J. Chem. Thermodynamics 54 (2012) 118–128
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J. Chem. Thermodynamics
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Steric parameters and excess properties of hydroxamic acids
Sandhya Patre, Piyush Thakur, Rama Pande ⇑School of Studies in Chemistry, Pt. Ravishankar Shukla University, Raipur, Chhattisgarh 492010, India
a r t i c l e i n f o a b s t r a c t
Article history:Received 26 November 2011Received in revised form 15 March 2012Accepted 17 March 2012Available online 27 March 2012
Keywords:DensityApparent molar volumeRefractive indexDMFHydroxamic acids
0021-9614/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.jct.2012.03.020
⇑ Corresponding author. Tel.: +91 9827198370; faxE-mail address: [emailprotected] (R. Pande
Steric parameters of N-phenylbenzo-, N-phenyl-4-methyl-3-nitrobenzo-, and N-phenyl-4-nitrobenzo-,hydroxamic acids were measured in N,N-dimethylformamide (DMF) as a function of their concentrationsat T = (298.15, 303.15, 308.15, and 313.15) K. The apparent molar volume (V/), limiting apparent molarvolume (V0
/) at infinite dilution and the slope (S�V ) are calculated from the experimental values of density(q) by applying the Masson’s equation. The apparent molar expansibility at infinite dilution (/0
E), molarvolume (V) and the excess molar volume (VE) are also computed. The refractive indices (n) have been usedto calculate the steric parameters, viz. molar refraction (RM), polarizability (a) and excess molar refraction(R) of these molecules. The results show the strong solute–solvent interactions present in the system andthus, help to explore the molecular structure.
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1. Introduction
There are several correlations between steric parameters andthermophysical properties that indicate the importance of thisparameter [1]. Properties such as densities, refractive indices andtheir variation with temperature and composition of the solutionare useful to design engineering processes and in chemical and bio-logical industries [2–5]. The steric and excess properties measure-ments are expected to shed some light on both solute–solvent andsolvent–solvent interactions. The parameters, apparent molar vol-umes and limiting apparent molar volumes of dilute solutions canbe used for the development of molecular models for describingthe thermodynamic behaviour of solutions. The V0
/ depends uponmolecular size, shape, interactions, and structural effects amongthe solvent [6]. Excess properties of solutions, such as deviationin molar refraction called excess molar refraction, RE
M and VE areuseful for the design of separation techniques and to test theoriesof solutions [7].
N,N-Dimethylformamide (DMF) is a versatile solvent with largedipole moment and a relatively high dielectric constant [8]. Thehydroxamic acid functionality, –C(@O)�N�OH, is a key structuralconstituent of many biomolecules, some of which, are naturallyoccurring [9] and others, such as peroxidase, matrix metallopro-teinase and urease inhibitors [10,11] are of synthetic origin.Hydroxamic acid derivatives have received increasing attentiondue to their biological activity especially as enzyme inhibitors[12] and metal chelators [13]. Hydroxamic acids are versatile re-
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agents in analytical chemistry [14,15] and are widely used in med-icine as analgetics, anti-inflamatories [16], antibiotics [17],anticancer agents [18], antifungal and hypotentive agents [19].Extensive work has been carried out to study the volumetric andsteric parameters of various binary and liquid mixtures in bothaqueous and aquo-organic phase. Recently, Sahin and Ayranci[20] have studied the volumetric properties at different tempera-tures using various solvents. Anouti et al. [21] have investigatedvolumetric properties and refractive index of binary mixture. Ivonaet al. [22] studied the densities and refractive indices of ternarymixture at different temperatures.
Over the past decade, our research group has made someremarkable efforts to study the steric and excess properties of bin-ary and pure systems of different derivatives of hydroxamic acids.The data are lacking in the literature on the densities and opticalproperties of PBHA, PMNHA, and PNHA in pure DMF at differenttemperatures. Therefore, in the present paper, we report q, n ofsolution over entire range of concentration and at temperatures,T = (298.15, 303.15, 308.15, and 313.15) K. These data are furtherused to calculate V/, V0
/, /0E , VE, nE and RM, in order to understand
molecular behaviour and the nature of solute–solvent interactions[23–25].
2. Experimental
2.1. Materials
Three hydroxamic acids namely N-phenylbenzohydroxamicacid (PBHA), N-phenyl-4-methyl-3-nitrobenzohydroxamic acid(PMNHA) and N-phenyl-4-nitrobenzohydroxamic acid (PNHA)
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S. Patre et al. / J. Chem. Thermodynamics 54 (2012) 118–128 119
were prepared by the procedure reported in the literature [26]. Thehydroxamic acids were then purified by crystallizing thrice withbenzene and dried over phosphorus pentoxide in vacuum for sev-eral hours. The purity of the compounds was ascertained by deter-mining their melting temperatures, IR spectra, and elementalanalyses. Melting temperatures were determined with meltingpoint apparatus (TEMPO), and are uncorrected. The uncertaintyof measurements was ±1 �C. Elemental analyses were performedwith a Vario-EL analysis apparatus. IR spectra were recorded witha FTIR 8400 series Shimazdu (Japan) using KBr pellets. The datawere tallied with the literature [27]. DMF, Merck (mass fractionpurity > 0.998) was used without further purification. Stock solu-tions of PBHA (0.2345 M), PMNHA (0.1838 M), and PNHA(0.1936 M) were prepared in DMF. Solutions of varying concentra-tions were then obtained from the stock solution by mass dilutiontechnique. Uncertainties in solution concentration were estimatedto be ±0.001 unit. The characteristics of synthesized compoundsand specification of the purity of sample are given in tables 1and 1a.
2.2. Measurement of density, q
Densities of DMF and hydroxamic acid solutions were deter-mined using a 103 cm3 double-armed pycnometer at temperaturesT = (298.15, 303.15, 308.15, and 313.15) K. The pycnometer wascalibrated thrice at each temperature with freshly prepared tripledistilled water and data were averaged. The estimated precision
TABLE 1Characteristics of hydroxamic acids.
S.No.
Hydroxamic acids 3D structure Meltingtempera
Observed
I N– phenylbenzohydroxamic acid,(C13H11NO2)
122 �C
II N–phenyl-4-methyl-3-nitrobenzohydroxamic acid,(C14H12N2O4)
117 �C
III N-phenyl-4-nitrobenzohydroxamic acid,(C13H10N2O4)
168 �C
a Reference [28].b Reference [29].c Reference [30].
TABLE 1aSpecifications of the chemical sample. GC = Gas–liquid chromatography.
Chemical name Source Mass fraction purity
N,N-Dimethylformamide (DMF) Merck >0.998
of the measurements of solutions is ±3 � 10�4 g � cm�3 and theuncertainty in the density measurements is ±2 � 10�4 g � cm�3.
2.3. Measurement of refractive index, n
Steric parameters were measured as refractive indices with athermostatted Abbe’s refractometer as a function of solutes’ con-centration at T = (298.15, 303.15, 308.15, and 313.15) K. The refrac-tometer was calibrated by measuring the refractive indices of tripledistilled water and solvent at known temperature. Temperaturewas controlled by circulating water around prism of the refractom-eter from thermostatically controlled and adequately stirred waterbath (accuracy ±0.1 �C). The sample solutions were directly in-jected into prism assembly by means of an airtight hypodermicsyringe. The error in refractive index measurement is less than±0.0001 units. Table 2 reports the densities and refractive indicesof DMF and hydroxamic acids.
3. Results and discussion
The q and n values of PBHA, PMNHA, and PNHA in DMF atT = (298.15, 303.15, 308.15, and 313.15) K are presented as a func-tion of their concentrations in table 3. Figures 1 and 2 show that qand n increase with an increase in the concentration of hydroxamicacids, respectively.
tureIR (cm�1) Elemental analyses
Reported Observed Observed Theoretical
t(O–H)/cm�1
t(C@O)/cm�1
t(C–N)/cm�1
t(N–O)/cm�1
C H N C H N
121 �Ca 3100 1642 1340 915 73.29 4.91 6.46 73.23 5.20 6.57
117 �Cb
119 �Cc3080 1647 1350 946 61.67 4.04 9.93 61.76 4.44 10.29
168 �Ca 3186 1612 1349 916 60.46 3.81 10.73 60.47 3.90 10.85
Purification method Analysis method
Chemical used without further purification GC
Table 2Properties of DMF and hydroxamic acids at different temperatures.
T/K DMF Hydroxamic acids
q0/(g � cm�3) no q1/(g � cm�3) n1
(Exptl.) (Lit.) (Exptl.) (Lit.) I II III I II III
298.15 0.9452 0.9445a,b 1.4270 1.4270j 0.9458 1.4370 0.9456 1.4269 1.4371 1.42750.9442c 1.42817d
0.9439d 1.4282k,l
0.94387e 1.4275m
0.94403f 1.4288d
0.94421g
303.15 0.9397 0.9397h 1.4253 1.4245b 0.9404 1.4335 0.9402 1.4257 1.4336 1.42590.9398b
0.9395d
0.93945g
308.15 0.9356 0.9356h 1.4230 1.4220b 0.9363 1.4302 0.9362 1.4241 1.4302 1.4238313.15 0.9302 0.9298i 1.4210 1.4205b 0.9312 1.4285 0.9309 1.4221 1.4286 1.4220
0.92986g
0.9302b
a Reference [31].b Reference [32].c Reference [33].d Reference [34].e Reference [35].f Reference [36].g Reference [37].h Reference [38].i Reference [39].j Reference [40].k Reference [41].l Reference [42].m Reference [43].
120 S. Patre et al. / J. Chem. Thermodynamics 54 (2012) 118–128
3.1. Volumetric studies
The experimental values of solutions’ q are used to calculate theV/ by means of the following expression [44]:
V/ ¼ 1000ðq0 � qÞ=Cqq0 þM2=q; ð1Þ
where V/ is the apparent molar volumes, C is the molarity of solutein the solutions, M2 is the molar mass of the solute and q0 and q arethe densities of DMF and the solutions, respectively. The values of Vand V/ are listed in table 3. The positive values of V/ for all the mol-ecules indicate strong solute–solvent interactions. These interac-tions are strengthened with increasing concentration at aparticular temperature and are weakened with a rise in tempera-ture at a constant solutes’ concentration as shown in figure 3. Theapparent molar volume at infinite dilution is calculated by aleast-squares treatment of the plot of V/ vs C1/2 using Masson’sexpression [45]:
V/ ¼ V0/ þ S�V C1=2; ð2Þ
where V0/ is the apparent molar volume at infinite dilution and S�V is
the experimental slope. The data are listed in table 4. The V0/ is re-
garded as resulting from solute–solvent interactions. The positivevalues indicate the presence of strong solute–solvent interactions.These interactions are weakened with a rise in temperature asshown in figure 4.
The temperature dependence of V0/ [46] for the compounds
studied is expressed by the equation:
V0/ ¼ aþ bT þ cT2: ð3Þ
The temperature T is expressed in Kelvin. The coefficients a, b, and cwere estimated by the least-square fitting of the V0
/ in equation (3)and the following equations are formulated:
V0/ ¼ �5867:524ð�3617:909Þ þ 40:628ð�23:691ÞT
� 0:069ð�0:038ÞT2; ð4Þ
V0/ ¼ �3202:809ð�2368:541Þ � 18:989ð�15:509ÞT
þ 0:028ð�0:025ÞT2; ð5Þ
V0/ ¼ �741:115ð�237:021Þ þ 7:163ð�1:552ÞT
� 0:014ð�0:002ÞT2: ð6Þ
The limiting apparent molar expansibilities are obtained by dif-ferentiating equation (3) with respect to temperature:
/0E ¼ ð@V0
/=@TÞP ¼ bþ 2cT; ð7Þ
where /0E is apparent molar expansibilities at infinite dilution and p
is the pressure. The /0E values are an important indicator of solute–
solvent interactions. The data of /0E of the solutes in the solvent can
be useful in interpreting the structure making or breaking proper-ties of the solutes. It is evident from table 4 that the values of /0
E
are negative (i.e., decreasing volume with increasing temperature)which show highly hydrophobic characters of these molecules.From the apparent molar volume at infinite dilution V0
/, the valuesof the thermal expansion coefficients of the solute at infinite dilu-tion a2 are also determined using the following equation [47] andare given in table 4:
a2 ¼ ð1=@V0/Þð@V0
/=@TÞP ¼ /0E=V0
/: ð8Þ
Furthermore, the values of thermal expansion coefficient, a2, asin table 4 show a decrease with increasing temperature. When thetemperature is increased, the density of the solution decreases, ta-ble 3, resulting in the thermal expansivity coefficient, a2.The He-pler’s constant, @2V//oT2, Hepler [48] has been calculated usingequation (3) and the values are listed in table 4. According to He-pler, the sign of @2V//oT2 is a better criterion in characterisingthe structure making and breaking ability of the solutes in solu-tions. If @2V//oT2 is positive, the solute is a structure maker and ithas a negative value for a structure breaker solute. In the present
TABLE 3Density, q, refractive index, n, apparent molar volume, V/, molar volume, V, refractivity, l, specific refraction, RS, molar refraction, RM, polarizability, a, of hydroxamic acids in DMFat different temperatures.
M, solute/(mol � kg�1) q/(g � cm�3) n V//(cm3 �mol�1) V/(cm3 �mol�1) l RS/cm�3 RM/(cm3 �mol�1) a/(cm3 �mol�1)
PBHAT = 298.15 K
0.0234 0.9475 1.4275 115.522 77.418 0.4275 0.2712 19.897 0.78900.0469 0.9497 1.4277 117.630 77.508 0.4277 0.2707 19.928 0.79030.0703 0.9518 1.4280 119.740 77.605 0.4280 0.2703 19.966 0.79170.0938 0.9539 1.4285 120.659 77.703 0.4285 0.2699 20.011 0.79350.1172 0.9559 1.4288 122.059 77.809 0.4288 0.2695 20.051 0.79510.1407 0.9579 1.4289 122.903 77.916 0.4289 0.2690 20.082 0.79640.1641 0.9599 1.4295 123.430 78.023 0.4295 0.2688 20.134 0.79840.1876 0.9618 1.4300 124.359 78.138 0.4300 0.2685 20.185 0.80040.2110 0.9637 1.4305 125.024 78.254 0.4305 0.2683 20.235 0.80240.2345 0.9654 1.4310 126.466 78.387 0.4310 0.2681 20.290 0.8046
PBHAT = 303.15 K
0.0234 0.9421 1.4260 110.722 77.8641 0.4260 0.2719 19.950 0.79110.0469 0.9444 1.4269 112.855 77.9460 0.4269 0.2718 20.008 0.79340.0703 0.9466 1.4271 114.990 78.0364 0.4271 0.2712 20.039 0.79470.0938 0.9488 1.4274 115.919 78.1269 0.4274 0.2708 20.075 0.79610.1172 0.9509 1.4275 117.334 78.2261 0.4275 0.2702 20.105 0.79730.1407 0.9530 1.4280 118.186 78.3255 0.4280 0.2699 20.151 0.79910.1641 0.9549 1.4285 120.101 78.4419 0.4285 0.2697 20.201 0.80110.1876 0.9569 1.4289 120.866 78.5503 0.4289 0.2693 20.246 0.80290.2110 0.9588 1.4295 121.942 78.6675 0.4295 0.2691 20.301 0.80500.2345 0.9607 1.4300 122.750 78.7850 0.4300 0.2688 20.352 0.8071
PBHAT = 308.15 K
0.0234 0.9381 1.4238 105.827 78.197 0.4238 0.2718 19.945 0.79090.0469 0.9405 1.4249 107.980 78.271 0.4249 0.2718 20.009 0.79350.0703 0.9428 1.4259 110.134 78.354 0.4259 0.2717 20.072 0.79600.0938 0.9451 1.4266 111.071 78.437 0.4266 0.2714 20.122 0.79790.1172 0.9473 1.4270 112.498 78.528 0.4270 0.2710 20.162 0.79950.1407 0.9495 1.4273 113.357 78.620 0.4273 0.2705 20.198 0.80090.1641 0.9515 1.4276 115.286 78.729 0.4276 0.2701 20.238 0.80250.1876 0.9536 1.4280 116.056 78.829 0.4280 0.2697 20.281 0.80420.2110 0.9556 1.4282 117.138 78.939 0.4282 0.2693 20.317 0.80570.2345 0.9575 1.4288 118.440 79.057 0.4288 0.2691 20.372 0.8079
PBHAT = 313.15 K
0.0234 0.9329 1.4220 95.879 78.634 0.4220 0.2723 19.982 0.79240.0469 0.9354 1.4230 100.524 78.701 0.4230 0.2722 20.040 0.79470.0703 0.9378 1.4240 103.525 78.776 0.4240 0.2720 20.101 0.79710.0938 0.9401 1.4250 106.117 78.860 0.4250 0.2719 20.164 0.79960.1172 0.9424 1.4261 107.561 78.944 0.4261 0.2719 20.231 0.80230.1407 0.9445 1.4265 110.072 79.045 0.4265 0.2715 20.274 0.80400.1641 0.9466 1.4271 111.788 79.146 0.4271 0.2712 20.325 0.80600.1876 0.9486 1.4273 113.624 79.257 0.4273 0.2708 20.361 0.80740.2110 0.9506 1.4274 114.992 79.367 0.4274 0.2703 20.394 0.80870.2345 0.9525 1.4275 116.528 79.487 0.4275 0.2698 20.429 0.8101
PMNHAT = 298.15 K
0.0184 0.9478 1.4391 129.136 77.424 0.4391 0.2775 20.369 0.80770.0368 0.9502 1.4406 134.869 77.527 0.4406 0.2776 20.456 0.81120.0551 0.9526 1.4420 136.544 77.631 0.4420 0.2777 20.540 0.81450.0735 0.9548 1.4440 140.249 77.751 0.4440 0.2782 20.653 0.81900.0919 0.9570 1.4470 142.333 77.872 0.4470 0.2791 20.806 0.82510.1103 0.9591 1.4483 144.622 78.001 0.4483 0.2792 20.893 0.82850.1286 0.9611 1.4496 147.031 78.139 0.4496 0.2794 20.983 0.83210.1470 0.9631 1.4520 148.754 78.278 0.4520 0.2801 21.117 0.83740.1654 0.9650 1.4535 150.698 78.425 0.4535 0.2803 21.217 0.84140.1838 0.9669 1.4550 152.188 78.573 0.4550 0.2806 21.318 0.8454
PMNHAT = 303.15 K
0.0184 0.9424 1.4350 122.802 77.870 0.4350 0.2768 20.319 0.80580.0368 0.9449 1.4370 128.605 77.966 0.4370 0.2772 20.426 0.81000.0551 0.9474 1.4390 130.303 78.062 0.4390 0.2776 20.532 0.81420.0735 0.9497 1.4410 134.053 78.175 0.4410 0.2780 20.643 0.81860.0919 0.9520 1.4441 136.162 78.289 0.4441 0.2790 20.800 0.82480.1103 0.9542 1.4455 138.478 78.411 0.4455 0.2791 20.889 0.82840.1286 0.9563 1.4466 140.913 78.542 0.4466 0.2791 20.969 0.83150.1470 0.9584 1.4480 142.654 78.674 0.4480 0.2793 21.061 0.83520.1654 0.9604 1.4500 144.618 78.814 0.4500 0.2798 21.180 0.83990.1838 0.9623 1.4520 146.740 78.964 0.4520 0.2803 21.302 0.8447
(continued on next page)
S. Patre et al. / J. Chem. Thermodynamics 54 (2012) 118–128 121
TABLE 3 (continued)
M, solute/(mol � kg�1) q/(g � cm�3) n V//(cm3 �mol�1) V/(cm3 �mol�1) l RS/cm�3 RM/(cm3 �mol�1) a/(cm3 �mol�1)
PMNHAT = 308.15 K
0.0184 0.9384 1.4320 116.397 78.203 0.4320 0.2763 20.283 0.80430.0368 0.9410 1.4343 122.256 78.291 0.4343 0.2769 20.401 0.80900.0551 0.9435 1.4360 126.042 78.388 0.4360 0.2771 20.495 0.81280.0735 0.9459 1.4380 129.309 78.494 0.4380 0.2775 20.605 0.81710.0919 0.9482 1.4400 132.369 78.609 0.4400 0.2779 20.717 0.82150.1103 0.9504 1.4420 135.326 78.732 0.4420 0.2784 20.831 0.82610.1286 0.9526 1.4430 137.340 78.856 0.4430 0.2783 20.905 0.82900.1470 0.9547 1.4460 139.540 78.988 0.4460 0.2793 21.063 0.83530.1654 0.9567 1.4480 141.866 79.130 0.4480 0.2798 21.183 0.84000.1838 0.9587 1.4494 143.659 79.272 0.4494 0.2799 21.279 0.8438
PMNHAT = 313.15 K
0.0184 0.9331 1.4299 109.776 78.649 0.4299 0.2767 20.312 0.80550.0368 0.9358 1.4320 115.710 78.730 0.4320 0.2771 20.420 0.80980.0551 0.9384 1.4340 119.546 78.819 0.4340 0.2775 20.526 0.81400.0735 0.9409 1.4354 122.855 78.918 0.4354 0.2776 20.609 0.81730.0919 0.9433 1.4370 125.953 79.025 0.4370 0.2777 20.703 0.82100.1103 0.9457 1.4390 127.902 79.133 0.4390 0.2781 20.814 0.82540.1286 0.9479 1.4410 130.984 79.258 0.4410 0.2785 20.929 0.83000.1470 0.9501 1.4429 133.210 79.383 0.4429 0.2789 21.041 0.83440.1654 0.9522 1.4440 135.561 79.517 0.4440 0.2790 21.122 0.83760.1838 0.9543 1.4450 137.374 79.652 0.4450 0.2794 21.240 0.8423
PNHAT = 298.15 K
0.0194 0.9475 1.4280 139.902 77.443 0.4280 0.2715 19.924 0.79010.0387 0.9497 1.4289 142.454 77.557 0.4289 0.2713 19.990 0.79270.0581 0.9519 1.4294 143.082 77.671 0.4294 0.2710 20.040 0.79470.0775 0.9540 1.4299 144.676 77.793 0.4299 0.2707 20.092 0.79670.0968 0.9561 1.4300 145.501 77.917 0.4300 0.2701 20.127 0.79820.1162 0.9582 1.4305 145.943 78.040 0.4305 0.2698 20.180 0.80020.1355 0.9602 1.4315 146.994 78.172 0.4315 0.2698 20.255 0.80320.1549 0.9622 1.4325 147.702 78.305 0.4325 0.2698 20.330 0.80620.1743 0.9642 1.4329 148.183 78.438 0.4329 0.2694 20.381 0.80820.1936 0.9661 1.4330 149.085 78.580 0.4330 0.2690 20.422 0.8099
PNHAT = 303.15 K
0.0194 0.9421 1.4264 134.089 77.888 0.4264 0.2721 19.973 0.79200.0387 0.9444 1.4274 136.672 77.995 0.4274 0.2720 20.041 0.79470.0581 0.9467 1.4279 137.308 78.102 0.4279 0.2717 20.089 0.79670.0775 0.9489 1.4285 138.920 78.218 0.4285 0.2714 20.144 0.79880.0968 0.9511 1.4290 139.755 78.334 0.4290 0.2710 20.194 0.80080.1162 0.9532 1.4295 141.176 78.459 0.4295 0.2707 20.247 0.80290.1355 0.9553 1.4302 142.099 78.584 0.4302 0.2705 20.308 0.80530.1549 0.9574 1.4311 142.710 78.710 0.4311 0.2704 20.378 0.80810.1743 0.9594 1.4319 143.765 78.844 0.4319 0.2702 20.446 0.81080.1936 0.9614 1.4322 144.546 78.979 0.4322 0.2698 20.493 0.8127
PNHAT = 308.15 K
0.0194 0.9381 1.4242 128.160 78.222 0.4242 0.2721 19.968 0.79180.0387 0.9405 1.4254 130.768 78.321 0.4254 0.2720 20.043 0.79480.0581 0.9428 1.4259 133.376 78.429 0.4259 0.2717 20.091 0.79670.0775 0.9451 1.4266 134.512 78.537 0.4266 0.2714 20.148 0.79900.0968 0.9473 1.4271 136.239 78.654 0.4271 0.2710 20.198 0.80100.1162 0.9495 1.4276 137.280 78.772 0.4276 0.2707 20.249 0.80300.1355 0.9516 1.4286 138.773 78.898 0.4286 0.2706 20.323 0.80590.1549 0.9537 1.4292 139.811 79.025 0.4292 0.2704 20.381 0.80820.1743 0.9558 1.4301 140.546 79.152 0.4301 0.2703 20.451 0.81100.1936 0.9578 1.4304 141.662 79.288 0.4304 0.2699 20.498 0.8129
PNHAT = 313.15 K
0.0194 0.9328 1.4223 122.078 78.668 0.4223 0.2726 20.003 0.79320.0387 0.9353 1.4235 124.719 78.760 0.4235 0.2725 20.076 0.79610.0581 0.9377 1.4244 127.361 78.861 0.4244 0.2723 20.139 0.79860.0775 0.9400 1.4249 130.002 78.970 0.4249 0.2719 20.188 0.80060.0968 0.9423 1.4258 131.453 79.080 0.4258 0.2718 20.254 0.80320.1162 0.9445 1.4266 133.302 79.198 0.4266 0.2716 20.317 0.80570.1355 0.9467 1.4271 134.528 79.317 0.4271 0.2712 20.369 0.80770.1549 0.9488 1.4275 136.111 79.445 0.4275 0.2709 20.418 0.80970.1743 0.9508 1.4284 137.934 79.582 0.4284 0.2708 20.491 0.81260.1936 0.9529 1.4291 138.730 79.711 0.4291 0.2705 20.553 0.8151
M is the olarities of hydroxamic acids in the solvent (DMF). Standard uncertainties u are u(M) = 0.0001, u(q) = 2 � 10�4 g � cm�3, u(n) = 0.0002, u(V/) = 0.003 cm3 �mol�1,u(V) = 0.001 cm3 �mol�1, u(l) = 0.0001, u(RS) = 0.0001 cm�3, u(RM) = 0.006 cm3 �mol�1, u(a) = 0.0003 cm3 �mol�1.
122 S. Patre et al. / J. Chem. Thermodynamics 54 (2012) 118–128
0.00 0.01 0.02
1.422
1.423
1.424
1.425
1.426
1.427
1.428
1.429
1.430
1.431
n
M
0.00 0.01 0.02 0.03 0.04 0.051.4281.4301.4321.4341.4361.4381.4401.4421.4441.4461.4481.4501.4521.4541.456
(B)
n
M/mol.kg-1
FIGURE 2. Plot of refractive index (n) vs concentration (M) of (A) PBHA, (B) PMNHA, andand ", 313.15 K.
0.00 0.01 0.02 0.03 0.04 0.05
0.936
0.942
0.948
0.954
0.960
0.966
0.00 0.01 0.02 0.03 0.04 0.05
0.936
0.942
0.948
0.954
0.960
0.966
(C)
ρ /
( g
. cm
-3 )
M/mol.kg-1
0.00 0.01 0.02 0.03 0.04 0.05
0.936
0.942
0.948
0.954
0.960
0.966
(B)
ρ /
( g
. cm
-3 )
M/mol.kg-1
(A)
ρ /
( g
. cm
-3 )
M/mol.kg-1
FIGURE 1. Plot of density (q) vs concentration (M) of (A) PBHA, (B) PMNHA, and (C)PNHA in DMF at different temperatures: j, 298.15 K; d, 303.15 K; J, 308.15 K; and", 313.15 K.
S. Patre et al. / J. Chem. Thermodynamics 54 (2012) 118–128 123
investigation, the observed positive values of Hepler’s constant,@2V//oT2, for three molecules suggest the structure promoter nat-ure of these solutes in solution.
The molar volume, V, of the solutions has been computed fromthe measured values of q, using the equation [49]:
V ¼ ðx1M1 þ x2M2Þ=q; ð9Þ
where x1, M1 and x2, M2 are the mole fraction and molar mass of thesolvent and solute, respectively. The data are listed in table 3.
3.2. Optical properties
The refractive indices, n, data have been used to calculaterefractivity l (=n � 1) and specific refraction, Rs, of these reagentswhich are presented in table 3. The values of the Rs are also com-puted as a function of their concentration in DMF following theequation (10), proposed by Lorentz and Lorenz:
Rs ¼ ðn2 � 1Þ=ðn2 þ 2Þ � 1=q ð10Þ
0.03 0.04 0.05
(A)
/mol.kg-1
0.00 0.01 0.02 0.03 0.04 0.05
1.422
1.423
1.424
1.425
1.426
1.427
1.428
1.429
1.430
1.431
1.432
1.433
(C)
n
M/mol.kg-1
(C) PNHA in DMF at different temperatures: j, 298.15 K; d, 303.15 K; J, 308.15 K;
0.00 0.01 0.02 0.03 0.04 0.05
96
102
108
114
120
126
(A)
Vφ /
( c
m 3. m
ol -1
)
M/mol.kg-1
0.00 0.01 0.02 0.03 0.04 0.05
110
120
130
140
150
(B)
Vφ /
( c
m 3. m
ol -1
)
M/mol.kg-1
0.00 0.01 0.02 0.03 0.04 0.05120
124
128
132
136
140
144
148
(C)
Vφ /
( c
m 3. m
ol -1
)
M/mol.kg-1
FIGURE 3. Plot of apparent molar volume (V/) vs concentration (M) of (A) PBHA, (B) PMNHA, and (C) PNHA in DMF at different temperatures: j, 298.15 K; d, 303.15 K;J, 308.15 K; and ", 313.15 K.
TABLE 4Apparent molar volume at infinite dilution, V0
/ , experimental slop, S�V , and apparent molar expansibilities at infinite dilution, /0E , thermal expansion coefficient, a2, Hepler’s
constant, o2V//oT2, of hydroxamic acids in DMF at different temperatures.
T/K V0//(cm3 �mol�1) S�V / (cm3 �mol�3/2 � dm�3/2) /0
E/cm3 �mol�1) a2/K�1o2V0
// oT2/(cm3 �mol�1)
PBHA298.15 110.986(±0.34) 31.369(±0.95) �0.5167 �0.0046303.15 104.990(±0.30) 36.554(±0.84) �1.2067 �0.0114 �0.1380308.15 99.878(±0.35) 37.496(±0.98) �1.8967 �0.0189313.15 86.980(±0.33) 61.270(±0.94) �2.5867 �0.0297
PMNHA298.15 118.989(±0.51) 77.656(±1.62) �2.2926 �0.0192303.15 112.322(±0.54) 79.487(±1.71) �2.0126 �0.0179 +0.0560308.15 104.267(±0.27) 92.400(±0.83) �1.7327 �0.0166313.15 97.500(±0.31) 93.198(±0.99) �1.4526 �0.0149
PNHA298.15 136.284(±0.32) 29.004(±0.97) �1.1852 �0.0087303.15 129.439(±0.29) 34.112(±0.89) �1.3252 �0.0102 �0.0280308.15 122.170(±0.26) 44.597(±0.80) �1.4652 �0.0119313.15 113.909(±0.26) 56.654(±0.81) �1.6052 �0.0140
Standard uncertainties u are u(T) = 0.01 K, u(V0/) = 0.003 cm3 �mol�1, u(S�V ) = 0.0004 cm3 �mol�3/2 � dm�3/2, u(/0
E) = 0.0006 cm3 �mol�1, u(a2) = 0.0001 K�1, u(o2V//oT2) = 0.0001 cm3 �mol�1.
124 S. Patre et al. / J. Chem. Thermodynamics 54 (2012) 118–128
296 300 304 308 312
90
100
110
120
130
140
Vφ0 /
(cm
3. m
ol -1
)
T/K
FIGURE 4. Plot of apparent molar volume at infinite dilution (V0/) vs T = (298.15,
303.15 308.15, and 313.15) K of (j) PBHA, (d) PMNHA, and (") PNHA in DMF.
S. Patre et al. / J. Chem. Thermodynamics 54 (2012) 118–128 125
The n of a material is estimated in terms of the molar refraction,RM, which quantifies the intrinsic refractive power of the structuralunits constituting that material. A definition proposed for RM thatincorporates both of the key physical factors determining the n,is the molar refraction according to Lorentz and Lorentz [50]:
RM ¼ ½ðn2 � 1=n2 þ 2Þ� � V ; ð11Þ
TABLE 5Excess molar volume, VE, refractive index deviation, nE, and molar refraction deviation, RE
M
Mole fraction, x2 VE/(cm3 �mol�1) nE
T = 298.15 K 303.15 K 308.15 K 313.15 K 298.15 K 3
PBHA0.0018 �0.1881 �0.1985 �0.2086 �0.2278 0.0005 00.0036 �0.3685 �0.3892 �0.4093 �0.4391 0.0007 00.0055 �0.5411 �0.5721 �0.6020 �0.6423 0.0010 00.0073 �0.7142 �0.7553 �0.7952 �0.8375 0.0015 00.0091 �0.8795 �0.9308 �0.9804 �1.0332 0.0018 00.0110 �1.0453 �1.1067 �1.1661 �1.2126 0.0019 00.0128 �1.2116 �1.2667 �1.3357 �1.3924 0.0025 00.0147 �1.3702 �1.4353 �1.5141 �1.5643 0.0030 00.0165 �1.5293 �1.5962 �1.6846 �1.7367 0.0035 00.0184 �1.6726 �1.7576 �1.8474 �1.9012 0.0040 0
PMNH0.0014 �0.2125 �0.2233 �0.2335 �0.2447 0.0120 00.0028 �0.4093 �0.4306 �0.4509 �0.4730 0.0135 00.0043 �0.6065 �0.6383 �0.6604 �0.6933 0.0149 00.0057 �0.7880 �0.8302 �0.8622 �0.9058 0.0169 00.0072 �0.9701 �1.0226 �1.0563 �1.1105 0.0199 00.0086 �1.1446 �1.2074 �1.2426 �1.3157 0.0212 00.0101 �1.3116 �1.3845 �1.4295 �1.5047 0.0224 00.0115 �1.4791 �1.5622 �1.6087 �1.6944 0.0248 00.0130 �1.6392 �1.7323 �1.7803 �1.8763 0.0263 00.0144 �1.7998 �1.8948 �1.9525 �2.0588 0.0278 0
PNHA0.0015 �0.1882 �0.1987 �0.2087 �0.2195 0.0010 00.0030 �0.3688 �0.3896 -0.4096 �0.4311 0.0018 00.0045 �0.5499 �0.5811 �0.6027 �0.6348 0.0023 00.0060 �0.7235 �0.7648 �0.7963 �0.8306 0.0028 00.0075 �0.8975 �0.9491 �0.9822 �1.0269 0.0029 00.0091 �1.0721 �1.1258 �1.1686 �1.2154 0.0034 00.0106 �1.2392 �1.3030 �1.3473 �1.4045 0.0044 00.0121 �1.4068 �1.4807 �1.5266 �1.5858 0.0054 00.0137 �1.5750 �1.6508 �1.7064 �1.7593 0.0058 00.0152 �1.7356 �1.8215 �1.8786 �1.9418 0.0059 0
Standard uncertainties u are u(x2) = 0.0001, u(VE) = 0.0003 cm3 �mol�1, u(nE) = 0.0002, u(
where V is the molar volume. The values of RM are reported in table3. Values of RM increase linearly with concentration and are propor-tional to the dispersive forces. Thus, the increasing magnitude of RM
for PBHA, PMNHA, and PNHA in DMF indicates strong solute–solvent interactions.
The n related to the polarizability, a, depends on geometry ofthe molecules, a is a fundamental molecular property of greatimportance, it defines the nature of intermolecular attractive forcefor non-polar molecules. Therefore, in order to gain further infor-mation about specific intermolecular interactions of any kind, aof the system is computed by equation:
a ¼ 3RM=4pN; ð12Þ
where a is the electronic polarizability and N is Avogadro’s number.a of molecules is one of the most significant electric properties,which characterises the ability of the electronic system to be dis-torted by the external electric filed. table 3 enlists the values of aand shows that a, of hydroxamic acid solutions increases with con-centration. This trend is slightly influenced by temperature and theobvious decrease with temperature indicates the presence of inter-molecular and intramolecular interactions between the moleculesof the solute and the solvent. The n characteristics show that the di-pole in the compound lies perpendicular to the longer axis of themolecules and is responsible for the intermolecular attractionswhich is further accompanied by increase in the value of RM anda with increasing concentration of solution because of mutual com-pensation of dipoles.
, of hydroxamic acids in DMF at different temperatures.
REM
03.15 K 308.15 K 313.15 K 298.15 K 303.15 K 308.15 K 313.15 K
.0006 0.0007 0.0009 �0.0279 �0.0222 �0.0204 �0.0165
.0015 0.0018 0.0019 �0.0660 �0.0342 �0.0263 �0.0288
.0017 0.0028 0.0029 �0.0981 �0.0728 �0.0343 �0.0390
.0020 0.0035 0.0039 �0.1220 �0.1073 �0.0548 �0.0471
.0021 0.0039 0.0050 �0.1521 �0.1481 �0.0855 �0.0511
.0026 0.0042 0.0054 �0.1905 �0.1725 �0.1204 �0.0800
.0031 0.0045 0.0060 �0.2085 �0.1928 �0.1512 �0.1006
.0035 0.0049 0.0062 �0.2285 �0.2194 �0.1801 �0.1358
.0041 0.0051 0.0063 �0.2487 �0.2357 �0.2152 �0.1752
.0046 0.0057 0.0064 �0.2647 �0.2561 �0.2316 �0.2126
A.0096 0.0089 0.0088 0.4334 0.3371 0.3084 0.3045.0116 0.0112 0.0109 0.4418 0.3642 0.3458 0.3319.0136 0.0129 0.0129 0.4462 0.3912 0.3608 0.3574.0156 0.0149 0.0143 0.4791 0.4225 0.3902 0.3602.0187 0.0169 0.0159 0.5523 0.4985 0.4218 0.3734.0201 0.0189 0.0179 0.5591 0.5076 0.4555 0.4031.0212 0.0199 0.0199 0.5680 0.5066 0.4482 0.4372.0226 0.0229 0.0218 0.6214 0.5178 0.5251 0.4671.0245 0.0248 0.0229 0.6406 0.5556 0.5632 0.4662.0265 0.0262 0.0238 0.6598 0.5957 0.5767 0.5024
.0010 0.0011 0.0012 �0.0077 �0.0059 �0.0038 �0.0019
.0020 0.0023 0.0024 �0.0174 �0.0138 �0.0056 -0.0059
.0025 0.0028 0.0033 -0.0435 �0.0423 �0.0342 �0.0203
.0031 0.0035 0.0038 �0.0676 �0.0646 �0.0546 �0.0492
.0036 0.0040 0.0047 �0.1081 �0.0912 �0.0812 �0.0615
.0041 0.0045 0.0055 �0.1323 �0.1157 �0.1079 �0.0759
.0048 0.0055 0.0060 �0.1341 �0.1320 �0.1119 �0.1029
.0057 0.0061 0.0064 �0.1359 �0.1402 �0.1324 �0.1320
.0065 0.0070 0.0073 �0.1623 �0.1504 �0.1406 �0.1382
.0068 0.0073 0.0080 �0.1991 �0.1813 �0.1717 �0.1549
REM) = 0.0003.
0.000 0.004 0.008 0.012 0.016 0.020
-2.0
-1.6
-1.2
-0.8
-0.4
0.0
0.000 0.004 0.008 0.012 0.016
-2.0
-1.6
-1.2
-0.8
-0.4
0.0(B)
VE /
(cm
3 ·
mol
-1 )
x2
0.000 0.004 0.008 0.012 0.016-2.0
-1.6
-1.2
-0.8
-0.4
0.0(C)
V E
/ (c
m3 ·
mol
-1)
x2
(A)
VE /(
cm 3 ·m
ol -1
)
x2
FIGURE 5. Plot of excess molar volume (VE) vs mole fraction (x2) of (A) PBHA, (B)PMNHA, and (C) PNHA in DMF at different temperatures: j, 298.15 K; d, 303.15 K;N, 308.15 K; and ., 313.15 K.
0.000 0.004 0.0080.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
nE
0.000 0.004 0.008 0.012 0.016
0.008
0.012
0.016
0.020
0.024
0.028
(B)
nE
x2
FIGURE 6. Plot of refractive index deviation (nE) vs mole fraction (x2) of (A) PBHA, (B) PJ, 308.15 K; and ", 313.15 K.
126 S. Patre et al. / J. Chem. Thermodynamics 54 (2012) 118–128
3.3. Excess properties
The excess properties of the solution are calculated using thefollowing equation:
YE ¼ Y � ðx1Y1 þ x2Y2Þ; ð13Þ
where YE represents the excess molar volume, VE, or refractive indexdeviation, nE, or molar refraction deviation, RE
M . The VE, nE and REM of
DMF, PBHA, PMNHA, PNHA, and their solutions are denoted by Y1,Y2 and Y, respectively; x1 and x2, are mole fractions of solvent andsolute, respectively. The calculated values are listed in table 5.According to Nakata and Sakurai [51], the sign of nE is opposite tothat of VE, if the behaviour of n is not linear between n1 and n2. Thisrule is truly fulfilled for all the hydroxamic acids. The values of nE
are positive over the entire concentration range and at differenttemperatures. Thus, dispersion forces in the solution are higherthan in solvent. VE is influenced by: (i) physical interactions mainlydue to dispersive force, (ii) the dipole–dipole and donor–acceptorinteraction between unlike molecules, and (iii) the filling of smallermolecules into the voids created by bigger molecules. VE is a mea-sure of the deviations from the actual property if the system be-haves ideally and gives information on molecular interactionsbetween the solvent molecules of the solution and are influencedby effects such as differences in shape and size of solvent molecules,
0.012 0.016 0.020
(A)
x2
0.000 0.004 0.008 0.012 0.016
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
(C)
nE
x2
MNHA, and (C) PNHA in DMF at different temperatures: j, 298.15 K; d, 303.15 K;
0.000 0.004 0.008 0.012 0.016 0.020-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
(A)
R E
M
x2
0.000 0.004 0.008 0.012 0.016-0.22
-0.20
-0.18
-0.16
-0.14
-0.12
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
(C)
RE M
x2
0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
(B)
RE M
x2
FIGURE 7. Plot of molar refraction deviation (REM) vs mole fraction (x2) of (A) PBHA, (B) PMNHA, and (C) PNHA in DMF at different temperatures: j, 298.15 K; d, 303.15 K;
J, 308.15 K; and ", 313.15 K.
S. Patre et al. / J. Chem. Thermodynamics 54 (2012) 118–128 127
reorientation of the solvent molecules in the solution, and intermo-lecular interactions [52,53]. It is well known that VE is the result ofseveral opposing effects. Interaction between like molecules lead toincreased VE values, while negative contribution arises from inter-actions between unlike molecules, or structural effects as changein free volume or interstitial accommodation. For the investigatedsystems, the negative VE values may be due to interactions betweenunlike molecules as shown in figure 5.
The refractive index deviation, nE, is positive over the wholeconcentration range and at various temperatures. As indicatedin figure 6, the value increases with temperature. The knowledgeof VE helps in understanding the molecular orientation and tostudy the extent of intermolecular interactions between solventmolecules of the solution. The negative values of RE
M throughoutthe concentration and temperature range, as shown in figure 7,indicate the presence of strong intermolecular interactions.
We can remark that the effect of temperature is not very signif-icant for the hydroxamic acids due to the smaller nE and VE valueswith increase in temperature.
4. Conclusions
Physicochemical properties of PBHA, PMNHA, and PNHA aresubject to numerous investigations today. Using density and
refractive index data, the other related parameters, viz, apparentmolar volume, apparent molar volume at infinite dilution, expansi-bility, molar refraction and excess properties have been computed.The thermal expansion coefficients of the three molecules are alsodetermined. The behaviour of the molecules suggests strong sol-ute–solvent interactions in the system. These data are of furtherimportance in biological, physical, and environmental chemistry.
Acknowledgements
The authors are thankful to University Grants Commission, NewDelhi for providing Fellowships to Sandhya Patre and Piyush Tha-kur and financial assistance under SAP program.
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JCT-11-530
