (003) 7846 (003) 7784 (002) 7721 (002) 7656 (002) mdash18834 8075 (003) 8020 (004) 7959 (003) 7899 (003) 7841 (002) 7782 (003) 7721 (003) mdash

982

984

986

988

990

992

994

996

998

1000

1002

0984 3023 6414Molality (molkg)

29815303153081531315

31815323153281533315

Den

sity

(kg

m3 )

Figure 2 Density of the (piperazine +water) system as a function of piperazine molality at various temperatures


760

780

800

820

840

860

880

900

920

06978 14000 22148 30544 37151 51007 59003 74725 92198 140079Molality (molkg)

29315298153031530815

31315318153231532815

Den

sity

(kg

m3 )

Figure 3 Density of the (piperazine +methanol) system as a function of piperazine molality at various temperatures

750

760

770

780

790

800

810

03478 08416 10951 13359 18834

Den

sity

(gm

3 )

Molality (molkg)

29315298153031530815

313153181532315

Figure 4 Density of the (piperazine + acetone) system as a function of piperazine molality at various temperatures


Table 4 Apparent molar volume (m3mol) of the binary mixtures (piperazine +water) (piperazine +methanol) and (piperazine + acetone)as a function of the molality and temperature at atmospheric pressure with the standard uncertainty u (Vϕ)plusmn035times10minus6m3mol

Temperature (K) 29315 29815 30315 30815 31315 31815 32315 32815Molality (molkg) of piperazine Binary system apparent molar volumes 106 timesVϕ (m3mol)

System (piperazine +water)09838 mdash 8502 8516 8532 8549 8567 8588 861330226 mdash 8543 8557 8572 8589 8608 8628 865064138 mdash 8537 8552 8568 8587 8606 8627 8650

System (piperazine +methanol)06978 7502 7524 7550 7584 7607 7638 7732 783914000 7696 7705 7718 7715 7748 7797 7869 793222148 7769 7784 7802 7813 7844 7883 7939 798830544 7829 7846 7865 7878 7911 7948 7998 804137151 7848 7866 7886 7903 7931 7967 8011 804951007 7949 7970 7993 8013 8030 8066 8107 814559003 7961 7982 8004 8024 8054 8090 8129 816874725 8052 8075 8100 8123 8155 8189 8229 826892198 8069 8092 8118 8143 8177 8211 8247 828414007 8243 8271 8301 8331 8366 8407 8455 8493

System (piperazine + acetone)03478 9737 9838 9939 10211 10476 10733 11096 mdash08416 9520 9588 9672 9809 9943 10086 10250 mdash10951 9414 9491 9575 9722 9865 10024 10194 mdash13359 9275 9269 9415 9549 9678 9816 9971 mdash18834 9202 9232 9337 9436 9506 9577 9669 mdash

85000

85200

85400

85600

85800

86000

86200

86400

86600

02000 12000 22000 32000 42000 52000 62000 72000Molality (molkg)

29815303153081531315

318153231532815

29815303153081531315

318153231532815

Appa

rent

mol

ar v

olum

e

Figure 5 Apparent molar volume (Vϕ) of the binary mixture (piperazine +water) as a function of piperazine molality at differenttemperatures


746000

766000

786000

806000

826000

846000

02000 22000 42000 62000 82000 102000 122000 142000Molality (molkg)

29315298153031530815

31315318153231532815

29315298153031530815

31315318153231532815

Appa

rent

mol

ar v

olum

e

Figure 6 Apparent molar volume (Vϕ) of the binary mixture (piperazine +methanol) as a function of piperazine molality at differenttemperatures 2e correlations performed with the RedlichndashMayer equation are plotted as soliddashed lines

90

95

100

105

110

115

03478 08416 10951 13359 18834Molality (molkg)

29315298153031530815

313153181532315

29315298153031530815

313153181532315

Appa

rent

mol

ar v

olum

e (m

olm

3 )

Figure 7 Apparent molar volume (Vϕ) of the binary mixture (piperazine + acetone) as a function of piperazine molality at differenttemperatures 2e correlations performed with the RedlichndashMayer equation are plotted as soliddashed lines


V0ϕ A + BT + CT

2 (3)

where A B and C are empirical parameters and T is thetemperature 2e limiting apparent molar expansibility (E0

ϕ)can be obtained by differentiating Eq (3) with respect to thetemperature

E0ϕ

zV0ϕ

zT1113888 1113889 B + 2CT (4)

2e (E0ϕ) values for each binary system are tabulated in

Table 6 which gives important information related to thesolute to solvent interactions [32] Table 6 depicts that ateach temperature the (E0

ϕ) values are positive for all threebinary systems and decrease with rise in temperature

According to Heplerrsquos theory [33] the so-called Heplerrsquosconstant (z2V0

ϕzT2) can be used to classify a solute intotwo categories whether solute can act as a builder ofstructure or as a breaker of structure If the (z2V0

ϕzT2) valueis positive then the solute is favorable in development ormaking of structure Conversely if the (z2V0

ϕzT2) value isnegative then the solute will act as a structure breaker 2evalues of (z2V0

ϕzT2) are minus033 minus289 and minus1225 for thebinary mixtures that is (piperazine +water) (piperazine+methanol) and (piperazine + acetone) respectively 2uspiperazine acts as a structure breaker in solution 2e prooffor the effect of Heplerrsquos constant onmicroscopic structure isdiscussed in the literature [34]

2e isobaric thermal expansion coefficient αp of thesolute was calculated using the apparent molar volume andapparent molar expansibility at infinite dilution data

αp 1

V0ϕ

zV0ϕ

zT1113888 1113889

E0ϕ

V0ϕ (5)

2e isobaric thermal expansion coefficient αP is alsotabulated in Table 6 A higher value of αP was obtained foracetone and lower value of αP was obtained for water

4 Conclusion

In this work new density data for 2 binary mixtures(piperazine +methanol) and (piperazine + acetone) weremeasured from 29315K to 32815K It was found that thedensity of both the mixtures increases with increase intemperature but decreases with increase in concentrationSimilarly Vϕ values rise with increase in concentration ofpiperazine in methanol but decreases in case of acetoneAlso the apparent molar volume (Vϕ) limiting apparentmolar volume (V0

ϕ) apparent molar expansibility (E0ϕ)

Heplerrsquos constant and isobaric thermal expansion co-efficient (αP) were calculated and reported in this work 2elimiting apparent molar volume V0

ϕ increases with tem-perature which highlights the strong interactions of thesolute with the solvent 2e positive apparent molar ex-pansibility (E0

ϕ) decreases with temperature which indicates

Table 5 Values of the limiting apparent molar volume (V0ϕ) along with the Sv and Bv parameters to be used in the RedlichndashMayer equation

for each of the 3 binary systems as a function of temperature

Temperature (K) 29315 29815 30315 30815 31315 31815 32315 32815System (piperazine+water)

106 times V0ϕ (m3middotmolminus1) mdash 8378 8394 8411 8430 8449 8471 8507

106 times Sv (m3middotkg12middotmolminus32) mdash 165 161 160 157 156 153 139106 timesBv (m3middotkgmiddotmolminus2) mdash minus040 minus039 minus039 minus038 minus037 minus036 minus033

System (piperazine+methanol)106 times V0

ϕ (m3middotmolminus1) 7257 7275 7299 7327 7357 7401 7548 7705106 times Sv (m3middotkg12middotmolminus32) 372 369 363 347 345 338 258 167106 timesBv (m3middotkgmiddotmolminus2) minus031 minus029 minus027 minus022 minus021 minus020 minus005 011

System (piperazine+ acetone)106 times V0

ϕ (m3middotmolminus1) 10268 10472 10589 11182 11701 12120 12950 mdash106 times Sv (m3middotkg12middotmolminus32) minus960 minus1154 minus1217 minus1919 minus2451 minus2762 minus3774 mdash106 timesBv (m3middotkgmiddotmolminus2) 126 168 214 466 621 667 1019 mdash

Table 6 2e limiting apparent molar expansibility (E0ϕ) and isobaric thermal expansion coefficient αP

Temperature (K) 29315 29815 30315 30815 31315 31815 32315 32815Binary mixtures

106 times E0ϕ (m3middotmolminus1middotKminus1)

Piperazine +water mdash 264 324 384 444 504 564 624Piperazine +methanol minus004 003 010 016 023 029 035 041Piperazine + acetone 2538 4678 6818 8958 11098 13238 15378 mdash

103 times αP (Kminus1)Piperazine +water mdash 031 039 046 053 060 067 073Piperazine +methanol minus039 028 095 162 228 293 352 408Piperazine + acetone 247 447 644 801 948 1092 1188 mdash


that the interactions increase with a rise in the temperatureof the solution 2e negative values of the Helperrsquos con-stant suggest that piperazine acts as a structure breaker inthe solvent 2e RedlichndashMayer equation was used tocorrelate the apparent molar volume with the standarddeviation u(Vϕ) plusmn035 times10minus6 molm3

Nomenclature

Vϕ Apparent molar volumeV0

ϕ Apparent molar volume at infinite dilutionρ Density of the solutionρ0 Density of the pure solventSV Empirical parameter of the apparent molar volumeBV Empirical parameter of the apparent molar volumeαP Isobaric thermal expansion coefficientE0ϕ Limiting apparent molar volume expansibility

M Molar mass of the solutem Molality of the solute

Data Availability

2e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

2e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

2is research was performed as part of the employment ofthe authors Consequently University of the Punjab andUniversity of Lorraine are warmly thanked 2e work de-scribed in this paper has been presented at the Chisa 2018International Conference that took place in Prague (CzechRepublic) in August 2018

References

[1] S Gupta and J D Olson ldquoIndustrial needs in physicalpropertiesrdquo Industrial amp Engineering Chemistry Researchvol 42 no 25 pp 6359ndash6374 2003

[2] K S Pitzer ldquo2ermodynamics of natural and industrialwatersrdquo Journal of Chemical ltermodynamics vol 25 no 1pp 7ndash26 1993

[3] F J Millero ldquoMolal volumes of electrolytesrdquo Chemical Re-views vol 71 no 2 pp 147ndash176 1971

[4] Y Marcus Ion Solvation Wiley New York NY USA 1985[5] F J Millero Water and Aqueous Solutions Structure lter-

modynamics and Transport Properties Chapter 13 R AHorne Ed Wiley Interscience New York NY USA 1972

[6] R Perkins T Andersen J O M Bockris and B E ConwayModern Aspects of Electrochemistry Kluwer Academic Pub-lishers Norwell MA USA 1969

[7] A Samanta and S S Bandyopadhyay ldquoDensity and viscosity ofaqueous solutions of piperazine and (2-amino-2-methyl-1-propanol + piperazine) from 298 to 333 Krdquo Journal ofChemical amp Engineering Data vol 51 no 2 pp 467ndash470 2006

[8] A L Kohl and R Nielsen Gas Purif Gulf ProfessionalPublishing Houston TX USA 1997

[9] A Lashanizadegan N S Tavare M Manteghian andD M Newsham ldquoTernary phase equilibrium diagrams foro-and p-chlorobenzoic acids and their complex with piper-azine in methanolrdquo Journal of Chemical amp Engineering Datavol 45 no 6 pp 1189ndash1194 2000

[10] G R Bond ldquoDetermination of piperazine as piperazinediacetaterdquo Analytical Chemistry vol 32 no 10 pp 1332ndash1334 1960

[11] A Muhammad M I A Mutalib T Murugesan andA Shafeeq ldquo2ermophysical properties of aqueous piperazineand aqueous (N-methyldiethanolamine + piperazine) solu-tions at temperatures (29815 to 33815) Krdquo Journal ofChemical amp Engineering Data vol 54 no 8 pp 2317ndash23212009

[12] G E Papanastasiou and I I Ziogas ldquoPhysical behavior ofsome reaction media 3 Density viscosity dielectric constantand refractive index changes of methanol + dioxane mixturesat several temperaturesrdquo Journal of Chemical amp EngineeringData vol 37 no 2 pp 167ndash172 1992

[13] C M Kinart W J Kinart and A C wiklinska ldquoDensity andviscosity at various temperatures for 2-methoxyethanol+acetone mixturesrdquo Journal of Chemical amp Engineering Datavol 47 no 1 pp 76ndash78 2002

[14] G Gonfa M A Bustam N Muhammad and S UllahldquoDensity and excess molar volume of binary mixture ofthiocyanate-based ionic liquids and methanol at temperatures29315ndash32315 Krdquo Journal of Molecular Liquids vol 211pp 734ndash741 2015

[15] G J Janz and R P T Tomkins Nonaqueous ElectrolytesHandbook Vol 1 Academic Press New York NY USA1972

[16] N Anwar and S Yasmeen ldquoVolumetric compressibility andviscosity studies of binary mixtures of [EMIM][NTf2] withethylacetatemethanol at (29815ndash32315) Krdquo Journal ofMolecular Liquids vol 224 pp 189ndash200 2016

[17] C H Tu H C Ku W F Wang and Y T Chou ldquoVolumetricand viscometric properties of methanol ethanol propan-2-oland 2-methylpropan-2-ol with a synthetic C6+ mixture from29815 K to 31815 Krdquo Journal of Chemical amp EngineeringData vol 46 no 2 pp 317ndash321 2001

[18] X H Fan Y P Chen and C S Su ldquoDensities and viscositiesof binary liquid mixtures of 1-ethyl-3-methylimidazoliumtetrafluoroborate with acetone methyl ethyl ketone andN-methyl-2-pyrrolidonerdquo Journal of the Taiwan Institute ofChemical Engineers vol 61 pp 117ndash123 2016

[19] C H Tu S L Lee and I H Peng ldquoExcess volumes andviscosities of binary mixtures of aliphatic alcohols (C1minusC4)with nitromethanerdquo Journal of Chemical amp Engineering Datavol 46 no 1 pp 151ndash155 2001

[20] S Enders H Kahl and J Winkelmann ldquoSurface tension of theternary system water + acetone + toluenerdquo Journal of Chemicalamp Engineering Data vol 52 no 3 pp 1072ndash1079 2007

[21] M Hafez and S Hartland ldquoDensities and viscosities of binarysystems toluene-acetone and 4-methyl-2-pentanone-aceticacid at 20 25 35 and 45 degree Crdquo Journal of Chemicalamp Engineering Data vol 21 no 2 pp 179ndash182 1976

[22] A Estrada-Baltazar A De Leon-Rodrıguez K R HallM Ramos-Estrada and G A Iglesias-Silva ldquoExperimentaldensities and excess volumes for binary mixtures containingpropionic acid acetone and water from 28315 K to 32315 Kat atmospheric pressurerdquo Journal of Chemical amp EngineeringData vol 48 no 6 pp 1425ndash1431 2003


[23] M M H Bhuiyan and M H Uddin ldquoExcess molar volumesand excess viscosities for mixtures of N N-dimethylforma-mide with methanol ethanol and 2-propanol at differenttemperaturesrdquo Journal of Molecular Liquids vol 138 no 1ndash3pp 139ndash146 2008

[24] D Cai J Yang H Da L Li H Wang and T Qiu ldquoDensitiesand viscosities of binary mixtures N N-dimethyl-N-(3-sulfopropyl) cyclohexylammonium tosylate with water andmethanol at T (30315 to 32815) Krdquo Journal of MolecularLiquids vol 229 pp 389ndash395 2017

[25] J Y Wu Y P Chen and C S Su ldquo2e densities and vis-cosities of a binary liquid mixture of 1-n-butyl-3-methylimidazolium tetrafluoroborate ([Bmim][BF4]) withacetone methyl ethyl ketone and N N-dimethylformamideat 30315 to 33315 Krdquo Journal of the Taiwan Institute ofChemical Engineers vol 45 no 5 pp 2205ndash2211 2014

[26] M T Zafarani-Moattar and H Shekaari ldquoApparent molarvolume and isentropic compressibility of ionic liquid 1-butyl-3-methylimidazolium bromide in water methanol and eth-anol at T (29815 to 31815) Krdquo Journal of Chemicalltermodynamics vol 37 no 10 pp 1029ndash1035 2005

[27] P Khanuja V R Chourey and A A Ansari ldquoApparent molarvolume and viscometric study of glucose in aqueous solutionrdquoJournal of Chemical and Pharmaceutical Research vol 4pp 3047ndash3050 2012

[28] O Redlich and D M Meyer ldquo2e molal volumes of elec-trolytesrdquo Chemical Reviews vol 64 no 3 pp 221ndash227 1964

[29] I Bahadur N Deenadayalu and D Ramjugernath ldquoEffects oftemperature and concentration on interactions in methanol+ethyl acetate and ethanol+ methyl acetate or ethyl acetatesystems Insights from apparent molar volume and apparentmolar isentropic compressibility studyrdquoltermochimica Actavol 577 pp 87ndash94 2014

[30] I Bahadur and N Deenadayalu ldquoApparent molar volume andisentropic compressibility for the binary systems methyl-trioctylammoniumbis(trifluoromethylsulfonyl)imide + methylacetate or methanol and (methanol + methyl acetate) at T

29815 30315 30815 and 31315 K and atmospheric pressurerdquoJournal of Solution Chemistry vol 40 pp 1528ndash1543 2011

[31] R S Sah P Pradhan and M N Roy ldquoSolutendashsolvent andsolventndashsolvent interactions of menthol in isopropyl alcoholand its binary mixtures with methyl salicylate by volumetricviscometric interferometric and refractive index techniquesrdquoltermochimica Acta vol 499 pp 149ndash154 2010

[32] H Shekaari S S Mousavi and Y Mansoori ldquo2ermophysicalproperties of ionic liquid 1-pentyl-3-methylimidazoliumchloride in water at different temperaturesrdquo InternationalJournal of ltermophysics vol 30 no 2 pp 499ndash514 2009

[33] L G Hepler ldquo2ermal expansion and structure in water andaqueous solutionsrdquo Canadian Journal of Chemistry vol 47no 24 pp 4613ndash4617 1969

[34] P K 2akur S Patre and R Pande ldquo2ermophysical andexcess properties of hydroxamic acids in DMSOrdquo Journal ofChemical ltermodynamics vol 58 pp 226ndash236 2013


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their eutectic blend usually uses a mixture of (piperazine+methanol) [9] as the solvent In chemical processes pi-perazine is present with crude products and has to beseparated In such a case acetone is classically used due to itsstronger molecular interaction with piperazine as comparedto the higher molecular weight ketone [10]

In conclusion the thermophysical properties of the 3 bi-nary systems (piperazine+water) (piperazine+ acetone) and(piperazine+methanol) are involved in many separationprocesses and thus need to be known Consequently it wasdecided to measure the densities of the (piperazine+ acetone)and (piperazine+methanol) systems in the temperature rangeof 29315 to 3281K and 29315 to 32315K respectively sincethey are not available in the open literature 2e concentrationof piperazine was varied from 06978 to 14007molkg andfrom 03478 to 18834molkg for methanol and acetone re-spectively2e density data for (piperazine+water) were takenfrom literature in the temperature range of 29815 to 32815K[11] For the 3 investigated binary systems the density datawere used for the calculation of the apparent molar volumelimiting apparent molar volume apparent molar expansivitiesHeplerrsquos constant and isobaric thermal expansion coefficient

2 Experimental Work

21Materials 2e chemicals used in this work are piperazine(purityge 99) methanol (ge994) and acetone (ge998)2ey were provided by Sigma-Aldrich (Germany) and wereused without any further purification or treatment2e purityof these chemicals used along with their source and CASnumber are tabulated in Table 12e deionized water has beenprepared in lab through alfa-pore machine (WAP-4)

22 Measurement of the Density An analytical digital vi-brating glass U-tube densitometer (DDM-2911 Rudolph)with an accuracy of 005 kgm3 was used to measure thedensity of the 2 mixtures piperazine +methanol andpiperazine + acetone A schematic diagram of the useddensitometer is illustrated in Figure 1 2e binary mixtureswere prepared by weight using a Sartorius analytical weightbalance with an uncertainty of plusmn000029 g (the corre-sponding uncertainty in molality was plusmn00004molkg) 2edensities of the pure solvents and their blends with piper-azine were measured in a temperature range varying from29815 to 33315K 2e calibration of the apparatus wasconducted by comparing the density of air and water at29315K and the barometric pressure Air was providedthrough a suction tube filled with silica balls to ensurea provision of dry air and double-distilled water was injectedthrough a syringe into the density meter Silica balls wereregularly heated to remove the moisture content absorbedfrom the atmospheric air Once calibrated the U-tubedensitometer was washed with distilled water and dried withacetone and air 2e density data reported in this study arean average of at least three runs To remove the air bubblesfrom the samples all the solutions were sonicated by usinga universal ultrasonic cleaner for 30min Later the sampleswere stored in vials and placed into a desiccator for 10minutes for proper mixing and settling For each

measurement the tube was washed with water and driedwith acetone During the measurements the air pump wasalways turned off to avoid irregularities due to vibrations

Table 2 shows the densities of the pure solvents(methanol and acetone) measured in this study in thetemperature range of 2931ndash32815K along with values re-ported in the literature An average deviation of approxi-mately 003 is observed between both sets of data whichsuggests that our data are consistent with previously mea-sured densities and that our equipment is reliable

3 Results and Discussion

2e densities of all three binary mixtures (piperazine +water)(piperazine +methanol) and (piperazine + acetone) asa function of the molality of piperazine and temperature arepresented in Table 3 and plotted in Figures 2ndash4 2e ex-periments cover the commercially significant concentrationrange of piperazine with water methanol and acetone that isconcentrations that are important for industrial applicationslike the design of gas processing technology liquid-liquidextraction and leaching More specifically the mixtures ofpiperazine +methanol were prepared in a concentrationrange of 2187wt to 30978wt (06978molkg to14007molkg) Similarly mixtures of piperazine + acetonewere prepared in concentration range from 198wt to 986wt (03478molkg to 18834molkg) It is observed that thedensity of the mixture increases with an increase in theconcentration of piperazine However the density decreaseswith an increase in the temperature

2e apparent molar volumes [26] (Vϕ) (in m3mol) ofpiperazine were calculated from the densities of the solutionsby using the equation given below

Vϕ M

ρ+

ρ0 minus ρm middot ρ middot ρ0

(1)

where m is the molality of piperazine (molkg) ρ and ρ0 aredensities (in kgm3) of the solution and pure solvent re-spectively andM is the molar mass of piperazine (in kgmol)2e apparent molar volume (Vϕ) of all three binary mixtures(piperazine +water) (piperazine +methanol) and (piperazine+ acetone) calculated from Equation (1) as a function ofmolality of piperazine and temperature is tabulated in Table 4and plotted in Figures 5ndash7 (denoted by markers) Figures 5ndash7show thatVϕ values rise with rise in temperature for each binarymixture highlighting that the overall order of the structure isimproved or increased in solution with rising temperature [27]2e influence of the molality depends on the studied systemthat is the apparent molar volumes may rise decrease orprogress through a maximum Our data were correlated withthe RedlichndashMayer equation [28]

Table 1 List of chemicals used in this work

Chemicals Purity Source CAS numberPiperazine ge99 Merck 110-85-0Methanol ge994 Merck 67-56-1Acetone ge998 Merck 67-64-1


Vϕ V0ϕ + Sv

m










Density (ρ0) kgm3









Vials

Dry air pipe


Waste container

Syringe


Drain pipeMouse


Display screen

M


Specific gravity

Air

Water

10474 kgm3











982

984

986

988

990

992

994

996

998

1000

1002


29815303153081531315

31815323153281533315

Den

sity

(kg

m3 )



760

780

800

820

840

860

880

900

920

06978 14000 22148 30544 37151 51007 59003 74725 92198 140079Molality (molkg)

29315298153031530815

31315318153231532815

Den

sity

(kg

m3 )


750

760

770

780

790

800

810

03478 08416 10951 13359 18834

Den

sity

(gm

3 )

Molality (molkg)

29315298153031530815

313153181532315








85000

85200

85400

85600

85800

86000

86200

86400

86600

02000 12000 22000 32000 42000 52000 62000 72000Molality (molkg)

29815303153081531315

318153231532815

29815303153081531315

318153231532815

Appa

rent

mol

ar v

olum

e



746000

766000

786000

806000

826000

846000

02000 22000 42000 62000 82000 102000 122000 142000Molality (molkg)

29315298153031530815

31315318153231532815

29315298153031530815

31315318153231532815

Appa

rent

mol

ar v

olum

e


90

95

100

105

110

115

03478 08416 10951 13359 18834Molality (molkg)

29315298153031530815

313153181532315

29315298153031530815

313153181532315

Appa

rent

mol

ar v

olum

e (m

olm

3 )



V0ϕ A + BT + CT

2 (3)



E0ϕ

zV0ϕ

zT1113888 1113889 B + 2CT (4)










αp 1

V0ϕ

zV0ϕ

zT1113888 1113889

E0ϕ

V0ϕ (5)


4 Conclusion






















Nomenclature




Data Availability




Acknowledgments


References








































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Vϕ V0ϕ + Sv

m










Density (ρ0) kgm3









Vials

Dry air pipe


Waste container

Syringe


Drain pipeMouse


Display screen

M


Specific gravity

Air

Water

10474 kgm3











982

984

986

988

990

992

994

996

998

1000

1002


29815303153081531315

31815323153281533315

Den

sity

(kg

m3 )



760

780

800

820

840

860

880

900

920

06978 14000 22148 30544 37151 51007 59003 74725 92198 140079Molality (molkg)

29315298153031530815

31315318153231532815

Den

sity

(kg

m3 )


750

760

770

780

790

800

810

03478 08416 10951 13359 18834

Den

sity

(gm

3 )

Molality (molkg)

29315298153031530815

313153181532315








85000

85200

85400

85600

85800

86000

86200

86400

86600

02000 12000 22000 32000 42000 52000 62000 72000Molality (molkg)

29815303153081531315

318153231532815

29815303153081531315

318153231532815

Appa

rent

mol

ar v

olum

e



746000

766000

786000

806000

826000

846000

02000 22000 42000 62000 82000 102000 122000 142000Molality (molkg)

29315298153031530815

31315318153231532815

29315298153031530815

31315318153231532815

Appa

rent

mol

ar v

olum

e


90

95

100

105

110

115

03478 08416 10951 13359 18834Molality (molkg)

29315298153031530815

313153181532315

29315298153031530815

313153181532315

Appa

rent

mol

ar v

olum

e (m

olm

3 )



V0ϕ A + BT + CT

2 (3)



E0ϕ

zV0ϕ

zT1113888 1113889 B + 2CT (4)










αp 1

V0ϕ

zV0ϕ

zT1113888 1113889

E0ϕ

V0ϕ (5)


4 Conclusion






















Nomenclature




Data Availability




Acknowledgments


References








































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










982

984

986

988

990

992

994

996

998

1000

1002


29815303153081531315

31815323153281533315

Den

sity

(kg

m3 )



760

780

800

820

840

860

880

900

920

06978 14000 22148 30544 37151 51007 59003 74725 92198 140079Molality (molkg)

29315298153031530815

31315318153231532815

Den

sity

(kg

m3 )


750

760

770

780

790

800

810

03478 08416 10951 13359 18834

Den

sity

(gm

3 )

Molality (molkg)

29315298153031530815

313153181532315








85000

85200

85400

85600

85800

86000

86200

86400

86600

02000 12000 22000 32000 42000 52000 62000 72000Molality (molkg)

29815303153081531315

318153231532815

29815303153081531315

318153231532815

Appa

rent

mol

ar v

olum

e



746000

766000

786000

806000

826000

846000

02000 22000 42000 62000 82000 102000 122000 142000Molality (molkg)

29315298153031530815

31315318153231532815

29315298153031530815

31315318153231532815

Appa

rent

mol

ar v

olum

e


90

95

100

105

110

115

03478 08416 10951 13359 18834Molality (molkg)

29315298153031530815

313153181532315

29315298153031530815

313153181532315

Appa

rent

mol

ar v

olum

e (m

olm

3 )



V0ϕ A + BT + CT

2 (3)



E0ϕ

zV0ϕ

zT1113888 1113889 B + 2CT (4)










αp 1

V0ϕ

zV0ϕ

zT1113888 1113889

E0ϕ

V0ϕ (5)


4 Conclusion






















Nomenclature




Data Availability




Acknowledgments


References








































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


760

780

800

820

840

860

880

900

920

06978 14000 22148 30544 37151 51007 59003 74725 92198 140079Molality (molkg)

29315298153031530815

31315318153231532815

Den

sity

(kg

m3 )


750

760

770

780

790

800

810

03478 08416 10951 13359 18834

Den

sity

(gm

3 )

Molality (molkg)

29315298153031530815

313153181532315








85000

85200

85400

85600

85800

86000

86200

86400

86600

02000 12000 22000 32000 42000 52000 62000 72000Molality (molkg)

29815303153081531315

318153231532815

29815303153081531315

318153231532815

Appa

rent

mol

ar v

olum

e



746000

766000

786000

806000

826000

846000

02000 22000 42000 62000 82000 102000 122000 142000Molality (molkg)

29315298153031530815

31315318153231532815

29315298153031530815

31315318153231532815

Appa

rent

mol

ar v

olum

e


90

95

100

105

110

115

03478 08416 10951 13359 18834Molality (molkg)

29315298153031530815

313153181532315

29315298153031530815

313153181532315

Appa

rent

mol

ar v

olum

e (m

olm

3 )



V0ϕ A + BT + CT

2 (3)



E0ϕ

zV0ϕ

zT1113888 1113889 B + 2CT (4)










αp 1

V0ϕ

zV0ϕ

zT1113888 1113889

E0ϕ

V0ϕ (5)


4 Conclusion






















Nomenclature




Data Availability




Acknowledgments


References








































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







85000

85200

85400

85600

85800

86000

86200

86400

86600

02000 12000 22000 32000 42000 52000 62000 72000Molality (molkg)

29815303153081531315

318153231532815

29815303153081531315

318153231532815

Appa

rent

mol

ar v

olum

e



746000

766000

786000

806000

826000

846000

02000 22000 42000 62000 82000 102000 122000 142000Molality (molkg)

29315298153031530815

31315318153231532815

29315298153031530815

31315318153231532815

Appa

rent

mol

ar v

olum

e


90

95

100

105

110

115

03478 08416 10951 13359 18834Molality (molkg)

29315298153031530815

313153181532315

29315298153031530815

313153181532315

Appa

rent

mol

ar v

olum

e (m

olm

3 )



V0ϕ A + BT + CT

2 (3)



E0ϕ

zV0ϕ

zT1113888 1113889 B + 2CT (4)










αp 1

V0ϕ

zV0ϕ

zT1113888 1113889

E0ϕ

V0ϕ (5)


4 Conclusion






















Nomenclature




Data Availability




Acknowledgments


References








































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


746000

766000

786000

806000

826000

846000

02000 22000 42000 62000 82000 102000 122000 142000Molality (molkg)

29315298153031530815

31315318153231532815

29315298153031530815

31315318153231532815

Appa

rent

mol

ar v

olum

e


90

95

100

105

110

115

03478 08416 10951 13359 18834Molality (molkg)

29315298153031530815

313153181532315

29315298153031530815

313153181532315

Appa

rent

mol

ar v

olum

e (m

olm

3 )



V0ϕ A + BT + CT

2 (3)



E0ϕ

zV0ϕ

zT1113888 1113889 B + 2CT (4)










αp 1

V0ϕ

zV0ϕ

zT1113888 1113889

E0ϕ

V0ϕ (5)


4 Conclusion






















Nomenclature




Data Availability




Acknowledgments


References








































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


V0ϕ A + BT + CT

2 (3)



E0ϕ

zV0ϕ

zT1113888 1113889 B + 2CT (4)










αp 1

V0ϕ

zV0ϕ

zT1113888 1113889

E0ϕ

V0ϕ (5)


4 Conclusion






















Nomenclature




Data Availability




Acknowledgments


References








































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Nomenclature




Data Availability




Acknowledgments


References








































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

Densities,ApparentMolarVolume,Expansivities,Hepler’s Constant ...downloads.hindawi.com/journals/ijce/2018/8689534.pdf · 2019-07-30 · V ϕ V 0 +S v m √ +B v ·m, (2) where V0