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Thermodynamic properties of vitamin B9
J. Chem. Thermodynamics 100 (2016) 185–190
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Thermodynamic properties of vitamin B9 A.V. Knyazev a,⇑, V.N. Emel’yanenko b,⇑, A.S. Shipilova a, M.I. Lelet a, E.V. Gusarova a, S.S. Knyazeva a, S.P. Verevkin b,⇑ a b
Lobachevsky State University of Nizhni Novgorod, Gagarin Prospekt 23/2, 603950 Nizhni Novgorod, Russia Department of Physical Chemistry, University of Rostock, Dr-Lorenz-Weg 1, D-18059 Rostock, Germany
a r t i c l e
i n f o
Article history: Received 5 March 2016 Received in revised form 1 May 2016 Accepted 4 May 2016 Available online 6 May 2016 Keywords: Vitamin B9 Folic acid dihydrate Adiabatic vacuum calorimetry Heat capacity Combustion calorimetry Thermodynamic functions
a b s t r a c t In the present work temperature dependence of heat capacity of vitamin B9 (folic acid dihydrate) has been measured for the first time in the range from (6 to 333) K by precision adiabatic vacuum calorimetry. Based on the experimental values, the thermodynamic functions of the vitamin B9, namely, the heat capacity, enthalpy H°(T) H°(0), entropy S°(T) S°(0) and Gibbs function G°(T) H°(0) have been determined for the range from T ? (0 to 333) K. The value of the fractal dimension D in the function of multifractal generalization of Debye’s theory of the heat capacity of solids was estimated and the character of heterodynamics of structure was detected. Enthalpy of combustion (8942.8 ± 7.5) kJmol1 of the vitamin B9 was measured for the first time using a high-precision combustion calorimeter. The standard molar enthalpy of formation in the crystalline state (1821.0 ± 7.9) kJmol1 of B9 at 298.15 K was derived from the combustion experiments. Using a combination of the adiabatic and combustion calorimetry results, the thermodynamic functions of formation of the folic acid dihydrate at T = 298.15 K and p = 0.1 MPa have been calculated. The low-temperature X-ray diffraction was used for the determination of coefficients of thermal expansion. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction
2. Experimental
Folic acid dihydrate (CAS: 75708-92-8) also known as folate (the natural form in body), vitamin M, vitamin B9, vitamin Bc (or folacin) are essential for numerous bodily functions. The human body needs folic acid to synthesizes DNA and methylates DNA as well as to act as a cofactor in certain biological reactions [1]. Vitamin B9 exists naturally in a wide variety of foods such as broccoli, cabbage, fruit and nuts. Folic acid is added to grain products in many countries [2]. This work is a continuation of systematic studies of vitamins B. Earlier in the articles [3–5], we have investigated the thermodynamic properties of vitamins B2, B3 and B12. The goals of this work include calorimetric determination of the standard thermodynamic functions of the nicotinic acid with the purpose of describing biochemical and industrial processes with its participation.
2.1. Sample Folic acid dihydrate was purchased from Fluka. We conducted additional recrystallization from an aqueous solution of the substance in order to increase the purity of the folic acid dihydrate. For control of purity of the substance, the mass spectrum of the vitamin B9 was recorded on a MALDI-TOF mass spectrometer AXIMA Confidence iDplusPerformance (Fig. 1S). For phase identification, an X-ray diffraction pattern of the vitamin B9 sample was recorded on a Shimadzu X-ray diffractometer XRD-6000 (CuKa radiation, geometry h–2h) in the 2h range from 5° to 60° with scan increment of 0.02° (Fig. 2S). The water content in folic acid dihydrate was determined by Karl Fischer titration. The mass spectrometry, X-ray data and Karl Fischer titration led us to conclude that the folic acid dihydrate sample studied (the content of impurities 0.1 wt%) was an individual crystalline compound (orthorhombic modification, space group P212121 [6]). 2.2. Apparatus and measurement procedure
⇑ Corresponding authors. E-mail addresses: [email protected] (A.V. Knyazev), [email protected] (V.N. Emel’yanenko). http://dx.doi.org/10.1016/j.jct.2016.05.001 0021-9614/Ó 2016 Elsevier Ltd. All rights reserved.
To measure the heat capacity C p of the tested substance over the range from 6 K to 333 K a BKT-3.0 automatic precision adiabatic
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vacuum calorimeter with discrete heating was used. The calorimeter design and the operation procedure were described earlier [7]. The calorimeter was tested by measuring the heat capacity of high-purity copper and reference samples of synthetic corundum and K-2 benzoic acid. The analysis of the results showed that standard uncertainty of the heat capacity of the substance at helium temperatures was within ±2%, then it decreased to ±0.5% as the temperature was rising to 40 K, and was equal to ±0.2% at T > 40 K. An isoperibol bomb calorimeter described previously [8] was used for the measurement of energies of combustion of the folic acid dihydrate. The solid sample was pressed into pellet and weighed with a microbalance with 106 g resolution. The combustion products were examined for carbon monoxide (Dräger tube) and unburned carbon, but none was detected. The energy equivalent of the calorimeter ecalor was determined with a standard reference sample of benzoic acid (sample SRM 39j, N.I.S.T.). The energy equivalent of the calorimeter ecalor = (14813.1 ± 0.9) JK1, thus the standard deviation of the mean from 7 experiments is 0.9 JK1. Correction for nitric acid formation was based on the titration with 0.1 moldm3 NaOH (aq.). The relative atomic masses used for the elements were calculated as the mean of the bounds of the interval of the standard atomic weights recommended by the IUPAC commission in 2011 [9] for each of these elements. For converting the energy of the actual bomb process to that of the isothermal process, and reducing to standard states, the conventional procedure was applied [10]. We used small polythene pieces as an auxiliary material in order to reach completeness of combustion. 3. Results and discussion 3.1. Heat capacity The C p measurements were carried out between 6 K and 333 K (Table 1S). The mass of the sample loaded in the calorimetric ampoules of the BKT-3.0 device was 0.2949 g. A total of 168 experimental C p values was obtained in two series of experiments. The heat capacity of the sample varied from 20% to 50% of the total heat capacity of calorimetric (ampoule + substance) over the range between 6 K and 333 K. The experimental points of C p within the temperature interval (20–333) K were fitted by means of the least-squares method and polynomial equations (Eqs. (1)–(3)) of the C p versus temperature have been obtained. The corresponding coefficients (A, B, C, etc.) are given in Table 1
C p ¼ A þ B ðT=30Þ þ C ðT=30Þ2 þ D ðT=30Þ3 þ E ðT=30Þ4 þ F ðT=30Þ5 þ G ðT=30Þ6 þ H ðT=30Þ7 þ I ðT=30Þ8 þ J ðT=30Þ9 ;
ð1Þ
Table 1 Coefficients in the fitting polynomials for folic acid dihydrate. T/K Polynomial’s type
6.3–10 1
10–25 3
20–100 1
100–333 2
A B C D E F G H I J
2.4938917 91.850044 958.48571 4317.7614 8572.8319 6821.9952
4.2662712 6.2866301 24.214347 65.003023 83.577930 46.889658 4.8644013 2.9375535
231.87740 1355.1228 3400.1325 4940.2233 4283.5119 2311.6547 781.53221 160.47354 18.240026 0.87755357
40706.225 168963.51 296798.79 287050.04 164973.33 56363.009 10600.679 846.99973
Fig. 1. Temperature dependence of heat capacity of folic acid dihydrate. Table 2 Thermodynamic functions of crystalline folic acid dihydrate; M = 477.43 gmol1. po = 0.1 MPa. T/K
0 4 5 6 7 8 9 10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15 300 310 320 330 333
(JK1mol1)
C p ðTÞ/
H ðTÞ H ð0Þ/ (kJmol1)
S ðTÞ/ (JK1mol1)
[ G ðTÞ H ð0Þ ]/(kJmol1)
0 0.1020 0.2491 0.5453 0.9120 1.566 2.515 3.778 11.59 23.04 37.08 53.06 68.97 84.24 98.58 112.2 138.8 164.4 186.3 204.7 224.7 244.1 262.0 280.1 298.3 316.4 334.1 351.6 369.0 386.3 403.7 421.1 438.6 456.1 473.7 491.2 508.6 525.9 531.3 543.1 560.3 574.4 577.6 595.2 613.1 631.7 637.5
0 0.000082 0.00025 0.00062 0.00132 0.00254 0.00456 0.00767 0.04596 0.1303 0.2802 0.5060 0.8111 1.195 1.652 2.179 3.434 4.952 6.710 8.666 10.81 13.16 15.69 18.40 21.29 24.36 27.62 31.05 34.65 38.43 42.38 46.50 50.80 55.27 59.92 64.75 69.74 74.92 76.58 80.26 85.78 90.40 91.47 97.33 103.4 109.6 111.5
0 0.0255 0.0623 0.1291 0.2371 0.3983 0.6346 0.962 3.956 8.733 15.36 23.55 32.93 43.15 53.90 65.00 87.81 111.2 134.6 157.6 180.2 202.6 224.6 246.2 267.7 288.9 309.9 330.6 351.2 371.6 391.9 412.0 432.0 451.9 471.7 491.4 511.0 530.5 536.6 549.9 569.3 585.0 588.6 607.8 627.0 646.1 651.9
0 0.000020 0.000062 0.000155 0.000335 0.000647 0.001156 0.001947 0.01337 0.04436 0.1039 0.2006 0.3413 0.5313 0.7737 1.071 1.834 2.829 4.058 5.520 7.209 9.123 11.26 13.61 16.18 18.97 21.96 25.16 28.57 32.19 36.00 40.02 44.24 48.66 53.28 58.10 63.11 68.32 70.0 73.72 79.31 84.02 85.10 91.09 97.26 103.6 105.6
ur(Cpo(T)) = ±2% (5 < T/K < 20); ±0.5% (20 < T/K < 40 K); ±0.2% (T > 40 K), ur(function values) = ±1% (T < 40 K); ±0.5% (40 < T/K < 80); ±0.2% (80 < T/K < 346), ur(p) = ±1% (level of confidence = 0.68).
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A.V. Knyazev et al. / J. Chem. Thermodynamics 100 (2016) 185–190 Table 3 Results for typical combustion experiments at T = 298.15 K (po = 0.1 MPa) for folic acid dihydrate.a m (substance)/g m0 (cotton)/g m 00 (polyethylene)/g DTc/K (ecalor)(DTc)/J (econt)(DTc)/J DUdecomp HNO3/J DUcorr/J m0 Dcu0 /J m00 Dcu00 /J Dcu° (cr)/(Jg1)
0.16927 0.001101 0.438827 1.59036 23558.2 25.67 43.6 8.72 18.66 20342.83 18727.8
Dcu° (cr)/(Jg1) u(Dcu°)/Jg1
18740.2 5.0b
0.214756 0.001155 0.419855 1.58897 23537.6 25.66 43.60 9.21 19.57 19463.34 18753.8
0.320272 0.000960 0.353620 1.51552 22449.5 24.38 55.55 9.88 16.27 16392.87 18731.9
0.321963 0.001293 0.408069 1.68759 24998.4 27.55 48.38 10.89 21.91 18916.98 18722.0
0.299304 0.001089 0.401443 1.63862 24273.1 26.95 48.98 10.42 18.45 18609.81 18751.3
0.206123 0.001222 0.388783 1.48109 21939.5 23.65 45.39 8.52 20.71 18022.93 18753.8
0.169560 0.001179 0.382150 1.41343 20937.3 22.53 38.82 7.85 19.98 17715.44 18741.0
a The definition of the symbols assigned according to Refs. [10,17] as follows: m(substance), m0 (cotton) and m00 (polyethylene) are, respectively, the mass of compound burnt, the mass of fuse (cotton) and auxiliary polyethylene used in each experiment, masses were corrected for buoyancy; V(bomb) = 0.32 dm3 is the internal volume of the calorimetric bomb; pi(gas) = 3.04 MPa is the initial oxygen pressure in the bomb; mi(H2O) = 1.00 g is the mass of water added to the bomb for dissolution of combustion gases; DTc = Tf Ti + DTcorr is the corrected temperature rise from initial temperature Ti to final temperature Tf, with the correction DTcorr for heat exchange during the experiment; econt is the energy equivalents of the bomb contents in their initial eicont and final states efcont, the contribution for the bomb content is calculated with (econt)(DTc) = (eicont) (Ti 298.15) + (efcont)(298.15 Tf + DTcorr.). DUdecomp HNO3 is the energy correction for the nitric acid formation. DUcorr is the correction to standard states. b Uncertainties in this table are expressed as the standard deviation of the mean from n experiments.
Table 4 Enthalpy of combustion and thermodynamic characteristics of formation of folic acid dihydrate (T = 298.15 K, p = 0.1 MPa). Compound
DcH°/(kJmol1)a
DfH°/(kJmol1)b
DfS°/(JK1mol1)
DfG°/(kJmol1)
C19H19N7O62H2O
8942.8 ± 7.5
1821.0 ± 7.9
2515.5 ± 9.5
1071 ± 8
a
Uncertainties correspond to expanded uncertainties of the mean (0.95 confidence level). b Uncertainty is twice the overall standard deviations and include the uncertainties from calibration, combustion energies of the auxiliary materials, and the uncertainties of the enthalpies of formation of the reaction products H2O and CO2.
Fig. 2. Plot of unit cell parameter versus temperature for folic acid dihydrate.
C p ¼ A þ B lnðT=30Þ þ C ln ðT=30Þ þ D ln ðT=30Þ þ E ln ðT=30Þ 2
5
3
6
4
7
þ F ln ðT=30Þ þ G ln ðT=30Þ þ H ln ðT=30Þ;
ð2Þ
ln C p ¼ A þ B lnðT=30Þ þ C ln ðT=30Þ þ D ln ðT=30Þ þ E ln ði=30Þ 2
5
6
3
7
þ F ln ðT=30Þ þ G ln ðT=30Þ þ H ln ðT=30Þ:
4
ð3Þ
Partitioning into 4 intervals of the temperature dependence of the heat capacity contributes to the best smoothing of the experimental curve. Their root mean square deviation from the averaging C p ¼ f ðTÞ curve was ±0.15% within the range T = (6 to 40) K, ±0.075% from T = (40 to 80) K and ±0.050% between T = (80 and 333) K. The experimental values of the molar heat capacity of folic
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Table 5 Parameters of unit cells and thermal expansion coefficients versus temperature for folic acid dihydrate. T/K
a/nm
150 175 200 225 250 275 300 325 350 375
0.7244 0.7248 0.7254 0.7263 0.7266 0.7276 0.7292 0.7297 0.7314 0.7322
a105/K1
4.9
b/nm (1.5) (1.6) (1.3) (1.3) (1.1) (1.1) (0.9) (0.9) (0.6) (0.8)
0.8664 0.8666 0.8670 0.8667 0.8666 0.8669 0.8665 0.8663 0.8656 0.8664
c/nm (1.7) (1.9) (1.6) (1.5) (1.3) (1.3) (1.0) (1.0) (0.7) (1.0)
0.3
3.245 3.248 3.248 3.248 3.250 3.250 3.251 3.252 3.252 3.252
(0.4) (0.4) (0.4) (0.3) (0.3) (0.3) (0.2) (0.2) (0.2) (0.2)
0.9
V/nm3
q/(gcm3)
2.037 2.040 2.043 2.045 2.046 2.050 2.054 2.056 2.059 2.063
1.556 1.554 1.552 1.550 1.549 1.546 1.543 1.542 1.540 1.537
(0.005) (0.005) (0.004) (0.004) (0.004) (0.004) (0.003) (0.003) (0.002) (0.003)
5.5
Standard uncertainties u are u(T) = 1 K, u(a) = 0.0016 nm, u(b) = 0.0019 nm, u(c) = 0.004 nm, u(V) = 5 10
3
nm , u(q) = 0.003 gcm3, ur(p) = ±1% (level of confidence = 0.68). 3
acid dihydrate over the range from 6 K to 333 K and the averaging C p ¼ f ðTÞ plot are presented in Fig. 1. The heat capacity C p of this substance gradually increases with rising temperature and does not show any peculiarities. From the experimental C p values within the range (25–50) K, the value of the fractal dimension D of the folic acid dihydrate was evaluated. According to the fractal theory of the heat capacity [11], D is the most important parameter that specifies the character of heterodynamics of the substance structure. For solids of a chain structure, the relation C p versus T at lower temperatures is proportional to T1, of a layer structure to T2 and of steric one to T3 [12]. In the fractal theory of the heat capacity, an exponent on T is the heat capacity function is denoted by D and is called the fractal dimension. This follows specifically from Eq. (4) [11]:
D T C v ¼ 3DðD þ 1ÞkNcðD þ 1ÞnðD þ 1Þ ; hmax
ð4Þ
where N is the number of atoms in a formula unit, k the Boltzmann constant, c(D + 1) the c-function, n(D + 1) the Riemann n-function, and hmax is the characteristic temperature. As follows from inferences [11], D can be evaluated from the experimental values on the temperature-dependent heat capacities from a slope of the corresponding rectilinear sections of the plot ln Cv versus ln T. Without a substantial uncertainty, it may be assumed that at T < 50 K C p ¼ C v . From the ln Cv versus ln T plot and Eq. (4), it was found that within the range (25–50) K, D = 2.0, hmax = 223.6 K for folic acid dihydrate. With these values of D and hmax, Eq. (4) reproduces the experimental C p values in the temperature range mentioned with an uncertainty of ±0.75%. The D-value points to the layer structure of folic acid dihydrate [12–14]. 3.2. Thermodynamic functions To calculate the standard thermodynamic functions (Table 2) of folic acid dihydrate, its C p values were extrapolated from the starting temperature of the measurement (approximately 7 K) to 0 K by Debye’s function of heat capacity [15]:
C p ¼ nD
Fig. 3. 2D thermal expansion diagrams for folic acid dihydrate.
hD ; T
ð5Þ
where D is the symbol of Debye’s function, n = 3 and hD(C19H19N7O62H2O) = 95.5 K are specially selected parameters [15]. Eq. (5) with the above parameters describes the experimental Cpo values of the compound between 6 K and 10 K with the relative standard uncertainty of ±2.7%. In calculating the functions, it was assumed that Eq. (4) reproduces the C p values of folic acid dihydrate at T < 6 K with the same relative standard uncertainty.
A.V. Knyazev et al. / J. Chem. Thermodynamics 100 (2016) 185–190
The calculations of H°(T) H°(0) and S°(T) S°(0) were made by the numerical integration of Cpo = f(T) and Cpo = f(ln T) curves, respectively, and the Gibbs function G°(T) H°(0) was estimated from the enthalpies and entropies at the corresponding temperatures [16]. It is suggested that the relative standard uncertainty of the function values is ±2% at T < 40 K, ±0.5% between 40 and 80 K and ±0.2% in the range from 80 K to 333 K. 3.3. Thermodynamic characteristics of folic acid dihydrate formation Experimental results from combustion experiments with the folic acid dihydrate are given in Table 3 and Table 2S. The value of the standard specific energy of combustion Dcu° = (18740.2 ± 5.0) Jg1 has been used to derive the standard molar enthalpy of combustion Dc Hm = (8942.8 ± 5.2) kJmol1, and the standard molar enthalpy of formation in the crystalline state Df Hm ðcrÞ = (1821.0 ± 5.7) kJmol1. Values of Dcu° and Dc Hm refer to reaction:
C19 H19 N7 O6 2H2 OðcrÞ þ 20:75 O2 ðgÞ ! 19 CO2 ðgÞ þ 11:5 H2 OðlÞ þ 3:5 N þ 2ðgÞ:
ð6Þ
The enthalpy of formation Df Hm ðcrÞ of the folic acid dihydrate was calculated from the enthalpic balance according to Eq. (6)
189
using standard molar enthalpies of formation of H2O (l) and CO2 (g) recommended by CODATA [9]. Uncertainties related to combustion experiments were calculated according to the guidelines presented in [10]. The uncertainties of the standard molar energy and enthalpy of combustion correspond to expanded uncertainties of the mean (0.95 level of confidence) and include the contribution from the calibration with benzoic acid and from the values of the auxiliary quantities used. The uncertainty assigned to Df Hm ðcrÞ is twice the overall standard deviation and includes the uncertainties from calibration, from the combustion energies of the auxiliary materials, and the uncertainties of the enthalpies of formation of the reaction products H2O and CO2. Experimental study of the folic acid dihydrate reported for the first time. From the absolute value of the entropy of the folic acid dihydrate (Table 2), carbon in the form of graphite, gaseous hydrogen, oxygen and nitrogen [18,19] the standard entropy of formation Df Sm of folic acid dihydrate at T = 298.15 K was calculated by methods described earlier [16]. The Gibbs function of formation Df Gm of the folic acid dihydrate was evaluated from the Df Hm and Df Sm values (Table 4). The values conform to the following process:
19 CðgrÞ þ 11:5 H2 ðgÞ þ 3:5 N2 ðgÞ þ 4 O2 ðgÞ ! C19 H19 N7 O6 2H2 OðcrÞ:
Fig. 4. 3D thermal expansion diagram and fragment of structure of folic acid dihydrate.
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The standard molar thermodynamic functions in the crystalline state collected in Table 4 can be used for optimization of methods of synthesis, as well as for validation of theoretical and empirical methods for prediction of thermodynamic properties.
(Lobachevsky State university of Nizhni Novgorod, project RFMEFI59414X0005).
3.4. Low-temperature and high-temperature X-ray diffraction
Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jct.2016.05.001.
Next task of the work was the X-ray diffraction investigation of compound with the purpose of definition of the thermal expansion coefficients. The temperature dependence of the unit cell parameters is plotted in Fig. 2 and Table 5 lists these parameters together with thermal expansion coefficients and densities. The temperature dependence of the unit cell parameters is described by the following linear relations:
a ¼ 3:57818 104 T=K þ 7:18367 ð150 6 T=K 6 375Þ; b ¼ 2:61818 104 T=K þ 8:67187 ð150 6 T=K 6 375Þ; c ¼ 3:04967 105 T=K þ 32:41475 ð150 6 T=K 6 375Þ; V ¼ 0:112242 T=K þ 2019:836 ð150 6 T=K 6 375Þ: The thermal expansion coefficient is the quantitative characteristic of thermal expansion. We used the formula aL ¼ 1L DDLT , where aL – coefficient of thermal expansion, L – unit cell parameter. The value of the thermal expansion coefficient in a given direction corresponds to length of radius-vector, which is traced from origin of coordinates to edge of figure of expansion. The thermal expansion of the folic acid dihydrate is anisotropic, and along the crystallographic axis, b occurs even with compression of the structure (Fig. 3). For the construction of the 3D version of the thermal expansion diagram algorithm for MaplesoftÓ can be used [20] (Fig. 4). These figures allow presenting the anisotropy of the thermal expansion of the crystal at a certain temperature [21]. We found that the lack there of a network of hydrogen bonds along the crystallographic direction a leads to an anomaly of high thermal deformation along this direction. 4. Conclusions The general aim of these investigations is to report the results of the thermodynamic study of the folic acid dihydrate. The heat capacity of this vitamin B9 is measured over the temperature range from (6 to 333) K. The thermodynamic functions are calculated and the fractal dimension D is evaluated. Thermochemical parameters of formation are determined by combining the data obtained by using combustion calorimetry and heat capacity measurements. Acknowledgements The work was performed with the financial support of the Russian Foundation of Basic Research (Project Number 16-0300288). The work carried out using the equipment center for collective use ‘‘New materials and energy saving technologies”
Appendix A. Supplementary data
References [1] S.J. Weinstein, T.J. Hartman, R. Stolzenberg-Solomon, et al., Null association between prostate cancer and serum folate, vitamin B6, vitamin B12, and homocysteine, Cancer Epidemiol. Biomarkers Prev. 12 (11 Pt 1) (2003) 1271– 1272. [2] M. Dietrich, C.J. Brown, G. Block, The effect of folate fortification of cereal-grain products on blood folate status, dietary folate intake, and dietary folate sources among adult non-supplement users in the United States, J. Am. Coll. Nutr. 24 (4) (2005) 266–274. [3] A.V. Knyazev, I.A. Letyanina, A.S. Plesovskikh, N.N. Smirnova, S.S. Knyazeva, Thermodynamic properties of vitamin B2, Thermochim. Acta 575 (2014) 12– 16. [4] A.V. Knyazev, N.N. Smirnova, A.S. Shipilova, A.N. Shushunov, E.V. Gusarova, S.S. Knyazeva, Thermodynamic properties and low-temperature X-ray diffraction of vitamin B3, Thermochim. Acta 604 (2015) 115–121. [5] A.V. Knyazev, N.N. Smirnova, A.S. Plesovskikh, A.N. Shushunov, S.S. Knyazeva, Low-temperature heat capacity and thermodynamic functions of vitamin B12, Thermochim. Acta 582 (2014) 35–39. [6] J.A. Kaduk, C.E. Crowder, K. Zhong, Crystal structure of folic acid dihydrate, Powder Diffr. 30 (1) (2015) 52–56. [7] R.M. Varushchenko, A.I. Druzhinina, E.L. Sorkin, Low-temperature heat capacity of 1-bromoperfluorooctane, J. Chem. Thermodyn. 29 (1997) 623–637. [8] V.N. V.N. Emel’yanenko, S.P. Verevkin, A. Heintz, J. Am. Chem. Soc. 129 (2007) 3930–3937. [9] M.E. Wieser, N. Holden, T.B. Coplen, J.K. Böhlke, M. Berglund, W.A. Brand, P. De Bièvre, M. Gröning, R.D. Loss, J. Meija, T. Hirata, T. Prohaska, R. Schoenberg, G. O’Connor, T. Walczyk, S. Yoneda, X.-K. Zhu, Pure Appl. Chem. 85 (2013) 1047– 1078. [10] G. Olofsson, Experimental chemical thermodynamics, in: S. Sunner, M. Mansson (Eds.), Combustion Calorimetry, vol. 1, Pergamon Press, 1976. [11] T.S. Yakubov, On the specific heat of solids that exhibit fractal character, Dokl. Acad. Sci. 310 (1990) 145–150. [12] V.V. Tarasov, The theory of the heat capacity of chain-layered structures, Zhurnal. Fiz. Khimii. 24 (1950) 111–128. [13] N.G. Chernorukov, N.N. Smirnova, A.V. Knyazev, M.N. Marochkina, T.A. Bykova, A.V. Ershova, The thermodynamic properties of calcium uranoborate, Russ. J. Phys. Chem. 80 (1) (2006) 37–41. [14] N.V. Karyakin, N.G. Chernorukov, E.V. Suleimanov, M.I. Alimzhanov, V.L. Trostin, A.V. Knyazev, The thermodynamic properties of uranyl pyrovanadate and uranovanadic acid, Russ. J. Phys. Chem. 74 (2000) 1226–1231. [15] P. Debye, Z ur Theorie der spezifischen Waerme, Ann. Phys. 39 (1912) 789– 839. [16] B.V. Lebedev, Application of precise calorimetry in study of polymers and polymerization processes, Thermochim. Acta 297 (1997) 143–149. [17] W.N. Hubbard, D.W. Scott, G. Waddington, Experimental thermochemistry, in: F.D. Rossini (Ed.), Interscience, New York, 1956, p. 75. [18] M.W. Chase, NIST-JANAF thermochemical tables, fourth., J. Phys. Chem. Ref. Data, 1998 (Monograph 9). [19] J.D. Cox, D.D. Wagman, V.A. Medvedev, CODATA Key Values for Thermodynamics, Hemisphere Publishing Corp, New York, 1984. [20] A.V. Knyazev, M.E. Komshina, A.V. Zhidkov, A.S. Plesovskikh, Crystal structure and thermal expansion of RbNaCaTh(Si8O20), Russ. J. Inorg. Chem. 58 (2013) 1172–1176. [21] A.V. Knyazev, N.N. Smirnova, A.S. Shipilova, V.N. Larina, E.V. Gusarova, S.S. Knyazeva, Combustion calorimetry and low-temperature X-ray diffraction of steroid hormone, J. Therm. Anal. Calorim. 123 (2016) 2201–2206.
JCT 16-180
Contents lists available at ScienceDirect
J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct
Thermodynamic properties of vitamin B9 A.V. Knyazev a,⇑, V.N. Emel’yanenko b,⇑, A.S. Shipilova a, M.I. Lelet a, E.V. Gusarova a, S.S. Knyazeva a, S.P. Verevkin b,⇑ a b
Lobachevsky State University of Nizhni Novgorod, Gagarin Prospekt 23/2, 603950 Nizhni Novgorod, Russia Department of Physical Chemistry, University of Rostock, Dr-Lorenz-Weg 1, D-18059 Rostock, Germany
a r t i c l e
i n f o
Article history: Received 5 March 2016 Received in revised form 1 May 2016 Accepted 4 May 2016 Available online 6 May 2016 Keywords: Vitamin B9 Folic acid dihydrate Adiabatic vacuum calorimetry Heat capacity Combustion calorimetry Thermodynamic functions
a b s t r a c t In the present work temperature dependence of heat capacity of vitamin B9 (folic acid dihydrate) has been measured for the first time in the range from (6 to 333) K by precision adiabatic vacuum calorimetry. Based on the experimental values, the thermodynamic functions of the vitamin B9, namely, the heat capacity, enthalpy H°(T) H°(0), entropy S°(T) S°(0) and Gibbs function G°(T) H°(0) have been determined for the range from T ? (0 to 333) K. The value of the fractal dimension D in the function of multifractal generalization of Debye’s theory of the heat capacity of solids was estimated and the character of heterodynamics of structure was detected. Enthalpy of combustion (8942.8 ± 7.5) kJmol1 of the vitamin B9 was measured for the first time using a high-precision combustion calorimeter. The standard molar enthalpy of formation in the crystalline state (1821.0 ± 7.9) kJmol1 of B9 at 298.15 K was derived from the combustion experiments. Using a combination of the adiabatic and combustion calorimetry results, the thermodynamic functions of formation of the folic acid dihydrate at T = 298.15 K and p = 0.1 MPa have been calculated. The low-temperature X-ray diffraction was used for the determination of coefficients of thermal expansion. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction
2. Experimental
Folic acid dihydrate (CAS: 75708-92-8) also known as folate (the natural form in body), vitamin M, vitamin B9, vitamin Bc (or folacin) are essential for numerous bodily functions. The human body needs folic acid to synthesizes DNA and methylates DNA as well as to act as a cofactor in certain biological reactions [1]. Vitamin B9 exists naturally in a wide variety of foods such as broccoli, cabbage, fruit and nuts. Folic acid is added to grain products in many countries [2]. This work is a continuation of systematic studies of vitamins B. Earlier in the articles [3–5], we have investigated the thermodynamic properties of vitamins B2, B3 and B12. The goals of this work include calorimetric determination of the standard thermodynamic functions of the nicotinic acid with the purpose of describing biochemical and industrial processes with its participation.
2.1. Sample Folic acid dihydrate was purchased from Fluka. We conducted additional recrystallization from an aqueous solution of the substance in order to increase the purity of the folic acid dihydrate. For control of purity of the substance, the mass spectrum of the vitamin B9 was recorded on a MALDI-TOF mass spectrometer AXIMA Confidence iDplusPerformance (Fig. 1S). For phase identification, an X-ray diffraction pattern of the vitamin B9 sample was recorded on a Shimadzu X-ray diffractometer XRD-6000 (CuKa radiation, geometry h–2h) in the 2h range from 5° to 60° with scan increment of 0.02° (Fig. 2S). The water content in folic acid dihydrate was determined by Karl Fischer titration. The mass spectrometry, X-ray data and Karl Fischer titration led us to conclude that the folic acid dihydrate sample studied (the content of impurities 0.1 wt%) was an individual crystalline compound (orthorhombic modification, space group P212121 [6]). 2.2. Apparatus and measurement procedure
⇑ Corresponding authors. E-mail addresses: [email protected] (A.V. Knyazev), [email protected] (V.N. Emel’yanenko). http://dx.doi.org/10.1016/j.jct.2016.05.001 0021-9614/Ó 2016 Elsevier Ltd. All rights reserved.
To measure the heat capacity C p of the tested substance over the range from 6 K to 333 K a BKT-3.0 automatic precision adiabatic
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vacuum calorimeter with discrete heating was used. The calorimeter design and the operation procedure were described earlier [7]. The calorimeter was tested by measuring the heat capacity of high-purity copper and reference samples of synthetic corundum and K-2 benzoic acid. The analysis of the results showed that standard uncertainty of the heat capacity of the substance at helium temperatures was within ±2%, then it decreased to ±0.5% as the temperature was rising to 40 K, and was equal to ±0.2% at T > 40 K. An isoperibol bomb calorimeter described previously [8] was used for the measurement of energies of combustion of the folic acid dihydrate. The solid sample was pressed into pellet and weighed with a microbalance with 106 g resolution. The combustion products were examined for carbon monoxide (Dräger tube) and unburned carbon, but none was detected. The energy equivalent of the calorimeter ecalor was determined with a standard reference sample of benzoic acid (sample SRM 39j, N.I.S.T.). The energy equivalent of the calorimeter ecalor = (14813.1 ± 0.9) JK1, thus the standard deviation of the mean from 7 experiments is 0.9 JK1. Correction for nitric acid formation was based on the titration with 0.1 moldm3 NaOH (aq.). The relative atomic masses used for the elements were calculated as the mean of the bounds of the interval of the standard atomic weights recommended by the IUPAC commission in 2011 [9] for each of these elements. For converting the energy of the actual bomb process to that of the isothermal process, and reducing to standard states, the conventional procedure was applied [10]. We used small polythene pieces as an auxiliary material in order to reach completeness of combustion. 3. Results and discussion 3.1. Heat capacity The C p measurements were carried out between 6 K and 333 K (Table 1S). The mass of the sample loaded in the calorimetric ampoules of the BKT-3.0 device was 0.2949 g. A total of 168 experimental C p values was obtained in two series of experiments. The heat capacity of the sample varied from 20% to 50% of the total heat capacity of calorimetric (ampoule + substance) over the range between 6 K and 333 K. The experimental points of C p within the temperature interval (20–333) K were fitted by means of the least-squares method and polynomial equations (Eqs. (1)–(3)) of the C p versus temperature have been obtained. The corresponding coefficients (A, B, C, etc.) are given in Table 1
C p ¼ A þ B ðT=30Þ þ C ðT=30Þ2 þ D ðT=30Þ3 þ E ðT=30Þ4 þ F ðT=30Þ5 þ G ðT=30Þ6 þ H ðT=30Þ7 þ I ðT=30Þ8 þ J ðT=30Þ9 ;
ð1Þ
Table 1 Coefficients in the fitting polynomials for folic acid dihydrate. T/K Polynomial’s type
6.3–10 1
10–25 3
20–100 1
100–333 2
A B C D E F G H I J
2.4938917 91.850044 958.48571 4317.7614 8572.8319 6821.9952
4.2662712 6.2866301 24.214347 65.003023 83.577930 46.889658 4.8644013 2.9375535
231.87740 1355.1228 3400.1325 4940.2233 4283.5119 2311.6547 781.53221 160.47354 18.240026 0.87755357
40706.225 168963.51 296798.79 287050.04 164973.33 56363.009 10600.679 846.99973
Fig. 1. Temperature dependence of heat capacity of folic acid dihydrate. Table 2 Thermodynamic functions of crystalline folic acid dihydrate; M = 477.43 gmol1. po = 0.1 MPa. T/K
0 4 5 6 7 8 9 10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15 300 310 320 330 333
(JK1mol1)
C p ðTÞ/
H ðTÞ H ð0Þ/ (kJmol1)
S ðTÞ/ (JK1mol1)
[ G ðTÞ H ð0Þ ]/(kJmol1)
0 0.1020 0.2491 0.5453 0.9120 1.566 2.515 3.778 11.59 23.04 37.08 53.06 68.97 84.24 98.58 112.2 138.8 164.4 186.3 204.7 224.7 244.1 262.0 280.1 298.3 316.4 334.1 351.6 369.0 386.3 403.7 421.1 438.6 456.1 473.7 491.2 508.6 525.9 531.3 543.1 560.3 574.4 577.6 595.2 613.1 631.7 637.5
0 0.000082 0.00025 0.00062 0.00132 0.00254 0.00456 0.00767 0.04596 0.1303 0.2802 0.5060 0.8111 1.195 1.652 2.179 3.434 4.952 6.710 8.666 10.81 13.16 15.69 18.40 21.29 24.36 27.62 31.05 34.65 38.43 42.38 46.50 50.80 55.27 59.92 64.75 69.74 74.92 76.58 80.26 85.78 90.40 91.47 97.33 103.4 109.6 111.5
0 0.0255 0.0623 0.1291 0.2371 0.3983 0.6346 0.962 3.956 8.733 15.36 23.55 32.93 43.15 53.90 65.00 87.81 111.2 134.6 157.6 180.2 202.6 224.6 246.2 267.7 288.9 309.9 330.6 351.2 371.6 391.9 412.0 432.0 451.9 471.7 491.4 511.0 530.5 536.6 549.9 569.3 585.0 588.6 607.8 627.0 646.1 651.9
0 0.000020 0.000062 0.000155 0.000335 0.000647 0.001156 0.001947 0.01337 0.04436 0.1039 0.2006 0.3413 0.5313 0.7737 1.071 1.834 2.829 4.058 5.520 7.209 9.123 11.26 13.61 16.18 18.97 21.96 25.16 28.57 32.19 36.00 40.02 44.24 48.66 53.28 58.10 63.11 68.32 70.0 73.72 79.31 84.02 85.10 91.09 97.26 103.6 105.6
ur(Cpo(T)) = ±2% (5 < T/K < 20); ±0.5% (20 < T/K < 40 K); ±0.2% (T > 40 K), ur(function values) = ±1% (T < 40 K); ±0.5% (40 < T/K < 80); ±0.2% (80 < T/K < 346), ur(p) = ±1% (level of confidence = 0.68).
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A.V. Knyazev et al. / J. Chem. Thermodynamics 100 (2016) 185–190 Table 3 Results for typical combustion experiments at T = 298.15 K (po = 0.1 MPa) for folic acid dihydrate.a m (substance)/g m0 (cotton)/g m 00 (polyethylene)/g DTc/K (ecalor)(DTc)/J (econt)(DTc)/J DUdecomp HNO3/J DUcorr/J m0 Dcu0 /J m00 Dcu00 /J Dcu° (cr)/(Jg1)
0.16927 0.001101 0.438827 1.59036 23558.2 25.67 43.6 8.72 18.66 20342.83 18727.8
Dcu° (cr)/(Jg1) u(Dcu°)/Jg1
18740.2 5.0b
0.214756 0.001155 0.419855 1.58897 23537.6 25.66 43.60 9.21 19.57 19463.34 18753.8
0.320272 0.000960 0.353620 1.51552 22449.5 24.38 55.55 9.88 16.27 16392.87 18731.9
0.321963 0.001293 0.408069 1.68759 24998.4 27.55 48.38 10.89 21.91 18916.98 18722.0
0.299304 0.001089 0.401443 1.63862 24273.1 26.95 48.98 10.42 18.45 18609.81 18751.3
0.206123 0.001222 0.388783 1.48109 21939.5 23.65 45.39 8.52 20.71 18022.93 18753.8
0.169560 0.001179 0.382150 1.41343 20937.3 22.53 38.82 7.85 19.98 17715.44 18741.0
a The definition of the symbols assigned according to Refs. [10,17] as follows: m(substance), m0 (cotton) and m00 (polyethylene) are, respectively, the mass of compound burnt, the mass of fuse (cotton) and auxiliary polyethylene used in each experiment, masses were corrected for buoyancy; V(bomb) = 0.32 dm3 is the internal volume of the calorimetric bomb; pi(gas) = 3.04 MPa is the initial oxygen pressure in the bomb; mi(H2O) = 1.00 g is the mass of water added to the bomb for dissolution of combustion gases; DTc = Tf Ti + DTcorr is the corrected temperature rise from initial temperature Ti to final temperature Tf, with the correction DTcorr for heat exchange during the experiment; econt is the energy equivalents of the bomb contents in their initial eicont and final states efcont, the contribution for the bomb content is calculated with (econt)(DTc) = (eicont) (Ti 298.15) + (efcont)(298.15 Tf + DTcorr.). DUdecomp HNO3 is the energy correction for the nitric acid formation. DUcorr is the correction to standard states. b Uncertainties in this table are expressed as the standard deviation of the mean from n experiments.
Table 4 Enthalpy of combustion and thermodynamic characteristics of formation of folic acid dihydrate (T = 298.15 K, p = 0.1 MPa). Compound
DcH°/(kJmol1)a
DfH°/(kJmol1)b
DfS°/(JK1mol1)
DfG°/(kJmol1)
C19H19N7O62H2O
8942.8 ± 7.5
1821.0 ± 7.9
2515.5 ± 9.5
1071 ± 8
a
Uncertainties correspond to expanded uncertainties of the mean (0.95 confidence level). b Uncertainty is twice the overall standard deviations and include the uncertainties from calibration, combustion energies of the auxiliary materials, and the uncertainties of the enthalpies of formation of the reaction products H2O and CO2.
Fig. 2. Plot of unit cell parameter versus temperature for folic acid dihydrate.
C p ¼ A þ B lnðT=30Þ þ C ln ðT=30Þ þ D ln ðT=30Þ þ E ln ðT=30Þ 2
5
3
6
4
7
þ F ln ðT=30Þ þ G ln ðT=30Þ þ H ln ðT=30Þ;
ð2Þ
ln C p ¼ A þ B lnðT=30Þ þ C ln ðT=30Þ þ D ln ðT=30Þ þ E ln ði=30Þ 2
5
6
3
7
þ F ln ðT=30Þ þ G ln ðT=30Þ þ H ln ðT=30Þ:
4
ð3Þ
Partitioning into 4 intervals of the temperature dependence of the heat capacity contributes to the best smoothing of the experimental curve. Their root mean square deviation from the averaging C p ¼ f ðTÞ curve was ±0.15% within the range T = (6 to 40) K, ±0.075% from T = (40 to 80) K and ±0.050% between T = (80 and 333) K. The experimental values of the molar heat capacity of folic
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Table 5 Parameters of unit cells and thermal expansion coefficients versus temperature for folic acid dihydrate. T/K
a/nm
150 175 200 225 250 275 300 325 350 375
0.7244 0.7248 0.7254 0.7263 0.7266 0.7276 0.7292 0.7297 0.7314 0.7322
a105/K1
4.9
b/nm (1.5) (1.6) (1.3) (1.3) (1.1) (1.1) (0.9) (0.9) (0.6) (0.8)
0.8664 0.8666 0.8670 0.8667 0.8666 0.8669 0.8665 0.8663 0.8656 0.8664
c/nm (1.7) (1.9) (1.6) (1.5) (1.3) (1.3) (1.0) (1.0) (0.7) (1.0)
0.3
3.245 3.248 3.248 3.248 3.250 3.250 3.251 3.252 3.252 3.252
(0.4) (0.4) (0.4) (0.3) (0.3) (0.3) (0.2) (0.2) (0.2) (0.2)
0.9
V/nm3
q/(gcm3)
2.037 2.040 2.043 2.045 2.046 2.050 2.054 2.056 2.059 2.063
1.556 1.554 1.552 1.550 1.549 1.546 1.543 1.542 1.540 1.537
(0.005) (0.005) (0.004) (0.004) (0.004) (0.004) (0.003) (0.003) (0.002) (0.003)
5.5
Standard uncertainties u are u(T) = 1 K, u(a) = 0.0016 nm, u(b) = 0.0019 nm, u(c) = 0.004 nm, u(V) = 5 10
3
nm , u(q) = 0.003 gcm3, ur(p) = ±1% (level of confidence = 0.68). 3
acid dihydrate over the range from 6 K to 333 K and the averaging C p ¼ f ðTÞ plot are presented in Fig. 1. The heat capacity C p of this substance gradually increases with rising temperature and does not show any peculiarities. From the experimental C p values within the range (25–50) K, the value of the fractal dimension D of the folic acid dihydrate was evaluated. According to the fractal theory of the heat capacity [11], D is the most important parameter that specifies the character of heterodynamics of the substance structure. For solids of a chain structure, the relation C p versus T at lower temperatures is proportional to T1, of a layer structure to T2 and of steric one to T3 [12]. In the fractal theory of the heat capacity, an exponent on T is the heat capacity function is denoted by D and is called the fractal dimension. This follows specifically from Eq. (4) [11]:
D T C v ¼ 3DðD þ 1ÞkNcðD þ 1ÞnðD þ 1Þ ; hmax
ð4Þ
where N is the number of atoms in a formula unit, k the Boltzmann constant, c(D + 1) the c-function, n(D + 1) the Riemann n-function, and hmax is the characteristic temperature. As follows from inferences [11], D can be evaluated from the experimental values on the temperature-dependent heat capacities from a slope of the corresponding rectilinear sections of the plot ln Cv versus ln T. Without a substantial uncertainty, it may be assumed that at T < 50 K C p ¼ C v . From the ln Cv versus ln T plot and Eq. (4), it was found that within the range (25–50) K, D = 2.0, hmax = 223.6 K for folic acid dihydrate. With these values of D and hmax, Eq. (4) reproduces the experimental C p values in the temperature range mentioned with an uncertainty of ±0.75%. The D-value points to the layer structure of folic acid dihydrate [12–14]. 3.2. Thermodynamic functions To calculate the standard thermodynamic functions (Table 2) of folic acid dihydrate, its C p values were extrapolated from the starting temperature of the measurement (approximately 7 K) to 0 K by Debye’s function of heat capacity [15]:
C p ¼ nD
Fig. 3. 2D thermal expansion diagrams for folic acid dihydrate.
hD ; T
ð5Þ
where D is the symbol of Debye’s function, n = 3 and hD(C19H19N7O62H2O) = 95.5 K are specially selected parameters [15]. Eq. (5) with the above parameters describes the experimental Cpo values of the compound between 6 K and 10 K with the relative standard uncertainty of ±2.7%. In calculating the functions, it was assumed that Eq. (4) reproduces the C p values of folic acid dihydrate at T < 6 K with the same relative standard uncertainty.
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The calculations of H°(T) H°(0) and S°(T) S°(0) were made by the numerical integration of Cpo = f(T) and Cpo = f(ln T) curves, respectively, and the Gibbs function G°(T) H°(0) was estimated from the enthalpies and entropies at the corresponding temperatures [16]. It is suggested that the relative standard uncertainty of the function values is ±2% at T < 40 K, ±0.5% between 40 and 80 K and ±0.2% in the range from 80 K to 333 K. 3.3. Thermodynamic characteristics of folic acid dihydrate formation Experimental results from combustion experiments with the folic acid dihydrate are given in Table 3 and Table 2S. The value of the standard specific energy of combustion Dcu° = (18740.2 ± 5.0) Jg1 has been used to derive the standard molar enthalpy of combustion Dc Hm = (8942.8 ± 5.2) kJmol1, and the standard molar enthalpy of formation in the crystalline state Df Hm ðcrÞ = (1821.0 ± 5.7) kJmol1. Values of Dcu° and Dc Hm refer to reaction:
C19 H19 N7 O6 2H2 OðcrÞ þ 20:75 O2 ðgÞ ! 19 CO2 ðgÞ þ 11:5 H2 OðlÞ þ 3:5 N þ 2ðgÞ:
ð6Þ
The enthalpy of formation Df Hm ðcrÞ of the folic acid dihydrate was calculated from the enthalpic balance according to Eq. (6)
189
using standard molar enthalpies of formation of H2O (l) and CO2 (g) recommended by CODATA [9]. Uncertainties related to combustion experiments were calculated according to the guidelines presented in [10]. The uncertainties of the standard molar energy and enthalpy of combustion correspond to expanded uncertainties of the mean (0.95 level of confidence) and include the contribution from the calibration with benzoic acid and from the values of the auxiliary quantities used. The uncertainty assigned to Df Hm ðcrÞ is twice the overall standard deviation and includes the uncertainties from calibration, from the combustion energies of the auxiliary materials, and the uncertainties of the enthalpies of formation of the reaction products H2O and CO2. Experimental study of the folic acid dihydrate reported for the first time. From the absolute value of the entropy of the folic acid dihydrate (Table 2), carbon in the form of graphite, gaseous hydrogen, oxygen and nitrogen [18,19] the standard entropy of formation Df Sm of folic acid dihydrate at T = 298.15 K was calculated by methods described earlier [16]. The Gibbs function of formation Df Gm of the folic acid dihydrate was evaluated from the Df Hm and Df Sm values (Table 4). The values conform to the following process:
19 CðgrÞ þ 11:5 H2 ðgÞ þ 3:5 N2 ðgÞ þ 4 O2 ðgÞ ! C19 H19 N7 O6 2H2 OðcrÞ:
Fig. 4. 3D thermal expansion diagram and fragment of structure of folic acid dihydrate.
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The standard molar thermodynamic functions in the crystalline state collected in Table 4 can be used for optimization of methods of synthesis, as well as for validation of theoretical and empirical methods for prediction of thermodynamic properties.
(Lobachevsky State university of Nizhni Novgorod, project RFMEFI59414X0005).
3.4. Low-temperature and high-temperature X-ray diffraction
Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jct.2016.05.001.
Next task of the work was the X-ray diffraction investigation of compound with the purpose of definition of the thermal expansion coefficients. The temperature dependence of the unit cell parameters is plotted in Fig. 2 and Table 5 lists these parameters together with thermal expansion coefficients and densities. The temperature dependence of the unit cell parameters is described by the following linear relations:
a ¼ 3:57818 104 T=K þ 7:18367 ð150 6 T=K 6 375Þ; b ¼ 2:61818 104 T=K þ 8:67187 ð150 6 T=K 6 375Þ; c ¼ 3:04967 105 T=K þ 32:41475 ð150 6 T=K 6 375Þ; V ¼ 0:112242 T=K þ 2019:836 ð150 6 T=K 6 375Þ: The thermal expansion coefficient is the quantitative characteristic of thermal expansion. We used the formula aL ¼ 1L DDLT , where aL – coefficient of thermal expansion, L – unit cell parameter. The value of the thermal expansion coefficient in a given direction corresponds to length of radius-vector, which is traced from origin of coordinates to edge of figure of expansion. The thermal expansion of the folic acid dihydrate is anisotropic, and along the crystallographic axis, b occurs even with compression of the structure (Fig. 3). For the construction of the 3D version of the thermal expansion diagram algorithm for MaplesoftÓ can be used [20] (Fig. 4). These figures allow presenting the anisotropy of the thermal expansion of the crystal at a certain temperature [21]. We found that the lack there of a network of hydrogen bonds along the crystallographic direction a leads to an anomaly of high thermal deformation along this direction. 4. Conclusions The general aim of these investigations is to report the results of the thermodynamic study of the folic acid dihydrate. The heat capacity of this vitamin B9 is measured over the temperature range from (6 to 333) K. The thermodynamic functions are calculated and the fractal dimension D is evaluated. Thermochemical parameters of formation are determined by combining the data obtained by using combustion calorimetry and heat capacity measurements. Acknowledgements The work was performed with the financial support of the Russian Foundation of Basic Research (Project Number 16-0300288). The work carried out using the equipment center for collective use ‘‘New materials and energy saving technologies”
Appendix A. Supplementary data
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JCT 16-180