Partial Molar Volumes and Partial Molar Isentropic Compressions of

Article pubs.acs.org/jced

Partial Molar Volumes and Partial Molar Isentropic Compressions of Selected Branched Diols at Infinite Dilution in Water at Temperatures T = (278 to 318) K and Atmospheric Pressure Ivan Cibulka*,† and Lubomír Hnědkovský‡ †

Department of Physical Chemistry, Institute of Chemical Technology, Technická 5, 166 28 Prague, Czech Republic Murdoch University, School of Veterinary & Life Sciences, Murdoch WA 6150, Australia

‡

ABSTRACT: Speed of sound and density data for dilute aqueous solutions of four branched diols derived from propane-1,3-diol (2-methyl-2propylpropane-1,3-diol, 2,2-diethylpropane-1,3-diol, and 2-ethyl-2-butylpropane-1,3-diol) and 3-methylpentane-1,5-diol were obtained using the Anton Paar DSA 5000 vibrating-tube densimeter and sound analyzer in the temperature range from (278.15 to 318.15) K and at atmospheric pressure. Standard molar isentropic compressions and standard molar volumes were evaluated from the measured data. Present data were combined with those obtained previously for related solutes, and relations to the structures of solute molecules are discussed. The predictions of standard molar volumes based on the group contribution approach were tested and analyzed.

1. INTRODUCTION Our recent studies1,2 were focused on the experimental investigation of volumetric behavior of selected alkane-α,ωdiols in dilute aqueous solutions. The knowledge of standard molar isentropic compressions and standard molar volumes was extended to the homologous series of the solutes with two hydroxyl groups separated by a straight hydrocarbon chain −(CH2)n− with n from 2 to 9 (except for n = 7). It was observed that both quantities are affected by the distance between the hydroxyl groups. The solutes investigated in the present study belong to the group of aliphatic diols with the same distance between the hydroxyl groups but with the branched hydrocarbon frame. Their molecular structures shown in Figure 1 along with the structures of some related solutes are derived from propane-1,3-diol by a substitution of the hydrogen atom(s) on the central carbon atom by alkyl group(s), that is, 2-alkylpropane-1,3-diol, 2,2-dialkylpropane-1,3-diol, or 2-alkyl(A1)-2-alkyl(A2)propane-1,3-diol. Besides propane-1,3-diol3 (G) some of the members of this series have been already studied: 2-methylpropane-1,3-diol4,5 (A) and 2,2-dimethylpropane-1,3-diol4 (B). Here we present experimental data on density and speed of sound for dilute aqueous solutions of 2-methyl-2-propylpropane-1,3-diol (C), 2,2-diethylpropane1,3-diol (D), and 2-ethyl-2-butylpropane-1,3-diol (E). In combination with the previous data for alkane-α,ω-diols1,3,6 several isomeric pairs of branched diol/straight-chain diol can be formed: 2-methylpropane-1,3-diol (A)/butane-1,4-diol (H), 2,2-dimethylpropane-1,3-diol (B)/pentane-1,5-diol (I), 2-methyl2-propylpropane-1,3-diol (C)/heptane-1,7-diol (J), 2,2-diethylpropane-1,3-diol (D)/heptane-1,7-diol (J), 2-ethyl-2-butylpropane-1,3-diol (E)/nonane-1,9-diol (K). Two branched diols, © XXXX American Chemical Society

Figure 1. Structures of solute molecules. Standard molar volumes and standard molar isentropic compressions of solutes C, D, E, F were measured in this work, the references to sources of data for other solutes are given as superscripts in parentheses. aOwing to the lack of data for aqueous heptane-1,7-diol the properties (standard molar volume, standard molar isentropic compression) were simulated by a linear interpolation between values reported for aqueous hexane-1,6diol and aqueous octane-1,8-diol in ref 1.

2-methyl-2-propylpropane-1,3-diol (C)/2,2-diethylpropane1,3-diol (D), are also isomeric pair. In addition the data for Received: April 16, 2013 Accepted: July 16, 2013

A

dx.doi.org/10.1021/je400361k | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Specifications of Chemical Samples of Solutes. All Samples Were from Sigma Aldrich and Were Used as Supplied

a

chemical name

formula

molecular structure (see Figure 1)

CAS RN

mass fraction puritya

mass fraction of waterb

2-methyl-2-propylpropane-1,3-diol (2,2-bis(hydroxymethyl)pentane) 2,2-diethylpropane-1,3-diol (3,3-bis(hydroxymethyl)pentane) 2-ethyl-2-butylpropane-1,3-diol (3,3-bis(hydroxymethyl)heptane) 3-methylpentane-1,5-diol

C7H16O2 C7H16O2 C9H20O2 C6H14O2

C D E F

78-26-2 115-76-4 115-84-4 4457-71-0

0.98 0.99 0.99 0.98

0.0011

Declared by the supplier. bDetermined by the Karl Fischer method.

Table 2. Values of Density ρ1 of and Speed of Sound c1 in Water (NIST)7 Used in Calculations of Standard Molar Isentropic Compression and Standard Molar Volume

aqueous 3-methylpentane-1,5-diol (an isomer to hexane-1,6diol) were also measured. Standard molar volumes and standard molar isentropic compressions evaluated from new experimental data along with the previously obtained values for other members of the series enable a discussion of the effects of the molecular structure on the investigated properties.

2. EXPERIMENTAL SECTION The specifications of the organic solutes are summarized in Table 1. They were used as obtained from the supplier. Water was purified by distillation and demineralization (Millipore RQ). Purified water left in contact with air, that is, containing dissolved air, was used as a calibration fluid for the densimeter and for the preparation of solutions. The vibrating-tube densimeter and sound analyzer manufactured by Anton Paar, model DSA 5000, with a built-in thermostat and equipped with the autosampler SP-1m (Anton Paar) was used for the measurements. The details concerning the experimental methodology can be found in our previous paper.3 The corrections to the content of water in the pure solute determined by the Karl Fischer method were applied for calculations of molalities of 3-methylpentane-1,5-diol. Five or six solutions of each solute were prepared in the molality ranges that were adjusted to the solubilities of the solutes in water: up to 0.24 mol·kg−1 for 2-methyl-2-propylpropane-1,3-diol, 0.3 mol·kg−1 for 2,2-diethylpropane-1,3-diol, 0.034 mol·kg−1 for 2-ethyl-2-butylpropane-1,3-diol, and 0.35 mol·kg−1 for 3-methylpentane-1,5-diol. To minimize the effects of both the device drifts and the systematic uncertainties in the calibration the measured speed of sound in water (c1) and density of water (ρ1) at each temperature and for each set of solutions were used to calculate the speed of sound differences Δc = c − c1 and density differences Δρ = ρ − ρ1 where c and ρ are the speed of sound in and the density of the solution, respectively. The measured differences Δc and Δρ were regarded as direct experimental data It was observed (see also ref 3 for details) that experimental values of c1 and ρ1 exhibited small systematic deviations from the values presented by the National Institute of Standards and Technology7 (NIST). The effect of these small deviations on the goal quantities (standard molar isentropic compressions, standard molar volumes) is negligible since in the differences Δ[(ρc)2] and Δρ (eqs 3 and 5) these systematic deviations cancel out. The values c1(NIST) and ρ1(NIST) were used for the evaluation of standard molar isentropic compressions and standard molar volumes as well as for the calculations of speeds of sound in and densities of solutions, that is, c = Δc(experimental) + c1(NIST) and ρ = Δρ(experimental) + ρ1(NIST) as needed for the evaluation of standard molar isentropic compressions. The values c1 and ρ1 extracted from the NIST database7 are summarized in Table 2.

T/K

ρ1/kg·m−3

c1/m·s−1

278.15 283.15 288.15 293.15 298.15 303.15 308.15 318.15

999.967 999.702 999.103 998.207 997.048 995.649 994.033 990.213

1426.17 1447.27 1465.93 1482.35 1496.70 1509.15 1519.85 1536.45

3. RESULTS 3.1. Direct Experimental Data. The measured values of the differences in density Δρ = ρ − ρ1 and the measured values of differences in speed of sound Δc = c − c1 along with the molalities of organic solutes m2 are recorded in Tables 3 and 4. Except for 3-methylpentane-1,5-diol at T = 298.15 K triplicate measurements were performed for each solution. 3.2. Standard Molar Volumes. The partial molar volume at infinite dilution (m2 → 0) of a solute V0m,2 (standard molar volume) can be calculated from the equation8 0 app = lim (V m,2 V m,2 )= m2 → 0

a ⎞ 1⎛ ⎜⎜M 2 − V ⎟⎟ ρ1 ⎝ ρ1 ⎠

(1)

Vapp m,2

where M2 is the molar mass, is the apparent molar volume, and m2 is the molality of the solute. The coefficient aV is an adjustable parameter of the fit of experimental values Δρ/m2 ρ − ρ1 Δρ = = aV + b V m2 + c Vm22 m2 m2

(2)

The values of the coefficients aV, bV, and cV obtained by using a least-squares method with unit weights are recorded in Table 5 along with the calculated standard molar volumes and estimated uncertainties. 3.3. Standard Molar Isentropic Compressions. Partial molar isentropic compression at infinite dilution (standard molar isentropic compression) of the solute 2 is defined as the derivative of standard molar volume V0m,2 with respect to pressure at constant entropy app ⎞ ⎛ ∂V 0 ⎞ ⎛ −∂V m,2 m,2 ⎟⎟ KS0,m,2 = lim ⎜ ⎟ = −⎜⎜ m2 → 0⎝ ∂p ⎠ ⎝ ∂p ⎠S S

B

(3)



Article

Table 3. Experimental Differences in Density Δρ = ρ − ρ1 Measured at Various Temperatures T/K and Molalities m2 for 2-Methyl-2-propylpropane-1,3-diol (aq), 2,2-Diethylpropane-1,3-diol (aq), 2-Ethyl-2-butylpropane-1,3-diol (aq), and 3-Methylpentane-1,5-diol (aq) at Atmospheric Pressurea Δρ/(kg·m−3) −1

m2/(mol·kg )

278.15 K

283.15 K

288.15 K

0.04066 0.04066 0.04066 0.08017 0.08017 0.08017 0.12102 0.12102 0.12102 0.16129 0.16129 0.16129 0.19981 0.19981 0.19981 0.23792 0.23792 0.23792

0.071 0.071 0.070 0.149 0.151 0.149 0.240 0.242 0.241 0.332 0.334 0.332 0.433 0.435 0.435 0.546 0.547 0.546

0.055 0.054 0.054 0.116 0.113 0.116 0.188 0.188 0.187 0.260 0.259 0.260 0.339 0.341 0.340 0.432 0.433 0.433

0.038 0.038 0.039 0.084 0.084 0.084 0.138 0.139 0.138 0.192 0.192 0.192 0.254 0.254 0.254 0.327 0.327 0.327

0.05007 0.05007 0.05007 0.10063 0.10063 0.10063 0.15030 0.15030 0.15030 0.19965 0.19965 0.19965 0.25031 0.25031 0.25031 0.30005 0.30005 0.30005

0.234 0.236 0.235 0.487 0.487 0.487 0.744 0.746 0.746 1.011 1.011 1.011 1.291 1.292 1.293 1.573 1.572 1.575

0.215 0.215 0.214 0.444 0.442 0.444 0.678 0.677 0.678 0.918 0.917 0.917 1.172 1.170 1.171 1.427 1.426 1.426

0.194 0.194 0.196 0.401 0.402 0.403 0.615 0.617 0.616 0.831 0.831 0.832 1.060 1.060 1.061 1.287 1.289 1.290

0.02882 0.02882 0.02882 0.03112 0.03112 0.03112 0.03298 0.03298 0.03298 0.03410 0.03410 0.03410 0.03433 0.03433 0.03433

0.055 0.057 0.057 0.059 0.062 0.061 0.063 0.065 0.065 0.066 0.067 0.068 0.065 0.068 0.069

0.035 0.035 0.036 0.037 0.039 0.039 0.041 0.040 0.042 0.042 0.043 0.043 0.042 0.043 0.043

0.0175 0.0170 0.0160 0.0195 0.0180 0.0170 0.0215 0.0200 0.0190 0.0225 0.0210 0.0200 0.0225 0.0200 0.0200

0.10004 0.10004 0.10004

0.020 0.022 0.021

−0.008 −0.008 −0.008

−0.0335 −0.0340 −0.0340

293.15 K

298.15 K

2-Methyl-2-propylpropane-1,3-diol (aq) 0.024 0.009 0.025 0.010 0.025 0.010 0.055 0.025 0.056 0.026 0.055 0.027 0.093 0.048 0.094 0.048 0.094 0.049 0.128 0.067 0.129 0.068 0.129 0.068 0.174 0.096 0.175 0.097 0.176 0.099 0.229 0.135 0.230 0.136 0.230 0.136 2,2-Diethylpropane-1,3-diol (aq) 0.177 0.159 0.177 0.160 0.177 0.159 0.364 0.328 0.366 0.329 0.366 0.330 0.557 0.502 0.557 0.503 0.558 0.502 0.752 0.675 0.752 0.676 0.753 0.676 0.957 0.858 0.957 0.858 0.958 0.858 1.161 1.038 1.161 1.039 1.162 1.039 2-Ethyl-2-butylpropane-1,3-diol (aq) 0.000 −0.018 0.000 −0.019 0.000 −0.019 0.000 −0.020 0.000 −0.019 0.000 −0.020 0.000 −0.020 0.000 −0.020 0.000 −0.021 0.001 −0.021 0.000 −0.021 0.000 −0.022 0.000 −0.022 −0.001 −0.022 0.000 −0.022 3-Methylpentane-1,5-diol (aq) −0.057 −0.081 −0.058 −0.081 −0.058 C

303.15 K

308.15 K

318.15 K

−0.003 −0.003 −0.003 −0.001 −0.001 −0.001 0.007 0.007 0.007 0.009 0.009 0.011 0.023 0.023 0.023 0.045 0.046 0.046

−0.015 −0.015 −0.015 −0.026 −0.027 −0.028 −0.034 −0.034 −0.035 −0.047 −0.047 −0.047 −0.049 −0.050 −0.049 −0.045 −0.045 −0.045

−0.042 −0.042 −0.041 −0.080 −0.082 −0.080 −0.118 −0.117 −0.116 −0.161 −0.162 −0.161 −0.192 −0.194 −0.192 −0.219 −0.219 −0.219

0.144 0.143 0.144 0.294 0.296 0.295 0.449 0.451 0.450 0.602 0.602 0.604 0.764 0.764 0.764 0.922 0.922 0.923

0.126 0.128 0.129 0.260 0.262 0.263 0.397 0.397 0.398 0.531 0.532 0.532 0.671 0.671 0.672 0.808 0.807 0.809

0.094 0.094 0.096 0.193 0.193 0.194 0.294 0.294 0.293 0.389 0.390 0.391 0.487 0.489 0.490 0.583 0.584 0.586

−0.035 −0.035 −0.035 −0.036 −0.037 −0.036 −0.039 −0.040 −0.039 −0.039 −0.040 −0.040 −0.040 −0.041 −0.040

−0.052 −0.048 −0.049 −0.056 −0.052 −0.053 −0.057 −0.055 −0.056 −0.059 −0.057 −0.058 −0.061 −0.058 −0.058

−0.078 −0.080 −0.077 −0.087 −0.086 −0.083 −0.090 −0.090 −0.087 −0.094 −0.093 −0.091 −0.096 −0.096 −0.092

−0.102 −0.102 −0.103

−0.122 −0.121 −0.122

−0.161 −0.162 −0.162



Article

Table 3. continued Δρ/(kg·m−3) m2/(mol·kg−1) 0.14998 0.14998 0.14998 0.20001 0.20001 0.20001 0.24992 0.24992 0.24992 0.30002 0.30002 0.30002 0.34952 0.34952 0.34952

278.15 K 0.050 0.051 0.051 0.089 0.090 0.090 0.137 0.140 0.140 0.196 0.198 0.197 0.261 0.263 0.263

283.15 K 0.005 0.005 0.004 0.027 0.027 0.026 0.057 0.058 0.057 0.096 0.095 0.095 0.141 0.140 0.140

288.15 K −0.0355 −0.0360 −0.0360 −0.0305 −0.0300 −0.0310 −0.0165 −0.0170 −0.0180 0.0035 0.0030 0.0030 0.0295 0.0300 0.0300

293.15 K

298.15 K

3-Methylpentane-1,5-diol (aq) −0.073 −0.108 −0.074 −0.109 −0.074 −0.081 −0.131 −0.082 −0.131 −0.083 −0.083 −0.146 −0.084 −0.146 −0.084 −0.079 −0.157 −0.079 −0.156 −0.080 −0.069 −0.163 −0.069 −0.162 −0.069

303.15 K

308.15 K

318.15 K

−0.142 −0.142 −0.143 −0.177 −0.176 −0.177 −0.206 −0.206 −0.206 −0.231 −0.230 −0.230 −0.251 −0.250 −0.250

−0.173 −0.173 −0.174 −0.220 −0.220 −0.221 −0.262 −0.260 −0.263 −0.300 −0.298 −0.300 −0.334 −0.331 −0.334

−0.235 −0.236 −0.236 −0.305 −0.307 −0.305 −0.372 −0.372 −0.371 −0.434 −0.436 −0.434 −0.494 −0.494 −0.494

a Standard uncertainties are u(T) = 0.01 K, u(m2) = 3·10−5 mol·kg−1, and the combined expanded uncertainty is Uc(Δρ) = 3·10−2 kg·m−3 (level of confidence = 0.95).

Table 4. Experimental Differences in Speed of Sound Δc = c − c1 Measured at Various Temperatures T/K and Molalities m2 for 2-Methyl-2-propylpropane-1,3-diol (aq), 2,2-Diethylpropane-1,3-diol (aq), 2-Ethyl-2-butylpropane-1,3-diol (aq), and 3-Methylpentane-1,5-diol (aq) at Atmospheric Pressurea Δc/(m·s−1) m2/(mol·kg−1)

278.15

283.15

288.15

0.04066 0.04066 0.04066 0.08017 0.08017 0.08017 0.12102 0.12102 0.12102 0.16129 0.16129 0.16129 0.19981 0.19981 0.19981 0.23792 0.23792 0.23792

5.71 5.72 5.72 11.18 11.18 11.19 16.71 16.72 16.73 22.15 22.16 22.15 27.18 27.18 27.18 32.10 32.13 32.14

5.26 5.26 5.27 10.28 10.27 10.29 15.38 15.38 15.37 20.34 20.34 20.36 24.97 24.97 24.99 29.49 29.49 29.52

4.86 4.87 4.87 9.50 9.50 9.51 14.16 14.16 14.18 18.74 18.74 18.76 22.99 22.98 23.00 27.11 27.13 27.15

0.05007 0.05007 0.05007 0.10063 0.10063 0.10063 0.15030 0.15030 0.15030 0.19965 0.19965 0.19965 0.25031 0.25031 0.25031

6.87 6.90 6.87 13.68 13.70 13.68 20.21 20.22 20.21 26.60 26.62 26.59 33.01 33.02 33.03

6.33 6.34 6.35 12.61 12.60 12.62 18.65 18.65 18.66 24.53 24.53 24.53 30.44 30.45 30.46

5.88 5.88 5.89 11.67 11.67 11.68 17.22 17.22 17.23 22.67 22.65 22.66 28.09 28.09 28.10

293.15

298.15

2-Methyl-2-propylpropane-1,3-diol (aq) 4.48 4.11 4.48 4.12 4.47 4.12 8.75 8.02 8.73 8.04 8.74 8.04 13.03 11.96 13.02 11.98 13.03 11.99 17.21 15.81 17.22 15.83 17.23 15.84 21.12 19.37 21.12 19.39 21.13 19.40 24.92 22.83 24.91 22.84 24.93 22.86 2,2-Diethylpropane-1,3-diol (aq) 5.41 5.01 5.41 5.01 5.42 5.02 10.77 9.94 10.77 9.95 10.78 9.96 15.90 14.67 15.90 14.68 15.90 14.69 20.89 19.26 20.88 19.27 20.90 19.28 25.89 23.83 25.89 23.84 25.90 23.86 D

303.15

308.15

318.15

3.79 3.79 3.80 7.38 7.39 7.39 10.99 11.00 11.01 14.50 14.51 14.52 17.73 17.75 17.76 20.89 20.90 20.91

3.47 3.46 3.48 6.74 6.75 6.77 10.04 10.04 10.07 13.24 13.25 13.25 16.19 16.21 16.22 19.05 19.07 19.08

2.89 2.91 2.89 5.62 5.64 5.62 8.35 8.37 8.35 10.96 10.99 10.96 13.35 13.35 13.36 15.62 15.63 15.65

4.62 4.63 4.63 9.17 9.18 9.18 13.51 13.52 13.53 17.71 17.72 17.73 21.90 21.91 21.93

4.25 4.25 4.24 8.41 8.42 8.42 12.40 12.41 12.41 16.26 16.27 16.27 20.09 20.10 20.11

3.57 3.56 3.58 7.08 7.07 7.07 10.40 10.39 10.40 13.56 13.55 13.57 16.67 16.67 16.68



Article

Table 4. continued Δc/(m·s−1) m2/(mol·kg−1)

278.15

283.15

288.15

0.30005 0.30005 0.30005

39.20 39.21 39.20

36.10 36.11 36.13

33.30 33.29 33.30

0.02882 0.02882 0.02882 0.03112 0.03112 0.03112 0.03298 0.03298 0.03298 0.03410 0.03410 0.03410 0.03433 0.03433 0.03433

5.21 5.18 5.20 5.61 5.58 5.61 5.94 5.91 5.93 6.14 6.12 6.14 6.17 6.16 6.17

4.78 4.77 4.78 5.16 5.14 5.16 5.46 5.45 5.46 5.63 5.63 5.64 5.68 5.67 5.68

4.44 4.43 4.41 4.77 4.77 4.76 5.04 5.04 5.04 5.22 5.22 5.21 5.25 5.25 5.25

0.10004 0.10004 0.10004 0.14998 0.14998 0.14998 0.20001 0.20001 0.20001 0.24992 0.24992 0.24992 0.30002 0.30002 0.30002 0.34952 0.34952 0.34952

10.74 10.74 10.73 15.96 15.97 15.96 21.11 21.12 21.11 26.15 26.17 26.16 31.13 31.15 31.14 35.96 36.00 35.99

9.84 9.83 9.83 14.63 14.62 14.62 19.36 19.35 19.35 23.99 23.99 23.99 28.55 28.56 28.56 32.99 32.99 32.98

9.07 9.07 9.07 13.43 13.48 13.47 17.81 17.81 17.80 22.03 22.07 22.08 26.24 26.26 26.27 30.31 30.32 30.33

293.15

298.15

2,2-Diethylpropane-1,3-diol (aq) 30.66 28.19 30.67 28.19 30.68 28.21 2-Ethyl-2-butylpropane-1,3-diol (aq) 4.05 3.76 4.05 3.72 4.05 3.73 4.36 4.05 4.37 4.01 4.37 4.02 4.62 4.29 4.63 4.24 4.63 4.26 4.77 4.43 4.79 4.39 4.78 4.40 4.80 4.46 4.81 4.42 4.81 4.43 3-Methylpentane-1,5-diol (aq) 8.33 7.64 8.33 7.65 8.32 12.36 11.37 12.37 11.36 12.36 16.34 15.02 16.34 15.02 16.34 20.24 18.59 20.24 18.58 20.24 24.07 22.12 24.08 22.12 24.08 27.80 25.50 27.80 25.49 27.81

303.15

308.15

318.15

25.89 25.90 25.92

23.72 23.72 23.73

19.61 19.61 19.62

3.42 3.42 3.43 3.68 3.69 3.69 3.89 3.91 3.90 4.03 4.03 4.03 4.06 4.05 4.06

3.12 3.12 3.10 3.36 3.35 3.34 3.55 3.55 3.55 3.68 3.67 3.65 3.70 3.69 3.67

2.57 2.57 2.56 2.77 2.76 2.76 2.93 2.92 2.92 3.02 3.02 3.02 3.04 3.03 3.03

7.03 7.03 7.04 10.43 10.44 10.45 13.78 13.78 13.79 17.02 17.04 17.05 20.24 20.25 20.25 23.41 23.35 23.35

6.36 6.52 6.31 9.47 9.65 9.42 12.53 12.73 12.59 15.52 15.69 15.60 18.50 18.46 18.53 21.36 21.25 21.37

5.29 5.21 5.39 7.71 7.71 7.96 10.19 9.61 10.77 12.70 12.30 13.18 15.20 14.73 15.48 17.58 17.04 17.55

a Standard uncertainties are u(T) = 0.01 K, u(m2) = 3·10−5 mol·kg−1, and the combined expanded uncertainty is Uc(Δc) = 0.3 m·s−1 at T = 318.15 K, and Uc(Δc) = 0.1 m·s−1 at lower temperatures (level of confidence = 0.95).

about ± 0.1 m·s−1 at temperatures from (278 to 298) K and ± 0.3 m·s−1 at 318 K. Because of the low solubility of 2-ethyl-2-butylpropane1,3-diol no concentration dependences (2) and (5) were considered (bV = cV = bK = 0) and the parameters aV and aK were evaluated as the averages of experimental values of Δρ/m2 and Δ[(ρc)2]/m2, respectively. The dependences (2) for 2-methyl-2-propylpropane-1,3-diol were found to be linear and thus cV = 0.

On the basis of this definition it is possible to derive3 the expression for standard molar isentropic compression KS0,m,2 =

aK ⎞ 1 ⎛ ⎜ ⎟⎟ M − ⎜ 2 (ρ1c1)2 ⎝ (ρ1c1)2 ⎠

(4)

where aK is an adjustable parameter of the fit of experimental values of the differences Δ[(ρc)2] = (ρc)2 − (ρ1c1)2 in the form (ρc)2 − (ρ1c1)2 Δ[(ρc)2 ] = = aK + bK m2 m2 m2

4. DISCUSSION No data for the present solutes in dilute aqueous solutions have been found in the literature for a comparison. 4.1. Dependences of Standard Molar Volumes on Temperature. The dependences are shown in Figures 2 and 3 o o o (plots V m,2 (T) and V m,2 (T) − V m,2 (T = 278.15 K), respectively). It can be seen in Figure 2 that the standard

(5)

The values of the coefficients aK, bK were obtained from measured data by using a least-squares method with unit weights and are recorded in Table 5 along with calculated values of K0S,m,2. Uncertainties σ(K0S,m,2) are affected mainly by the uncertainty in the speed of sound which was estimated to be E



Article

Table 5. Coefficients aV, bV, and cV of eq 2, Standard Molar Volumes V0m,2, Coefficients aK, and bK of eq 5, and Standard Molar Isentropic Compressions K0S,m,2, for {2-Methyl-2-propylpropane-1,3-diol(2) or 2,2-Diethylpropane-1,3-diol(2) or 2-Ethyl-2-butylpropane-1,3-diol(2) or 3-Methylpentane-1,5-diol(2) + Water(1)}. The Uncertainties σ(V0m,2) and σ(K0S,m,2) Represent the Combined Expanded Uncertainties T

aV

bV

cV

V0m,2 ± σ(V0m,2)

aK·10−12

bK·10−12

K0S,m,2 ± σ(K0S,m,2)

K

kg2·m−3·mol−1

kg3·m−3·mol−2

kg4·m−3·mol−3

cm3·mol−1

kg3·m−4·s−2·mol−1

kg4·m−4·s−2·mol−2

cm3·mol−1·GPa−1

278.15 283.15 288.15 293.15 298.15 303.15 308.15 318.15

1.6428 1.2443 0.8814 0.5450 0.1948 −0.1057 −0.4162 −1.0444

2.7119 2.3614 2.0299 1.7124 1.5319 1.1785 0.8970 0.4536

278.15 283.15 288.15 293.15 298.15 303.15 308.15 318.15

4.5538 4.1541 3.7732 3.4352 3.0977 2.8044 2.4868 1.8554

3.0767 2.6982 2.4912 2.1543 1.9900 1.5179 1.3232 0.8804

278.15 283.15 288.15 293.15 298.15 303.15 308.15 318.15

1.9614 1.2395 0.6014 0.0032 −0.6325 −1.1825 −1.7183 −2.7278

278.15 283.15 288.15 293.15 298.15 303.15 308.15 318.15

−0.0556 −0.3164 −0.5427 −0.7612 −0.9730 −1.1811 −1.3456 −1.7138

2.8203 2.5186 2.1657 1.9424 1.8062 1.6960 1.3628 1.0205

2-Methyl-2-propylpropane-1,3-diol (aq) 130.56 ± 0.09 131.00 ± 0.09 131.44 ± 0.09 131.89 ± 0.09 132.40 ± 0.09 132.89 ± 0.09 133.42 ± 0.11 134.57 ± 0.13 2,2-Diethylpropane-1,3-diol (aq) −2.5883 127.65 ± 0.05 −2.3724 128.08 ± 0.05 −2.5321 128.54 ± 0.05 −2.3577 128.99 ± 0.05 −2.6095 129.48 ± 0.05 −2.0816 129.95 ± 0.05 −2.1387 130.48 ± 0.05 −1.9305 131.62 ± 0.06 2-Ethyl-2-butylpropane-1,3-diol (aq) 158.30 ± 0.16 159.06 ± 0.16 159.80 ± 0.17 160.54 ± 0.15 161.36 ± 0.15 162.15 ± 0.16 162.96 ± 0.18 164.62 ± 0.19 3-Methylpentane-1,5-diol (aq) −1.4774 118.23 ± 0.02 −1.3307 118.53 ± 0.02 −1.0620 118.82 ± 0.02 −0.9463 119.15 ± 0.02 −1.0095 119.50 ± 0.02 −1.0526 119.88 ± 0.02 −0.6812 120.25 ± 0.02 −0.4594 121.09 ± 0.03

0.4113 0.3827 0.3572 0.3305 0.3053 0.2818 0.2574 0.2134

−0.0512 −0.0525 −0.0606 −0.0602 −0.0622 −0.0692 −0.0684 −0.0783

−34.4 −24.2 −16.0 −8.6 −2.2 3.3 8.5 17.3

± ± ± ± ± ± ± ±

0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.4

0.4144 0.3875 0.3638 0.3386 0.3158 0.2930 0.2699 0.2277

−0.0472 −0.0463 −0.0536 −0.0522 −0.0574 −0.0597 −0.0583 −0.0662

−35.2 −25.3 −17.4 −10.3 −4.3 1.1 6.1 14.6

± ± ± ± ± ± ± ±

0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.3

−47.5 −34.1 −23.3 −13.3 −5.2 2.5 9.6 21.7

± ± ± ± ± ± ± ±

1.0 0.8 0.8 0.7 0.9 0.7 1.0 1.5

−17.14 −9.23 −3.06 2.47 7.62 11.27 15.31 22.27

± ± ± ± ± ± ± ±

0.10 0.05 0.13 0.04 0.20 0.08 0.38 0.56

0.5222 0.4847 0.4511 0.4147 0.3826 0.3492 0.3158 0.2547 0.3112 0.2878 0.2676 0.2469 0.2254 0.2094 0.1900 0.1542

−0.0306 −0.0280 −0.0306 −0.0305 −0.0228 −0.0320 −0.0274 −0.0297

(hydroxyl groups) and hydrophobic (hydrocarbon frame) parts of the solute molecule, that is, in our case with the decreasing number of carbon atoms. On the other hand the structural arrangement of the hydrocarbon frame plays a role as can be seen from the curve for 3-methylpentane-1,5-diol (F) which does not fit between the trends in the propane-1,3-diol series. Similarly the standard molar isentropic compressions of two isomers 2-methylpropane-1,3-diol (C) and 2,2-diethylpropane-1,3-diol (D) differ by more than would correspond to experimental uncertainties. 4.3. Effect of the Branched Structures. In Figure 1 the branched diols are paired with the corresponding alkaneα,ω-diols, that is, the solutes in each pair branched diol/ straight-chain diol have the same number of carbon atoms. Thus the effect of branching can be observed by a comparison of the property of the branched diol with that of the corresponding straight-chain diol. There are two effects, however, since the distance between the hydroxyl groups is constant in the branched solutes A through E while it is variable in alkane-α,ω-diols from

molar volumes of two isomers 2-methyl-2-propylpropane1,3-diol (C) and 2,2-diethylpropane-1,3-diol (D) differ significantly, the volumes of the symmetrical isomer (D) are smaller by about 3 cm3·mol−1. On the other hand the standard volumes of these isomers relative to that at T = 278.15 K are nearly identical as shown in Figure 3. The distances between neighboring curves in Figure 2 correspond to the contributions of the methylene group to the standard molar volume (two contributions for curves n = 7 and n = 9). The dependence of the standard volume on the number of carbon atoms is monotonous, the curves are not, however, equidistant, likely due to various branching of particular hydrocarbon frames. This effect is discussed below (section 4.3). 4.2. Dependences of Standard Molar Isentropic Compression on Temperature. The dependences are shown in Figure 4. In the series of substituted propane-1,3diols the standard molar isentropic compression obeys the general rule observed previously1,3,4 that the positive slope (∂K0S,m,2/∂T) decreases with increasing ratio between hydrophilic F



Article

Figure 2. Plot of the standard molar volumes V0m,2 against temperature T. The lines are to aid the eye. Integer numbers denote the numbers of carbon atoms in the solute molecule: ●, propane-1,3-diol (G)3; ○, 2-methylpropane-1,3-diol (A)4; ▲, 2,2-dimethylpropane-1,3-diol (B)4; □, 2-methyl-2-propylpropane-1,3-diol (C); ■, 2,2-diethylpropane-1,3diol (D); Δ, 2-ethyl-2-butylpropane-1,3-diol (E); ▼, 3-methylpentane1,5-diol (F).

Figure 4. Plot of standard molar isentropic compression K0S,m,2 against temperature T. The lines are to aid the eye. Integer numbers denote the number of carbon atoms in the solute molecule: ●, propane-1,3diol (G)3; ○, 2-methylpropane-1,3-diol (A)4; ▲, 2,2-dimethylpropane1,3-diol (B)4; □, 2-methyl-2-propylpropane-1,3-diol (C); ■, 2,2diethylpropane-1,3-diol (D); Δ, 2-ethyl-2-butylpropane-1,3-diol (E); ▼, 3-methylpentane-1,5-diol (F).

Figure 3. Plot of the differences V0m,2 (T) − V0m,2 (T = 278.15 K) against temperature T. The lines are to aid the eye. Integer numbers denote the number of carbon atoms in the solute molecule: ●, propane-1,3-diol (G)3; ○, 2-methylpropane-1,3-diol (A)4; ▲, 2,2dimethylpropane-1,3-diol (B)4; □, 2-methyl-2-propylpropane-1,3-diol (C); ■, 2,2-diethylpropane-1,3-diol (D); Δ, 2-ethyl-2-butylpropane1,3-diol (E); ▼, 3-methylpentane-1,5-diol (F).

Figure 5. Plot of the differences ΔV0m,2 = Vm,20 (branched diol)−V0m,2 (straight-chain diol) against temperature T. The lines are to aid the eye. Letters denote solute pairs (see Figure 1): ○, {2-methylpropane1,3-diol (A)−butane-1,4-diol (H)}; ▲, {2,2-dimethylpropane-1,3-diol (B)−pentane-1,5-diol (I)}; □, {2-methyl-2-propylpropane-1,3-diol (C)−heptane-1,7-diol (J)}; ■, {2,2-diethylpropane-1,3-diol (D)− heptane-1,7-diol (J)}; Δ, {2-ethyl-2-butylpropane-1,3-diol (E)− nonane-1,9-diol (K)}; ▼, {3-methylpentane-1,5-diol (F)− hexane1,6-diol (L)}.

H through K. As it was observed1 the effect of the distance between the hydroxyl groups is moderate for standard volumes and negligible for standard isentropic compression for n ≥ 3, and thus it can be assumed that the effect of branching is likely to be predominant. Figures 5 and 6 present the plots of the differences between the property of the branched diol and that of the corresponding straight-chain diol. With the exception of the standard molar isentropic compressions for the pair {3-methylpentane-1,5-diol

(F) hexane-1,6-diol (L)} the property values of the branched isomers are smaller than those of the corresponding straightchain isomers. Obviously, the differences are smaller for the group of pairs for monoalkyl substituted diols with the tertiary carbon atom, that is, {2-methylpropane-1,3-diol (A)−butane-1,4diol (H)} and {3-methylpentane-1,5-diol (F)−hexane-1,6-diol (L)} G



Article

298.15 K and atmospheric pressure for 425 aqueous nonionic solutes. The structural correction proposed by Cabani et al.10 for polyfunctional solutes has been applied for the present predictions performed for bifunctional diols. Table 6. Comparison of Standard Molar Volumes Calculated Using Group Contributions Taken from References 9 and 10 with the Experimental Values experimental

calculated reference 9

Figure 6. Plot of the differences ΔK0S,m,2 = K0S,m,2 (branched diol)−K0S,m,2 (straight-chain diol) against temperature T. Error bars were evaluated using uncertainties σ(K0S,m,2) from Table 5. The lines are to aid the eye. Letters denote solute pairs (see Figure 1): ○, {2-methylpropane-1,3-diol (A)−butane-1,4-diol (H)}; ▲, {2,2-dimethylpropane-1,3-diol (B)− pentane-1,5-diol (I)}; □, {2-methyl-2-propylpropane-1,3-diol (C)− heptane-1,7-diol (J)}; ■, {2,2-diethylpropane-1,3-diol (D)−heptane1,7-diol (J)}; Δ, {2-ethyl-2-butylpropane-1,3-diol (E)−nonane-1,9diol (K)}; ▼, {3-methylpentane-1,5-diol (F)−hexane-1,6-diol (L)}.

compared to the group of pairs for 2,2-dialkylpropane-1,3-diols which comprise a quaternary carbon atom: {2,2-dimethylpropane1,3-diol (B)−pentane-1,5-diol (I)}, 2-methyl-2-propylpropane-1,3diol (C)−heptane-1,7-diol (J)}, {2,2-diethylpropane-1,3-diol (D)− heptane-1,7-diol (J)}, and {2-ethyl-2-butylpropane-1,3-diol (E)− nonane-1,9-diol (K)}. Within the latter group of isomeric pairs those with shorter substituted alkyls {B−I} exhibit smaller differences than those with larger alkyls {E−K}. Branched isomers 2-methyl-2-propylpropane-1,3-diol (C) and 2,2-diethylpropane-1,3-diol (D) can be derived from 2,2dimethylpropane-1,3-diol (B) by an addition of two methylene groups. Since the values of both the standard molar volume and standard molar isentropic compression of 2,2-diethylpropane1,3-diol (D) are smaller than those of the isomeric 2-methyl2-propylpropane-1,3-diol (C) it seems likely that the effect of the symmetrical addition (one methylene group to each alkyl) is stronger than in the unsymmetrical case when one methyl group remains unchanged and the other is enlarged to the propyl group. On the basis of this consideration it might be expected that the properties of aqueous 2,2-dipropylpropane1,3-diol should be smaller than those of aqueous 2-ethyl-2butylpropane-1,3-diol (E). 4.4. Group Contribution Predictions of Standard Molar Volumes. Two sets of group contributions of the first order approach were employed for the predictions. Our contributions9 were obtained from experimental data for 21 aliphatic aqueous solutes (alcohols, ethers, ketones) in the temperature range from (298 to 573) K and pressures up to 30 MPa. Among these solutes four alkane-α,ω-diols (n = 2, 3, 4, 6) and one solute with the quaternary carbon atom (2,2-dimethylpropane-1,3-diol) were included. Therefore these solutes were omitted in the predictions performed in this work. Cabani et al.10 presented the group and structural contributions obtained by averaging over an extensive set of experimental values at

a

T

V0m,2

K

cm ·mol 3

V0m,2

(exp) −1

298.15 318.15

132.40 134.57

298.15 318.15

129.48 131.62

298.15 318.15

161.36 164.62

298.15 318.15

87.48 88.36

298.15 318.15

119.50 121.09

298.15 318.15

104.47 105.66

298.15 318.15

152.34 155.05

298.15 318.15

168.00 171.36

ref

(calc)

dev

reference 10 a

V0m,2

deva

(calc)

−1

cm ·mol 3

−1

cm ·mol 3

2-Methyl-2-propylpropane-1,3-diol (aq) 134.51 −2.12 134.77 136.55 −1.97 2,2-Diethylpropane-1,3-diol (aq) 134.51 −5.04 134.77 136.55 −4.93 2-Ethyl-2-butylpropane-1,3-diol (aq) 166.65 −5.29 166.37 169.44 −4.82 2-Methylpropane-1,3-diol (aq) 5 88.49 −1.01 86.90 5 89.09 −0.73 3-Methylpentane-1,5-diol (aq) 120.62 −1.12 119.67 121.98 −0.89 Pentane-1,5-diol (aq) 1 104.33 0.14 104.08 1 105.63 0.02 Octane-1,8-diol (aq) 1 152.54 −0.20 152.44 1 154.97 0.08 Nonane-1,9-diol (aq) 1 168.61 −0.61 168.42 1 171.42 −0.06

−2.37

−5.29

−5.00

0.58

−0.17

0.39

−0.09

−0.43

Deviation between experimental and calculated value.

Table 6 presents the results of the predictions of standard molar volumes of branched diols studied in this work along with the results for 2-methylpropane-1,3-diol and three alkaneα,ω-diols (n = 5, 8, 9) . The predicted values are compared with the experimental data (this work and refs 1 and 5). Performances of both group contribution methods (contribution sets) are very similar; the deviations of the predicted values from the experiment are of similar magnitudes and, with one exception, of the same signs. With few exceptions the predicted values are greater than the experimental ones. Both methods fail in predictions of standard volumes of highly branched diols (2,2-dialkylpropane1,3-diols; C, D, E) where the deviations are several cm3·mol−1. The predictions are much better for monomethylsubstituted diols (2-methylpropane-1,3-diol (A), 3-methylpentane-1,5-diol (F)), and very satisfactory agreement with the experiment is observed for selected alkane-α,ω-diols. In the case of our contributions9 the results for 2-methylpropane-1,3-diol, 3-methylpentane-1,5-diol, and these three alkane-α,ω-diols are true predictions since the experimental data of none of those solutes were employed for the evaluation of the contributions. The group contribution methods employed here are the methods of the first order, and thus each of them predict identical values of standard molar volumes for both isomeric H



Article

(6) Hnědkovský, L.; Cibulka, I. Partial Molar Isentropic Compressions and Partial Molar Volumes of Isomeric Butanediols at Infinite Dilution in Water at Temperatures T = (278 to 318) K and Atmospheric Pressure. J. Chem. Eng. Data 2013, 58, 388−397. (7) Harvey, A. H.; Peskin, A. P.; Klein, S. A. NIST/ASME Steam Properties, Formulation for General and Scientific Use. NIST Standard Reference Database 10, Version 2.11, 1996. (8) Hynek, V.; Hnědkovský, L.; Cibulka, I. A New Design of a Vibrating-Tube Densimeter and Partial Molar Volumes of Phenol(aq) at Temperatures from 298 to 573 K. J. Chem. Thermodyn. 1997, 29, 1237−1252. (9) Cibulka, I.; Hnědkovský, L. Group contribution Method for Standard Molar Volumes of Aqueous Aliphatic Alcohols, Ethers and Ketones in Extended Ranges of Temperature and Pressure. J. Chem. Thermodyn. 2011, 43, 1215−1223. (10) Cabani, S.; Gianni, P.; Mollica, V.; Lepori, L. Group Contributions to the Thermodynamic Properties of Non-ionic Organic Solutes in Dilute Aqueous Solutions. J. Solution Chem. 1981, 10, 563−595.

solutes 2-methyl-2-propylpropane-1,3-diol (C) and 2,2-diethylpropane-1,3-diol (D). This is in contradiction to the experiment; measured standard molar volumes differ by about 3 cm3·mol−1 in the experimental temperature range. This failure issues from the nature of the methods and cannot be removed by any re-evaluation of the group contributions using an extended set of experimental data without the introduction of properly designed structural contributions.

5. CONCLUSIONS New data on density and speed of sound in a dilute region were reported for aqueous branched diols derived from alkane-α,ωdiols, three from propane-1,3-diol and one diol from pentane1,5-diol. Experimental data were then employed for the evaluation of standard molar volumes and standard molar isentropic compressions of the solutes in the temperature range (278 to 318) K. In combination with data available for several other solutes, the relations between the structure of solute molecules and values of the standard properties and their trends within the series of the solutes were discussed. It was observed that the standard molar volumes and standard molar isentropic compressions of branched diols are systematically lower than those of corresponding alkaneα,ω-diols with the same number of carbon atoms. Two published group contribution methods were employed for the predictions of standard molar volumes and the results were compared with the experiment. Satisfactory predictions were obtained for straightchain diols (alkane-α,ω-diols) and monoalkyl substituted derivatives. On the other hand substantial deficiencies were observed in predictions of standard volumes of highly branched diols and thus the demand for the improvements is clearly indicated.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +420 220444063. E-mail [email protected]. Funding

Support from the Ministry of Education, Youth and Sports of the Czech Republic (fund MSM6046137307) is acknowledged. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Hnědkovský, L.; Cibulka, I. Partial Molar Volumes and Partial Molar Isentropic Compressions of Selected Alkane-α,ω-diols at Infinite Dilution in Water at Temperatures T = (278 to 318) K and Atmospheric Pressure. J. Chem. Eng. Data 2013, 58, 1724−1734. (2) Cibulka, I.; Hnědkovský, L. Partial Molar Volumes of Organic Solutes in Water. XXIV. Selected Alkane-α,ω-diols at Temperatures T = 298 to 573 K and Pressures up to 30 MPa. J. Chem. Thermodyn. 2013, 64, 231−238. (3) Katriňaḱ , T.; Hnědkovský, L.; Cibulka, I. Partial Molar Volumes and Partial Molar Isentropic Compressions of Three Polyhydric Alcohols Derived from Propane at Infinite Dilution in Water at Temperatures T = (278 to 318) K and Atmospheric Pressure. J. Chem. Eng. Data 2012, 57, 1152−1159. (4) Šimurka, L.; Cibulka, I.; Hnědkovský, L. Partial Molar Isentropic Compressions and Partial Molar Volumes of Selected Branched Aliphatic Alcohols at Infinite Dilution in Water at Temperatures T = (278 to 318) K and Atmospheric Pressure. J. Chem. Eng. Data 2012, 57, 1570−1580. (5) Šimurka, L.; Cibulka, I.; Hnědkovský, L. Partial Molar Volumes of Selected Aliphatic Alcohols at Infinite Dilution in Water at Temperatures T = (278 to 573) K and Pressures up to 30 MPa. J. Chem. Eng. Data 2011, 56, 4564−4576. I


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