Excess Molar Enthalpies and Heat Capacities of - American Chemical

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Excess Molar Enthalpies and Heat Capacities of {2-Methylpiperidine−Water} and {N‑Methylpiperidine−Water} Systems of Low to Moderate Amine Compositions Yohann Coulier,*,†,‡ Karine Ballerat-Busserolles,†,‡ Javier Mesones,§ Alexander Lowe,†,‡ and Jean-Yves Coxam*,†,‡ †

Institut de Chimie de Clermont-Ferrand, Clermont Université, Université Blaise Pascal, BP 10448, F-63000 Clermont-Ferrand, France CNRS, UMR 6296, ICCF, BP 80026, F-63171 Aubière, France § CREVER, Mechanical Engineering Department, Universitat Rovira i Virgili, Avenida Països Catalans 26, 43007 Tarragona, Spain ‡

ABSTRACT: The systems {methylpiperidine−water} show partial miscibility that depends on the nature of the amine isomer. A thermodynamic analysis of these systems requires knowledge of excess properties of methylpiperidine isomers with water. Excess molar enthalpies were measured at pressure 0.5 MPa and temperatures from (303.15 to 338.15) K and from (308.15 to 328.15) K for 2-methylpiperidine and N-methylpiperidine, respectively. Specific heat capacities of pure and aqueous solutions of both methylpiperidine isomers were determined at 0.1 MPa and temperatures from (283.15 to 333.15) K.

1. INTRODUCTION The two isomers of methylpiperidine investigated here, namely, 2-methylpiperidine and N-methylpiperidine, undergo a liquid− liquid phase separation in aqueous solution as a function of temperature. The phase diagrams of {methylpiperidine−water} systems were previously established,1 and the lower critical solution temperatures (LCST) were found to be about (339 and 316) K for 2-methylpiperidine and N-methylpiperidine, respectively. To complete the thermodynamic study of these binary systems, an experimental determination of excess properties was carried out. No value for excess molar enthalpies (HE) and excess molar heat capacities (CEp ) were available in the literature for {2-methylpiperidine−water} and {N-methylpiperidine− water} systems. In this work excess molar enthalpies were obtained from heat of mixing of methylpiperidines with water, using a flowcalorimetric technique. Experiments were performed at constant pressure of 0.5 MPa and at temperatures between (303.15 and 338.15) K for 2-methylpiperidine and between (308.15 and 328.15) K for N-methylpiperidine. CEp were obtained from the experimental heat capacities (Cp) of pure amines and aqueous solutions, which were measured with a micro-differential scanning calorimeter (micro-DSC) at 0.1 MPa and temperatures ranging from (283.15 to 333.15) K. The HE and CEp values were correlated as a function of mole fraction and temperature employing a Redlich−Kister equation. The excess molar enthalpies of methylpiperidine at infinite dilutions were determined using the method proposed by Maham et al.2 © 2015 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Materials. 2-Methylpiperidine and N-methylpiperidine were used without any further purification. Solutions for isobaric heat capacity measurements were prepared by dissolution in distilled and degassed water (resistivity, 18.2 MΩ·cm) with an uncertainty in the molar fraction of less than ± 10−4. Suppliers, purities, and CAS numbers of all chemicals used in this study are given in Table 1. 2.2. Techniques. 2.2.1. Excess Molar Enthalpies. Excess molar enthalpies were determined from the heat of mixing measurements of pure methylpiperidines with water using a BT2.15 calorimeter from SETARAM. The calorimetric technique is similar to the one used for the determination of the heat of mixing of gas with liquid.3 A schematic of the experimental setup is given in Figure 1. Experiments are performed in a dynamic mode at constant temperature and pressure. The pure fluids, supplied by two high-pressure syringe pumps (model 260DM from ISCO), mix in a cell designed in the laboratory. These pumps provide stable volumetric flow rates with a relative uncertainty of 0.3 %. To avoid corrosion of the ISCO pumps, pure methylpiperidine flows from a sample loop, located at the output of the syringe pump, to the mixing cell. The pump is then filled with water instead of pure amine. The sample loop (30 mL) is made of a narrow inox tube (1.6 mm o.d., 1 mm i.d.) in order to limit diffusion of water in Received: September 12, 2014 Accepted: May 15, 2015 Published: May 27, 2015 1563

DOI: 10.1021/je5008444 J. Chem. Eng. Data 2015, 60, 1563−1571

Journal of Chemical & Engineering Data

Article

Table 1. Suppliers, CAS Numbers, Stated Purities (Mass Fraction w), and Water Content (Mass Fraction wW) of Chemicals Used in This Study chemical

source

CAS no.

w/%

2-methylpiperidine (racemate) N-methylpiperidine nitrogen n-octane

Sigma-Aldrich Sigma-Aldrich Air Products Sigma-Aldrich

109-05-7 626-67-5 7727-37-9 111-65-9

98.3 99.9 99.995 >99

wW/% 0.9

0.001

The experimental procedure is similar to the one described by Origlia-Luster et al.6 First a blank experiment is performed by filling both sample and reference cells with nitrogen (N2). Then the sample cell is filled with pure methylpiperidine or a binary {methylpiperidine−water} mixture while the reference cell is filled with N2. An experimental run is made of a 20 min isothermal step at 278.15 K followed by temperature scanning (0.5 K·min−1) up to 333.15 K. Experiments are carried out at constant pressure of 0.1 MPa in both sample and reference cells. Volumetric heat capacities of the solutions (ρsCp,s) are then obtained from the difference between the thermal flux (dQ/dt) of the solution of interest and the thermal flux of the blank experiment as indicated in eq 2. ρs Cp ,s = ρN Cp ,N2 + KT [(dQ /dt )s − (dQ /dt )N2 ] 2

Figure 1. Schematic representation of the flow-calorimetric technique measuring the heat of mixing.

In eq 2, Cp,N2 and ρN2 are respectively the specific heat capacities and the density of nitrogen. KT is the calibration constant of the calorimeter obtained by using eq 2 at each temperature from measurements on water which has wellknown specific heat capacities and densities. 7,8 These calibration measurements were repeated three times to ensure the reproducibility of the constant value. Then the accuracy of KT was tested by measuring the molar heat capacity of pure n-octane. Our experimental molar isobaric heat capacities are reported together with literature values from NIST8 in Table 2. The mean percent relative deviation (% RD) is 0.08 %.

methylpiperidines. The pumps and the loop were temperature controlled at (303.15 ± 0.03) K using a Julabo heating circulator (model F12-EH). The pressure stays constant during the experiment within 0.02 MPa. Along the flow line the pressure is detected by electronic Drück pressure gauges with an accuracy of 0.25% of full scale (20 MPa). The temperature of the calorimeter is set up and controlled within 0.01 K using Setaram G11 electronics. HE is derived from the heat power of mixing detected by a thermopile surrounding the mixing cell (Figure 1). The calorimetric signal Δsignal (mV) is first converted into heat power using a calibration constant K (mV·mW−1) and, then, into molar enthalpy using the molar flow rates of the fluids (ṅa for the amine and ṅw for water) as indicated in eq 1. HE =

Δsignal K (nȧ + n ̇w )

(2)

Table 2. Experimental and Literature8 Molar Isobaric Heat Capacities of n-Octane Ta

(1)

The calorimetric signal Δsignal represents the difference between the signal recorded during mixing and a baseline signal recorded when only one of the fluids is flowing into the circuit. K is obtained by measuring the heat of mixing of ethanol and water and comparing the results to reference values from Ott et al.4,5 Taking into account uncertainties on fluid flow rates, thermopile calibration K, and calorimetric signal noises, the relative uncertainty on excess molar enthalpies is less than 5%. However, experimental heats of mixing at very low and high molar fractions can present bigger uncertainties. Indeed, these measurements require a large difference between the two fluids’ flow rates that can cause problems of mixing. Moreover, for those extreme concentrations, the mixing thermal flux is usually small and the noise over signal ratio increases, leading to a larger relative uncertainty on the measurement. 2.2.2. Isobaric Heat Capacities. Isobaric heat capacities were determined using a differential scanning microcalorimeter from SETARAM (microSC) equipped with liquid Cp cells of 1 mL inner volumes. The detection is based on the Calvet principle.

Cp,exp −1

−1

u(Cp,exp)b

Cp,lit

K

(J·mol ·K )

(J·mol−1·K−1)

(J·mol−1·K−1)

% RDc

283.15 288.15 293.15 298.15 303.16 308.15 313.16 318.15 323.15 328.15 333.15

248.16 250.10 252.24 253.98 256.50 258.05 260.87 262.70 264.78 267.24 269.31

0.05 0.05 0.05 0.04 0.05 0.04 0.05 0.06 0.05 0.05 0.06

248.23 250.36 252.32 254.34 256.40 258.28 260.66 262.86 265.09 267.36 269.67

0.03 0.10 0.03 0.14 0.04 0.09 0.08 0.06 0.12 0.05 0.13

a

Standard uncertainty of temperature is u(T) = 0.01 K. bu(Cp,exp) is the uncertainty of isobaric heat capacity. c% RD = |(Cp,exp − Cp,lit)/ Cp,lit|·100.

Densities of the solutions of methylpiperidine required in eq 2 to calculate the specific heat capacities are taken from Coulier et al.1 The uncertainty of isobaric heat capacity Cp,s is mainly due to the reproducibility of the heat flux signals. Including uncertainty on densities, isobaric heat capacity of nitrogen ,and calibration constant, the relative uncertainty of Cp,s is estimated to be less than 0.3 %. 1564



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Table 3. Excess Molar Enthalpies of {2-Methylpiperidine−Water} as a Function of Amine Molar Fraction (xa) and Temperature at p = 0.50 MPaa u(HE)c

HE xa

u(xa)

0.0295 0.0366 0.0921 0.1320 0.2337 0.3139

b

−1

HE

−1

(J·mol )

(J·mol )

0.0003 0.0004 0.0010 0.0015 0.0036 0.0058

−560 −653 −1176 −1300 −2231 −2478

20 22 35 40 70 75

0.0149 0.0212 0.0294 0.0365 0.0365 0.0481 0.0661 0.0704 0.0755

0.0002 0.0002 0.0004 0.0004 0.0004 0.0006 0.0008 0.0009 0.0009

−316 −410 −519 −603 −668 −735 −902 −915 −990

22 17 24 30 30 39 39 29 44

0.0150 0.0214 0.0248 0.0368 0.0485 0.0666 0.0818 0.1089 0.1439 0.1549 0.1865

0.0002 0.0002 0.0003 0.0005 0.0006 0.0008 0.0010 0.0014 0.0019 0.0021 0.0027

−263 −344 −385 −514 −635 −782 −905 −1119 −1307 −1391 −1581

18 17 20 29 38 37 46 54 52 52 51

0.0101 0.0129 0.0180 0.0236 0.0297 0.0354 0.0438 0.0576 0.0840 0.1089 0.1325 0.1865

0.0001 0.0002 0.0002 0.0003 0.0004 0.0004 0.0005 0.0007 0.0010 0.0014 0.0017 0.0027

−174 −212 −274 −331 −392 −434 −512 −609 −786 −926 −1075 −1424

13 17 23 30 38 23 56 22 22 22 51 60

0.0361 0.0589 0.1234 0.1807 0.2380 0.3601

0.0005 0.0007 0.0016 0.0025 0.0038 0.0077

−310 −560 −999 −1328 −1612 −1975

12 27 40 66 81 97

0.0101 0.0129 0.0180 0.0236 0.0354 0.0466 0.0576 0.0840

0.0001 0.0002 0.0002 0.0003 0.0004 0.0005 0.0007 0.0010

−141 −172 −228 −282 −369 −448 −522 −684

13 17 23 30 23 22 22 22

u(HE) −1

xa

u(xa)

(J·mol )

(J·mol−1)

0.3879 0.4778 0.5489 0.6697 0.7526

0.0088 0.0130 0.0169 0.0249 0.0313

−2621 −2628 −2493 −2044 −1616

75 131 125 143 113

0.1081 0.1539 0.1852 0.2326 0.3266 0.3964 0.4311 0.6388 0.7519

0.0014 0.0021 0.0027 0.0037 0.0064 0.0091 0.0107 0.0227 0.0312

−1209 −1530 −1779 −1990 −2385 −2547 −2500 −2095 −1552

55 53 51 95 44 77 88 147 109

0.2341 0.2764 0.3143 0.3419 0.3984 0.4331 0.4783 0.5340 0.6407 0.7370 0.7535

0.0037 0.0049 0.0060 0.0070 0.0092 0.0107 0.0130 0.0160 0.0228 0.0300 0.0313

−1842 −2019 −2130 −2233 −2284 −2287 −2271 −2192 −1892 −1505 −1441

74 81 85 89 91 114 114 110 132 105 100

0.1865 0.2341 0.3143 0.3591 0.4331 0.4783 0.5284 0.5721 0.6197 0.6814 0.7534

0.0027 0.0037 0.0060 0.0076 0.0107 0.0130 0.0157 0.0183 0.0213 0.0257 0.0313

−1408 −1667 −1975 −2133 −2175 −2148 −2066 −1941 −1775 −1582 −1248

56 66 79 106 109 107 103 97 124 111 87

0.4840 0.5293 0.5999 0.6521 0.7894

0.0133 0.0157 0.0200 0.0236 0.0344

−1990 −1926 −1802 −1631 −1060

98 94 126 114 74

0.1865 0.2341 0.3143 0.3957 0.4331 0.4783 0.5284 0.5284

0.0027 0.0037 0.0060 0.0091 0.0107 0.0130 0.0157 0.0157

−1256 −1502 −1792 −1900 −1937 −1941 −1826 −1822

50 60 71 76 77 78 93 91

303.15 K

308.15 K

318.15 K

328.15 K

333.15 K

338.15 K

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Table 3. continued HE

u(HE)c

xa

u(xa)b

(J·mol−1)

(J·mol−1)

0.1089 0.1325 0.1451

0.0014 0.0017 0.0019

−829 −970 −1035

27 38 56

HE

u(HE)

xa

u(xa)

(J·mol−1)

(J·mol−1)

0.5790 0.6197 0.6814

0.0187 0.0213 0.0257

−1720 −1619 −1374

86 113 96

338.15 K

Standard uncertainties are u(T) = 0.01 K and u(p) = 100 kPa. bu(xa) is the uncertainty on molar fraction calculated from the uncertainty on fluid flow rates and water content in pure 2-methylpiperidine (0.9%). cu(HE) is the uncertainty on the experimental excess molar enthalpies. a

3. RESULTS AND DISCUSSION 3.1. Excess Molar Enthalpies. The excess molar enthalpies of {2-methylpiperidine−water} as a function of amine molar fraction were determined at (303.15, 308.15, 318.15, 328.15, 333.15, and 338.15) K, and at a constant pressure of 0.5 MPa. Experimental data are reported in Table 3 and represented in Figure 2. All of the experiments were performed at

For the two systems, {2-methylpiperidine−water} and {N-methylpiperidine−water}, an exothermic effect was observed during the mixing process which is due to the interaction of the amine group and the -OH in water. The decreasing exothermic effect when the temperature increases is caused by the diminution of the interactions between the two functional groups. The slightly larger exothermic effect observed for {2methylpiperidine−water}, compared to {N-methylpiperidine− water}, could be explained by the difference between the interactions with water. Specifically the hydrogen atom on the nitrogen can increase the hydrogen bonding network with water. These results can be correlated to the difference in LCST reported in a previous work,1 which shows greater solubility of 2-methylpiperidine in water. 3.2. Specific Heat Capacities. Molar heat capacities have been determined for pure methylpiperidines (C*p,a) and for monophasic binary aqueous solutions (Cp) at constant pressure of 0.1 MPa, for temperatures ranging from (283.15 to 333.15) K. Experimental values are reported in Table 5, together with literature isobaric heat capacities of pure water. Isobaric heat capacities of aqueous solutions of 2-methylpiperidine were measured at temperatures below the LCST (339 K) and at amine molar fractions xa from 0.18 to 0.95. Only heat capacities of pure methylpiperidine are available in the literature for comparison, and reported values are scattered. Messerly et al.9 determined saturation heat capacities of pure liquid 2-methylpiperidine at temperatures from (270 to 370) K. The 3 % mean deviation observed with our values is greater than the correction required to convert saturation heat capacities to isobaric heat capacities at 0.1 MPa. It is also greater than experimental uncertainties (0.05 % for Messerly et al.9 and 0.3 % for this work). Molar heat capacity determined by Conti et al.10 at 298.15 K is about 6 % lower than ours. Comparison between our data and reference values is represented in Figure 4. Isobaric heat capacities of aqueous solutions of N-methylpiperidine were studied at amine molar fractions ranging from 0.04 to 0.8. Temperature scans were limited by phase separations at 321 K for xa = 0.1983, at 317 K for xa = 0.0966, and at 316 K for xa = 0.0378. These temperatures are in agreement with the phase diagram previously established1 for this system. In the literature, isobaric heat capacity values are available only for pure N-methylpiperidine at 298.15 K and present a large deviation. Heat capacities from Verevkin11 and Conti et al.10 are respectively 1 % higher and 4 % lower than ours. Comparison between our experimental data and literature values is given in Figure 4. Excess molar heat capacities of methylpiperidines were derived from the experimental data using isobaric heat capacities of pure water (Cp,w) from Hill,7 following eq 3:

Figure 2. Excess molar enthalpies of {2-methylpiperidine−water} at 0.50 MPa: •, 303.15 K; ○, 308.15 K; ■, 318.15 K; □, 328.15 K; ▲, 333.15 K; Δ, 338.15; full line, Redlich−Kister correlation.

temperatures below the lower critical solution temperature (339 K). Figure 2 shows exothermic excess enthalpies with minimum values at amine molar fraction xa ≈ 0.40, increasing progressively from −2630 J·mol−1 at 303.15 K to −1940 J·mol−1 at 338.15 K. Excess molar enthalpies of N-methylpiperidine with water are determined on a shorter range of temperature, namely, (308.15, 318.15, and 328.15) K since the LCST of the system {N-methylpiperidine−water} is lower than the one of the {2-methylpiperidine−water} system. Experimental HE as a function of amine molar fraction (xa) are reported in Table 4 and represented in Figure 3. At 308.15 K the system {N-methylpiperidine−water} is monophasic over the whole range of composition. At (318.15 and 328.15) K, enthalpy curves exhibit a two-phase region for amine molar fractions ranging between approximately 0.03 and 0.14 and between 0.01 and 0.35, respectively. In this domain, excess molar enthalpies increase linearly with xa. This behavior was expected, according to the phase diagram of {N-methylpiperidine−water} determined in a previous work.1 At each temperature, the curves show exothermic enthalpies with a minimum value, in the onephase region, at amine molar fraction xa around 0.35. HE minimum value increases with temperature (−2400 J·K−1 at 308.15 K and −1950 J·K−1 at 318.15 K).

CpE = Cp − (xaC*p ,a + x wC*p ,w ) 1566

(3) DOI: 10.1021/je5008444 J. Chem. Eng. Data 2015, 60, 1563−1571


Article

Table 4. Excess Molar Enthalpies of {N-Methylpiperidine−Water} as a Function of Amine Molar Fraction (xa) and Temperature at p = 0.50 MPa u(HE)b

HE xa

u(xa)

0.0121 0.0145 0.0206 0.0324 0.0423 0.0728 0.0935 0.1054 0.1093 0.1284

a

−1

HE

−1

(J·mol )

(J·mol )

0.0001 0.0001 0.0001 0.0002 0.0003 0.0005 0.0006 0.0007 0.0007 0.0008

−279 −342 −433 −586 −678 −1023 −1255 −1345 −1326 −1512

20 24 30 27 30 38 56 55 46 54

0.0122 0.0146 0.0208 0.0327c 0.0427c 0.0653c 0.0901c 0.1101c 0.1513 0.1984 0.2414

0.0001 0.0001 0.0001 0.0002 0.0003 0.0004 0.0006 0.0007 0.0009 0.0011 0.0013

−223 −262 −331 −471 −559 −751 −957 −1127 −1460 −1744 −1948

10 12 17 26 29 33 37 45 51 54 65

0.0088 0.0110c 0.0146c 0.0175c 0.0218c 0.0242c 0.0358c 0.0561c 0.1062c 0.1750c 0.2290c

0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 0.0002 0.0004 0.0007 0.0010 0.0012

−157 −163 −191 −214 −244 −260 −307 −403 −681 −1043 −1333

12 15 19 23 29 19 28 28 53 70 46

u(HE) −1

xa

u(xa)

(J·mol )

(J·mol−1)

0.1407 0.1739 0.1971 0.2419 0.3293 0.3933 0.4692 0.5956 0.6884

0.0009 0.0010 0.0011 0.0013 0.0016 0.0017 0.0018 0.0017 0.0015

−1629 −1868 −1978 −2214 −2393 −2411 −2298 −1926 −1577

59 73 77 82 87 89 91 135 110

0.2708 0.3082 0.3577 0.4261 0.4712 0.5302 0.5976 0.5976 0.6499 0.6902

0.0014 0.0015 0.0016 0.0017 0.0018 0.0018 0.0017 0.0017 0.0016 0.0015

−2071 −2143 −2158 −2136 −2062 −1914 −1697 −1714 −1545 −1355

88 83 85 85 82 77 118 120 108 95

0.2708c 0.2937c 0.3355c 0.3577c 0.3841c 0.4261 0.4975 0.5531 0.5976 0.6645 0.7481

0.0014 0.0015 0.0016 0.0016 0.0017 0.0017 0.0018 0.0017 0.0017 0.0016 0.0013

−1574 −1704 −1882 −1928 −1947 −1921 −1795 −1673 −1530 −1305 −1028

44 84 79 48 73 68 99 88 107 91 72

308.15 K

318.15 K

328.15 K

a u(xa) is the uncertainty of molar fraction calculated from the uncertainties of fluid flow rates. bu(HE) is the uncertainty of the experimental excess molar enthalpies. cMolar fraction corresponding to the two phases domain. Standard uncertainties are u(T) = 0.01 K and u(p) = 100 kPa.

Excess molar heat capacities (CEp ) as a function of molar fraction of methylpiperidine are reported in Table 6. The (0.1 to 0.3) J·mol−1·K−1 uncertainties on CEp in Table 6 were estimated using basic principles of error propagation in eq 3. The CEp values are positive for the two systems, {2-methylpiperidine−water} and {N-methylpiperidine−water}. This result is consistent with the increase of the excess molar enthalpy with the temperature, observed in the previous section. From its thermodynamic definition, CEp is proportional to the variation of entropy against temperature as compared to that of the ideal solution. Positive CEp implies destruction of liquid structure as temperature is raised,12 which is in agreement with the fact that these two systems have a LCST. CEp were observed to increase with increasing temperature. At the same temperature and amine mole fraction, the CEp value of aqueous N-methylpiperidine solution is slightly larger than that of aqueous 2-methylpiperidine. This result is consistent with more favorable interactions with water in the case of 2-methylpiperidine.

Figure 3. Excess molar enthalpies of {N-methylpiperidine−water} at 0.50 MPa: ○, 308.15 K; □, 318.15 K; Δ, 328.15 K; full line, Redlich− Kister correlation; dashed line, linear connecting line in the two-phases region. 1567



Article

Table 5. Specific Heat Capacities of Pure and Aqueous Solution of Methylpiperidine Isomersb at p = 0.1 MPa as a Function of Temperaturea T

Cp

K

(J·mol−1·K−1)

283.15 288.15 293.15 298.15 303.16 308.15 313.16 318.15 323.15 328.15 333.15

xa = 1 215.38 216.85 217.34 218.00 218.99 219.60 220.18 221.03 221.40 222.07 222.76

xa = 0.9524 211.33 212.82 213.59 214.56 215.66 216.50 217.36 218.40 219.15 219.94 220.89

283.15 288.15 293.15 298.15 303.16 308.15 313.16 318.15 323.15 328.15 333.15

xa = 1 175.4 177.6 179.5 181.5 183.5 185.5 187.5 189.1 191.2 192.7 194.6

xa = 0.7952 161.3 163.8 166.1 168.4 170.7 174.0 175.9 178.0 180.3 182.7 184.1

2-Methylpiperidine xa = 0.7262 186.76 188.95 190.95 192.44 194.17 195.97 197.81 198.26 200.09 201.13 202.26 N-Methylpiperidine xa = 0.6178 xa = 0.4036 147.8 129.4 150.3 132.2 153.1 134.3 155.7 136.8 158.1 138.7 160.3 140.3 162.4 142.2 164.4 143.8 166.9 145.2 169.2 146.3 171.0 147.3 xa = 0.8503 201.45 202.97 204.25 205.80 207.09 208.61 209.74 211.14 212.58 213.60 215.02

xa = 0.3726 139.21 141.02 142.81 144.60 146.44 147.98 149.55 150.82 152.15 153.44 154.60

xa = 0.1830 108.96 110.08 110.85 111.88 112.59 113.52 114.35 114.79 115.72 116.25 116.69

xa = 0 75.58 75.46 75.38 75.33 75.30 75.29 75.29 75.31 75.33 75.36 75.39

xa = 0.1983 109.6 111.0 112.5 113.8 114.8 116.2 117.5 118.7

xa = 0.0966 101.3 101.3 101.1 101.1 101.2 101.5 102.4

xa = 0.0378 93.4 92.0 90.6 89.5 88.6 88.1

a Specific heat capacities of water, Cp,w, are from Hill.7. Standard uncertainties are u(T) = 0.01 K, u(p) = 10 kPa, and u(xa) = 0.0001. bRelative uncertainty of Cp is 0.3%.

coefficients for excess molar enthalpy equation (aHi) were expressed as a function of temperature: aHi = ai0 + ai1T + ai2 ln(T )

(5)

Coefficients for excess heat capacity (aCpi) are then derived from those used for excess enthalpy: aCpi = ai1 + ai2 /T

Only excess properties measured in the miscibility domain were included in the regression for both isomers. Then the number of data available for N-methylpiperidine is reduced compared to 2-methylpiperidine. The parameters obtained for both isomers are listed in Table 7. The average relative deviations (ARD) between calculated and experimental excess molar enthalpies, reported in Table 8, are less than 5 %. ARD for excess molar heat capacities are about 4 %. The Redlisch−Kister correlations for HE are shown in Figures 2 and 3. For both properties, the calculated values are within the experimental uncertainty of the data. However, the lack of excess enthalpy measurements for molar fraction greater than 0.75 does not allow one to confirm the shape of the curves in this range of composition. In the same way, the few compositions investigated for heat capacities cannot give a good representation of the excess heat capacities with the Redlich−Kister equation. Excess partial molar enthalpies at infinite dilution were then determined from the Redlich−Kister equation for both isomers.

Figure 4. Comparison of molar heat capacities of pure methylpiperidines as a function of temperature from this work with values available in the literature. For 2-methylpiperidine: ■, this work; □, Conti et al.;10 Δ, Messerly et al.9 For N-methylpiperidine: •, this work; ∇, Conti et al.;10 ○, Verevkin.11 Dashed lines, connecting line.

3.3. Redlich−Kister Correlation. Excess molar heat capacities and enthalpies were fitted to a Redlich−Kister polynomial equation (eq 4): 7

X E = x wxa ∑ a Xi(x w − xa)i i=0

with X = H , Cp

(6)

(4)

In order to ensure the consistency between experimental enthalpy and heat capacity measurements, all of these data were adjusted together. For that purpose, the Redlich−Kister 1568


a

1569

6.32 7.10 7.89 8.68 9.35 11.05 11.38 12.14 12.88 13.98 13.89

283.15 288.15 293.15 298.15 303.16 308.15 313.16 318.15 323.15 328.15 333.15

xa = 0.7952

0.21 0.22 0.22 0.22 0.23 0.23 0.23 0.23 0.24 0.24 0.24

0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.31 0.31 0.31

10.59 11.76 13.38 14.81 15.91 16.92 17.77 18.82 20.05 21.36 21.93

7.00 7.29 8.16 9.16 9.61 10.61 11.25 11.93 13.05 13.49 14.32

u(CEp )

xa = 0.6178 0.19 0.19 0.19 0.20 0.20 0.20 0.20 0.20 0.21 0.21 0.21

0.27 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.29 0.29 0.29

(J·mol−1·K−1)

xa = 0.8503

(J·mol−1·K−1)

CEp (J·mol−1·K−1)

u(CEp )

CEp

14.27 15.28 16.44 17.43 18.08 19.04 19.91 20.82

11.54 12.88 14.54 16.11 17.60 18.92 20.27 21.21 22.40 23.41 24.30

u(CEp )

xa = 0.1983 0.13 0.13 0.13 0.14 0.14 0.14 0.14 0.14

0.17 0.17 0.17 0.17 0.18 0.18 0.18 0.18 0.18 0.18 0.18

(J·mol−1·K−1)

xa = 0.3726

(J·mol−1·K−1)

2-Methylpiperidine xa = 0.7262 9.66 0.25 10.82 0.25 12.49 0.25 13.51 0.25 14.53 0.25 15.89 0.25 17.31 0.26 17.14 0.26 18.69 0.26 19.24 0.26 19.85 0.26 N-Methylpiperidine xa = 0.4036 13.53 0.16 15.48 0.16 16.91 0.16 18.63 0.16 19.69 0.16 20.57 0.17 21.65 0.17 22.52 0.17 23.10 0.17 23.59 0.17 23.78 0.17

(J·mol−1·K−1)

CEp

16.10 15.98 15.69 15.57 15.46 15.55 16.30

7.80 8.75 9.49 10.45 11.00 11.83 12.55 12.81 13.66 14.05 14.33

u(CEp )

xa = 0.0966 0.12 0.12 0.12 0.12 0.12 0.13 0.13

0.13 0.13 0.13 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

(J·mol−1·K−1)

xa = 0.1830

(J·mol−1·K−1)

CEp

14.00 12.70 11.28 10.15 9.25 8.65

u(CEp )

0.12 0.12 0.12 0.12 0.12 0.12

(J·mol−1·K−1)

xa = 0.0378

(J·mol−1·K−1)

CEp

u(CEp ) is the uncertainty of the excess capacities calculated from propagation of the uncertainty of specific heat capacity. Standard uncertainties are u(T) = 0.01 K, u(p) = 10 kPa, and u(xa) = 0.0001.

2.60 2.70 3.00 3.35 3.51 3.77 4.08 4.31 4.70 4.86 5.15

283.15 288.15 293.15 298.15 303.16 308.15 313.16 318.15 323.15 328.15 333.15

(J·mol−1·K−1)

(J·mol−1·K−1)

K

xa = 0.9524

u(CEp )a

CEp

T

Table 6. Excess Molar Heat Capacities of {2-Methylpiperidine−Water} and {N-Methylpiperidine−Water} Systems as a Function of Temperature and Molar Fraction at p = 0.1 MPaa

Journal of Chemical & Engineering Data Article



Article

Table 7. aij Parameters Used in Equations 5 and 6 N-methylpiperidine

2-methylpiperidine i

ai0·103

ai1·102

ai2·104

ai0·105

ai1·102

ai2·104

0 1 2 3 4 5 6 7

418.7 −77.01 10.55 −46.77 −21.10 31.20 0.7623 −109.4

3.877 −0.5399 0.5031 0.5009 −2.563 −3.624 3.364 3.926

−9.569 1.605 −0.4712 0.3264 1.944 2.119 −2.089 −0.8344

4.275 −1.312 −4.556 2.012 10.040 9.152 5.971 1.594

3.902 −0.4335 −1.933 0.557 3.590 10.294 8.626 −0.938

−9.712 2.436 8.926 −3.865 −19.31 −21.23 −15.24 −2.547

Table 8. Redlich−Kister Coefficients for Excess Enthalpy Calculation (Equation 4) with Their Uncertainties, Average Relative Deviation (ARD) of the Estimate,a and Excess Partial Molar Enthalpy at Infinite Dilution (H̅ Ea )∞ N-methylpiperidine

2-methylpiperidine 303.15 K

308.15 K

aH0/(kJ·mol−1)

−10.6 ± 0.2

−10.2 ± 0.2

aH1/(kJ·mol−1) aH2/(kJ·mol−1) aH3/(kJ·mol−1)

328.15 K −8.45 ± 0.20

−1.66 ± 0.09 −1.67 ± 0.10

−1.70 ± 0.18

−1.12 ± 0.01 −0.95 ± 0.02

−0.597 ± 0.148

−12.9 ± 0.7

−12.6 ± 0.7

aH4/(kJ·mol )

12.3 ± 0.8

aH5/(kJ·mol−1)

42.4 ± 0.9

aH6/(kJ·mol−1)

333.15 K

338.15 K

308.15 K

318.15 K

328.15 K

−7.96 ± 0.20

−7.45 ± 0.20

−8.81 ± 0.34 −8.01 ± 0.34 −7.12 ± 0.34

−1.74 ± 0.18

−1.77 ± 0.19

−1.80 ± 0.19

−4.96 ± 0.57 −4.62 ± 0.58 −4.30 ± 0.50

−0.240 ± 0.015

−0.059 ± 0.015 0.122 ± 0.015 −3.65 ± 0.43 −2.74 ± 0.33 −1.91 ± 0.39

−12.0 ± 0.7

−11.4 ± 0.7

−11.1 ± 0.7

−10.82 ± 0.67 −3.12 ± 0.39 −3.80 ± 0.39 −4.44 ± 0.40

11.3 ± 0.8

9.38 ± 0.78

7.42 ± 0.79

6.43 ± 0.79

5.44 ± 0.80

8.05 ± 0.69

5.47 ± 0.69

3.09 ± 0.42

41.0 ± 0.9

38.0 ± 0.9

35.0 ± 0.9

33.6 ± 0.9

32.1 ± 0.9

15.8 ± 1.8

19.3 ± 1.8

23.0 ± 1.8

−16.6 ± 0.7

−15.3 ± 0.7

−12.6 ± 0.7

−9.87 ± 0.75

−8.51 ± 0.75

−7.14 ± 0.76

−10.4 ± 1.3

−6.67 ± 0.73 −2.76 ± 0.33

aH7/(kJ·mol−1)

−38.1 ± 0.8

−36.2 ± 0.8

−32.6 ± 1.0

−28.9 ± 1.0

−27.1 ± 1.0

−25.2 ± 1.0

−15.5 ± 2.0

−17.2 ± 2.0

−18.9 ± 2.0

ARD/%a

3

3

3

2

2

5

3

3

5

(H̅ Ea )∞/(kJ·mol−1)

−26.3 ± 1.7

−24.7 ± 1.7

−21.5 ± 1.8

−18.2 ± 1.9

−16.5 ± 1.9

−14.8 ± 1.9

−22.6 ± 3.2

−18.3 ± 3.0

−13.3 ± 3.0

−1

a

318.15 K −9.37 ± 0.20

ARD = ((1/n)Σni |(XEi,exp − XEi,cal)/XEi,exp|·100) with n being the number of experimental values.

They correspond to the sum of the aHi coefficients used in eq 42 and are listed in Table 8:

measured at temperatures ranging from (308.15 to 338.15) K for the {2-methylpiperidine−water} system and from (308.15 to 328.15) K for the {N-methylpiperidine−water} system. Excess molar heat capacities for both systems were determined at temperatures ranging from (283.15 to 333.15) K. All of these data were fitted together using a Redlich−Kister polynomial. Enthalpy and heat capacity data are consistent and will be used in a forthcoming work on the development of thermodynamic models representative of liquid−liquid equilibrium and calorimetric properties.

n

(H̅ aE)∞ =

∑ aHi i=0

(7)

The uncertainties on excess molar enthalpy at infinite dilution were calculated from the uncertainty of the Redlich− Kister parameters given in Table 8. They are less than 2 kJ·mol−1 for 2-methylpiperidine and 3.2 kJ·mol−1 for N-methylpiperidine. The excess molar enthalpy at infinite dilution of the 2-methylpiperidine was found to increase linearly with temperature. Our values were then extrapolated to 298.15 K to be compared with those of Berthon et al.13 A very good agreement between our data, (−28.0 ± 2.0) kJ·mol−1, and the one from Berthon et al.,13 (−27.14 ± 0.14) kJ·mol−1, was observed. Literature values for the excess molar enthalpy at infinite dilution of the N-methylpiperidine are available at 298.15 K.10,14 In the same way as for 2-methylpiperidine, we linearly extrapolate our data to 298.15 K. The extrapolated excess molar enthalpy at infinite dilution is (−27.4 ± 3.2) kJ·mol−1. The deviations (< 3.0 kJ·mol−1) observed by both Cabani et al., 14 (−30.00 ± 0.46) kJ·mol−1, and Dohnal and Rěhák,15 (−30.08 ± 0.14) kJ·mol−1, are within our estimated uncertainty.

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AUTHOR INFORMATION

Corresponding Authors

*(Y.C.) Tel.: + 33 (0)473407187. E-mail: yohann.coulier@ gmail.com. *(J.-Y.C.) Tel.: +33 (0)4 73 40 71 90. Fax: +33 (0)4 73 40 53 28. E-mail: [email protected]. Funding

This work is realized with the financial support of the French National Agency for Research (ANR, DACOOTA Project No. Anr-12-IS09-0001-01). We also thank the Contrat d’Objectifs Partagés (COP), CNRS-UBP, Auvergne Région, France for funding of the microSC calorimetric equipment. Notes

The authors declare no competing financial interest.

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4. CONCLUSIONS Thermodynamic properties of {2-methylpiperidine−water} and {N-methylpiperidine−water} were experimentally studied as a function of temperature. Molar excess enthalpies were

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