Zuoxiang Zeng*,Zhihong Yang,Weilan Xue*,Xiaonan Li

Chemical Engineering Thermodynamics

Vapor Pressure,Vaporization Enthalpy,Standard Enthalpy of Formation and Standard Entropy of n-Butyl Carbamate

Zuoxiang Zeng*,Zhihong Yang,Weilan Xue*,Xiaonan Li

Institute of Chemical Engineering,East China University of Science and Technology,Shanghai 200237,China

A R T I C L EI N F O

Article history:

n-Butyl carbamate

Vapor pressure

Standard enthalpy of formation

Standard entropy

The vapor pressures of n-butyl carbamate were measured in the temperature range from 372.37 K to 479.27 K and f i tted with Antoine equation.The compressibility factor of the vapor was calculated with the Virial equation and the second virial coeff i cient was determined by the Vetere model.Then the standard enthalpy of vaporization for n-butyl carbamate was estimated.The heat capacity was measured for the solid state (299.39-324.2 K)and liquid state(336.65-453.21 K)by means of adiabatic calorimeter.The standard enthalpy of formation ΔfH?[crystal(cr),298.15 K]and standard entropy S?(crystal,298.15 K)of the substance were calculated on the basis of the gas-phase standard enthalpy of formation ΔfH?(g,298.15 K) and gas-phase standard entropy S?(g,298.15 K),which were estimated by the Benson method.The results are acceptable,validated by a thermochemical cycle.

?2014TheChemicalIndustryandEngineeringSocietyofChina,andChemicalIndustryPress.Allrightsreserved.

1.Introduction

n-Butyl carbamate(BC,CASRN 592-35-8)is a white prismatic or schistic crystal and is also called butyl ester.It can be used as a curing agent for cement[1]and the intermediate for producing 1,6-hexamethylenediurethane[2],whichcancrackletoobtainisocyanate [3].

Vapor pressure data are critical for process design for evaporation, distillation and two-phase reactions.The vaporization enthalpy of a pure substance ΔvapH0(T),which can be obtained from the vapor pressure data,is also an important thermodynamic parameter.Especially, the standard enthalpy of vaporization ΔvapH?(crystal,298.15 K)is used for conversion of the enthalpy of formation between liquid state and ideal gas state[4].The heat capacity and the enthalpy of formation of BC,ΔfH0(T),are important quantities for the design of technological process with BC as a reactant or a product.

However,scarce experimental information on the thermodynamic propertiesofBCsuchasvaporpressureandstandardenthalpyofformationhasbeenreported.Inordertoprovidebetterdesignforchemicalreactors and separation equipment,the thermodynamic properties such as heat capacity,vapor pressure,and ΔvapH?(crystal,298.15 K)of BC are reported in this article.

Many techniques for determining vapor pressure are available[5,6]. In this study,a modif i ed Othmer still[7]is applied to measure the vapor pressure of BC.The vapor pressure and temperature are correlated by the Antoine equation.ΔvapH?(crystal,298.15 K)of BC is estimated based on the Othmer method.The values of standard enthalpy of formation ΔfH?(crystal,298.15 K)and standard entropy S?(crystal,298.15 K)of BC are calculated according to ΔfH?(g,298.15 K) and S?(g,298.15 K)obtained by the Benson method.A thermodynamic cycle is designed to validate the reliability of the values of ΔfH?(crystal,298.15 K)and S?(crystal,298.15 K).

2.Experimental

2.1.Materials

BC prepared in the laboratory[8]was recrystallized prior to use and its mass fraction purity determined by GC was higher than 99.0%.n-Butanol and urea purchased from Shanghai Chemistry Reagent Co. (China)are of analytical reagent grade.

2.2.Apparatus and procedures

2.2.1.Vapor pressure

The vapor pressure of BC was measured by a modif i ed Othmer still. The apparatus and procedures are similar to those in literature[9,10]. Brief l y,the apparatus included a vacuum pump,a temperature measurement system,and a pressure control and measurement system.Nitrogen was introduced into the system at the beginning to remove the air.The temperature was measured using thermocouples with an uncertaintyof±0.05 K,andthestillpressurewascontrolled at thedesired value and measured by a U-tube mercury manometer with an uncertainty of±0.03 kPa.The U-tube mercury manometer and thermometers were calibrated before experiments.All the measurements were conducted in a sequence of increasing pressure and the pressure wascontrolled at the desired value[11].The sample(about 100 ml)was heated with an electric heater and stirred well with a magnetic stirrer to provide isothermal condition and to prevent superheating.When the readings on the U-tube mercury manometer maintained constant for 10 min,the system reached thermal equilibrium,and the temperature and pressure were recorded.The experiment was repeated 3 to 4 times at each pressure and the average value was taken.

A vapor pressure measurementof water wasmade from 299.27 K to 374.43 K to check the accuracy of the apparatus.The results show that the apparatus is reliable.

2.2.2.Heat capacity

Aprecisionautomaticadiabaticcalorimeterwasusedtomeasurethe heat capacity of BC.The principles of operation and structure of the instrument were detailed in literature[12].Brief l y,the adiabatic system consists of a sample cell,inner and outer adiabatic shields,a high vacuum can,a high precision temperature controller,and two sets of sixjunctionchromel-copelthermocouple piles.Theheatcapacityof α-aluminumoxidewasmeasuredtovalidatethereliabilityofthesystem.The deviation between the experimental data and those of NIST[13]was within±0.4%over the temperature range from 298 K to 440 K.

The experiment was carried out by heating the sample and measuring the temperature alternately.The temperature increments were 1-5 K.Considering the effect of impurities in the substances,the estimated uncertainty of the Cpmeasurement was less than±0.8%.

2.2.3.Equilibrium constant measurement for BC synthesis

The reaction equation for BC synthesis is

Table 1Experimental vapor pressure data of n-butyl carbamate and calculated deviations

The apparatus and procedures are similar to that described in literature[14].Urea and n-butanol were charged into an autoclave reactor (300 cm3).The mixture was heated to the desired temperature after the system was evacuated.During the process,the sample was constantly stirred at the temperature for enough time for the reaction to reachequilibrium.Athermocouplewasappliedtomeasurethetemperature with uncertainty of±0.05 K.The system was airtight and generated ammonia was in the reactor.The pressure of the system was measuredusingapressuretransducer(PM10)connectedtoa1/2digital multimeter(YXS-4),with±0.002 kPa.When the temperature and pressure of the system remained unchanged for 20 min,the system achieved equilibrium,and samples were withdrawn from the liquid and vapor phases.The liquid phase was analyzed by HPLC(Waters 1515,USA)and GC(2000II,Shanghai,China).The vapor phase was analyzed using an online GC equipped with a thermal conductivity detector and an AT.AMINE capillary column.

3.Results and Discussion

3.1.Vapor pressure of BC

The experimental vapor pressure data for BC from 372.37 K to 479.2 K are listed in Table 1.

The experimental data are f i tted by the Antoine equation

where p isthesaturated vaporpressure attemperature T,and A,B and C are adjustable parameters.The parameters obtained by f i tting the experimental vapor pressures are presented in Table 2.

Fig.1 illustrates the deviation distribution of the correlations,where the deviation is def i ned as

where pexpis the experimental value and pcalis the calculated value from Eq.(1).

3.2.The enthalpy of vaporization at boiling point ΔvapH0(Tb)

The Clausius-Clapeyron equation is a general equation relating vaporpressureandenthalpyofvaporizationofapuresubstanceinequilibrium with the gas phase.It can be deduced as[15]

where ΔvapH0(T)is theenthalpy of vaporization at temperature T,ΔZ= ZG?ZLis the difference between the compressibility factors of vapor and liquid,and R is the gas constant.

Table 2The Antoine constants of n-butyl carbamate and ethyl butyrate

Fig.1.Deviation distribution of calculated values of the Antoine equation from the experimental vapor pressure for BC.

Table 3The thermodynamic properties of n-butyl carbamate and ethyl butyrate

Combining Eqs.(6)and(7),we obtain

The valueof ZLis sosmall compared with ZGthat itcan beneglected. By substituting Eq.(1)into Eq.(3),we obtain

where B1is the second virial coeff i cient,determined by the Vetere model[16].

Tcand Pcare needed to estimate the value of Z.In this article,the critical properties of BC are estimated by the Lydersen method[17]. Based on the data,Tcand Pcare estimated to be 681.4 K and 3.56MPa. As a result,ZGof BC at the normal boiling point is calculated to be 0.931.

According to Eq.(4)and the values of Antoine constants in Table 2, theenthalpyofvaporizationattheboilingpointΔvapH0(Tb)forBCiscalculated to be 54.98 kJ·mol?1,where Tbis 477.15 K[18].

3.3.Standard enthalpy of vaporization ΔvapH?(298.15 K)

As the Antoine constants are obtained by regressing the experimental data in the temperature range from 372.37 K to 479.27 K,Eq.(4) cannot be used to calculate the standard enthalpy of vaporization of BC.Here,the Othmer method[19]is applied to estimate the value of ΔvapH?(298.15 K).

Eq.(3)can be rewritten as

Eq.(6)refers to any substance with the assumption that the molar volume of liquid(or,in general,the volume of condensed phase)can be ignored compared to the molar volume of vapor.The same equation can be written for any other substance(the second substance)at the same temperature

where p′and ΔvapH0′(T)representthevapor pressure and thevaporization enthalpy of the second substance at temperature T,respectively, and ZG′is the gas compressibility factor of the second substance.

The second substance is usually referred to a standard substance.Its basic thermodynamic properties and the Antoine constants are available and it should be as similar to the substance under investigation as possible.In this paper,ethyl butyrate is chosen as the standard material and its Antoine constants[20]are also listed in Table 2 and other relevant parameters from NIST[21,22]are listed in Table 3.

Similarly,ZG′of ethyl butyrate at different temperatures(including 298.15 K)can be calculated and the results are listed in Table 3.The valuesofZG′decreaseastemperatureincreases.BCisasimilarsubstance, soitsZGshouldbe1at298.15K.Theresultsshowthatthecompressibility factor(ZG′,ZG)varies slightly in the temperature range,and can be consider＇ed as a constant equal to the mean value of com＇pressibility factor(ZG,ZG),which are listed in Table 3.Substituting ZGandZGinto Eq.(8),we obtain

Fig.2shows the plot of lgp of BC against lgp′of ethyl butyrate.The linear relationship between lgp and lgp′is obtained by the leastsquare regression method(R2=0.9985).In the temperature range from 372.37 K to 394 K,

Fig.2.Theplotoflgpofn-butylcarbamateagainstlgp′ofethylbutyrateinthetemperature range of 372.37 K to 394 K.

Table 4Experimental heat capacities of n-butyl carbamate at temperatures from 299.39 K to 453.21 K

Fig.3.The DSC curve of n-butyl carbamate.

Taking derivative on both sides of Eq.(10),we obtain

3.6.Verif i cation of ΔvapH?(298.15 K)

The sublimation enthalpy of BC at 298.15 K ΔsubH?(298.15K)can be expressed as

Comparing Eqs.(9)and(11),we f i nd that ΔvapH0(T)/ΔvapH0′(T) is independent of temperature even though ΔvapH0(T)and ΔvapH0′(T) are functions of temperature,so the value of ΔvapH?(298.15 K)/ΔvapH?′(298.15K)is1.768.AccordingtothevalueofΔvapH?′(298.15 K)inTable3, ΔvapH?(298.15K)ofBCiscalculatedas76.61 kJ·mol?1.

3.4.Heat capacity of BC

Table 4 presents measured heat capacities for BC.The temperature dependence of the heat capacity in solid(299.39-324.2 K)and liquid phase(336.65-453.21 K)is well described by following polynomial equations

3.5.Enthalpy of fusion for BC

From the adiabatic calorimeter measurement,we also obtain the value of enthalpy of fusion ΔfusH0(Tfus)for BC.Tfuswas measured to be 326.2±0.1 K by differential scanning calorimeter(DSC)[14].On the basis of Eq.(14),the value of ΔfusH0(Tfus)is determined to be 17.45 kJ·mol?1.

whereTiisatemperatureslightlylowerthantheinitialmeltingtemperature and Tfis a temperature slightly higher than the f i nal melting temperature,Q is the total energy added into the sample cell from Tito Tf, Cp(0)is the heat capacity of the sample cell from Tito Tf,Cp(cr)and Cp(l)are the heat capacities of the sample in the solid phase from Tito Tfusand in the liquid phase from Tfusto Tf,m is the mass of the sample, and n is the molar quantity of the sample.

TheDSCexperiments were performed on a DSC 200F3 from Netzsch InstrumentInc.tomeasureΔfusH0(Tfus)ofBC.Fig.3showstheDSCcurve andthevalues of ΔfusH0(Tfus)and Tfusarelisted inTable 5.Thedeviation of ΔfusH0(Tfus)measured by the two methods is 1.41%.

AccordingtoWatson'srelation[23],thevalueofΔvapH0(Tfus)ofBC is calculated to be 74.23 kJ·mol?1.

Theheat capacity of ideal gas Cp(g)is estimated by theJoback method[24]and Cp(g)of BC can be expressed as

The heat capacity difference[Cp(g)?Cp(cr)]can be obtained according to Eqs.(12)and(16).The value of integral term in Eq.(15)is calculated to be?0.98 kJ·mol?1.

The value of ΔsubH?(298.15 K)is calculated to be 92.91 kJ·mol?1, close to the literature value 94 kJ·mol?1[25].The deviation is?1.16%.

3.7.Estimation of ΔfH?(cr,298.15 K)and S?(cr,298.15 K)

At the standard state(298.15 K,0.1 MPa),BC is crystalline and the standard enthalpy of formation ΔfH?(cr,298.15 K)and standard entropy S?(cr,298.15 K)can be expressed as

Table 5The experimental values of ΔfusH(Tfus)and Tbfor n-butyl carbamate

where ΔfH?(g,298.15 K)is the gas-phase standard enthalpy of formation,S?(g,298.15 K)is the gas-phase standard entropy,and ΔsubH?(298.15 K)is the enthalpy of sublimation.

In this paper,the Benson method is applied to estimate ΔfH?(g,298.15 K)and S?(g,298.15 K)of BC.

Fig.4.The thermochemical cycle designed for verif i cation of ΔfH?(cr,298.15 K)and S?(cr,298.15 K)for BC.

where ΔfHj?(g,298.15 K)and Sj?(g,298.15 K)are the group contribution values,njis the number of contributions,σ is the symmetry number,and η is the number of possible optical isomers.Here,the symmetry number is 3 and there is no optical isomer.

According to the Benson method,the values of ΔfH?(g,298.15 K) and S?(g,298.15 K)are?515.08 kJ·mol?1and 444.36 J·mol?1·K?1, respectively.From Eqs.(17)and(18),ΔfHj?(cr,298.15 K) and Hj?(cr,298.15 K)of BC are estimated to be?607.99 kJ·mol?1and 132.74 J·mol?1·K?1.

3.8.Verif i cation of ΔfH?(cr,298.15 K)and Hj?(cr,298.15 K)

ThesynthesisreactionofBCfromn-butanolandureaisreversible.As the reaction occurs in the liquid phase,the experimental equilibrium constant(of the reaction can be related to activities

where aiis the activity of species in the solution at equilibrium state.

As n-butanol is present in high concentration and its molar fraction approaches 1,aC4H9OHcan be expressed as

where xC4H9OHis the molar fraction of n-butanol in the equilibrium system.

The standard state concentration of c0=1 mol·dm?3is introduced here as the concentrationsof BC and urea(cNH2CONH2)in themixture are 0.6 to 1.3 mol·dm?3.aBCand aNH2CONH2can be expressed as

where γBCandγNH2CONH2are theactivity coeff i cients of BCand urea,and they are approximately unity.

The vapor phase can be considered as a binary mixture(NH3+ C4H9OH)in which the partial pressures of BC and urea at the temperature are suff i ciently low and can be neglected.For ammonia,the standard state pressure p0=0.1 MPa,then aNH3can be determined by

where P is the pressure of the system,pNH3is the partial pressure of ammonia in the vapor phase,andyNH3is the molar fraction of ammonia in the vapor phase.

The equilibrium constant is

The equation ΔrG0=ΔrH0?TΔrS0permits us to evaluate the Gibbs energy change ΔrG0cal( T)of the reaction at temperature T according to thevaluesofΔfH?(cr,298.15 K)andS?(cr,298.15 K)ofBC.Wecandetermine the equilibriumconstant of thereaction ata given temperature based on experiments.Then the Gibbs energy change ΔrG0exp(T)of the reaction is obtained.Comparing ΔrG0exp(T)with ΔrG0cal(T),the availability of ΔfH?(cr,298.15 K)and S?(cr,298.15 K)can be validated.A thermochemical cycle including this reaction is shown in Fig.4.

Thermodynamic data of n-butanol,urea,and ammonia are given in Table 6.

Table 6Thermodynamic data of n-butanol,urea,and ammonia

Table 7Compositions in the equilibrium mixture and K0expof the reaction

where ΔrH20(T)and ΔrS20(T)are the standard enthalpy and entropy change at temperature T,expressed as

where ΔHiand ΔSi(i=1 to 4)are the enthalpy and entropy changes of the processes shown in Fig.4.The items on the right hand side of Eqs.(28)-(29)are calculated by Eqs.(A1)-(A10)in Appendix A.

Finally,we obtain

The equilibrium constants were measured in the temperature range from 413.15 K to 453.15 K,three times for each temperature.The compositions in the equilibrium mixture are presented in Table 7, with K0expand K0calcalculated by Eqs.(26)and(31).The average deviation(AAD)is 0.96%,which is de fi ned as

The result shows that the calculated values of ΔfH?(cr,298.15 K) and S?(cr,298.15 K)of BC are reliable.

4.Conclusions

With the vapor pressure of BC measured in the temperature range from 372.37 K to 479.27 K,and the compressibility factor of vapor calculatedby the Virial equation and the second virial coeff i cient determined by the Vetere model,the standard enthalpy of vaporization ΔvapH?(298.15 K)for n-butyl carbamate is estimated to be 76.61 kJ·mol?1.With the heat capacity of BC measured by adiabatic calorimeter,ΔfH?(cr,298.15 K)and S?(cr,298.15 K)are calculated to be?607.99 kJ·mol?1and 132.74 J·mol?1·K?1,respectively, based on ΔfH?(g,298.15 K)and S?(g,298.15 K)estimated by the Benson method.The results are acceptable,validated by a thermochemical cycle and the measurement of equilibrium constant.

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25 March 2013

*Corresponding authors.

E-mail addresses:zengzx@ecust.edu.cn(Z.Zeng),wlxue@ecust.edu.cn(W.Xue).

http://dx.doi.org/10.1016/j.cjche.2014.08.003

1004-9541/?2014 The Chemical Industry and Engineering Society of China,and Chemical Industry Press.All rights reserved.

Received in revised form 25 May 2013

Accepted 8 July 2013

Available online 20 August 2014