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Volumetric and transport properties of aqueous nab(oh)4 solutionsCHEMICAL ENGINEERING THERMODYNAMICS
Chinese Journal of Chemical Engineering, 21(9) 1048ü1056 (2013)
Volumetric and Transport Properties of Aqueous NaB(OH)4 Solutions*
ZHOU Yongquan (ઞ≮ޞ)1,2, FANG Chunhui (ᡵᱛ)1,*, FANG Yan (ᡵ㢩)1, and ZHU Fayan
1 CAS Key Laboratory of Salt lake Resources and Chemistry, Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Qinghai 810008, China 2 Graduate School of Chinese Academy of Social Sciences, Beijing 100039, China Abstract Density, pH, viscosity, conductivity and the Raman spectra of aqueous NaB(OH)4 solutions precisely
measured as functions of concentration at different temperatures (293.15, 298.15, 303.15, 313.15 and 323.15 K) are
presented. Polyborate distributions in aqueous NaB(OH)4 solution were calculated, covering all the concentration
range, B(OH) is the most dominant species, other polyborate anions are less than 5.0%. The volumetric and the
transport properties were discussed in detail, both of these properties indicate that B(OH) behaves as a struc- ture-disordered anion.
Keywords aqueous NaB(OH)4 solution, volumetric property, transport property, polyborate distribution
the properties (pH, density, conductivity and viscosity) of saturated NaB(OH)4 in aqueous alkaline solutions. Hydroxy-hydrated borates constitute the bulk of However, all those studies were under the concentration the mineral and optical material kingdom. Especially of 1.0 mol·L1 or a saturated single point. In the present the tetrahydridoborate ( BH ), as the reduction product paper, the density, electrical conductivity, viscosity, of B(OH) , are versatile reducing agents in various acidity and Raman spectra of aqueous NaB(OH)4 solu- organic and inorganic processes tions were assembled systematically. Not only the volu- . The percentage of hydrogen presented in NaBH metric and transport properties of aqueous NaB(OH)4 4 and released by hy- drolysis are 10.6% and 10.8%, respectively. Therefore, solution were deliberated, but also the chemical spe- cies distribution was given for the first time. 4 is the most attractive chemical hydride for H2 generation and storage in automotive fuel cell applica-tions [2, 3]. However, the extensive use of NaBH4 fuel 2 EXPERIMENTAL
would require the disposal of large quantities of the product NaB(OH)4. NaBH4 can be regenerated from NaB(OH)4 chemically . Unfortunately, most Commercially available metaborate [NaB(OH)42H2O, chemical regeneration syntheses proposed so far in- Sinopharm Chemical Reagent Co., AR] was recrystal- volve several reaction steps with high cost. Furthermore, lized twice from double-distilled water  (electrical the by-products, wastes, and greenhouse gas emissions conductivity, <1.0 S·cm1). The entire sample solu- have already aroused the growing concern from the tions were prepared by mass using double-distilled public. Luckily, the use of an electrolytic cell to re- water, and the overall relative uncertainty in the solu- duce NaB(OH)4 would not create large quantities of tion preparation was 0.1%. The borate solutions were by-products, wastes, or emissions. There are a number carefully protected from atmospheric CO2 and can be of patents indicating the possibility of electroreduction used about one week without concentration changes. of B(OH) to BH with 20% to 25% current effi- Densities, , of all the solutions were determined ciency and 20% to 80% yield on electrocatalytic hy- using a DMA4500 apparatus (Anton Paar, Austria) drogenation cathodes . However, reproduction of with an uncertainty of 0.00003 g·cm3 and tempera- these claims was facing a number of difficulties, some ture was controlled to ±0.03 K. The instrument was researchers even got the conclusion that direct electro- calibrated prior to initiation of each series of measure- reduction of NaB(OH)4 into NaBH4 was impossible . ments, using air and double-distilled water as refer- Physicochemical properties such as density, elec- ence substances. Electrical conductivity, , was meas- trical conductivity, viscosity, and acidity at moderate ured with an YSI 3200 conductivity meter (YSI, USA) temperatures, affect the H2 generation and storage using black-platinized electrode with a reproducibility system as well as the electrochemical recyclability of of 0.3%. The constant of electrode was calibrated using sodium metaborate. The density of NaB(OH)4 solu- six NaCl standard solutions (0.0001, 0.001, 0.01, 0.1, tions has been measured at moderate temperatures by 0.5 and 1.0 mol·kg1). A standard solution was measured Ward et al. , Corti et al.  and Ganopolsky et al every five measurements, the constant recalibrated if . The conductivity and viscosity have been studied the deviation ı0.3%. Acidity, pH, of all the solutions by Corti et al. [13, 15], and Cloutier et al.  reported was measured using an Orion 310P-01 pH meter Received 2012-05-07, accepted 2012-09-13. * Supported by the National Natural Science Foundation of China (20873172) and Main Direction Program of Knowledge In- novation of Chinese Academy of Sciences (KZCX2-EW-307). ** To whom correspondence should be addressed. E-mail: email@example.com; firstname.lastname@example.org Chin. J. Chem. Eng., Vol. 21, No. 9, September 2013
(Thermo, USA) with a reproducibility of 0.5%. The Table 1 pH of aqueous NaB(OH)4 solutions as functions of
pH electrode was calibrated using three pH standard concentration at 298.15 and 323.15 K
solutions (4.003, 6.864 and 9.182), a standard solution was used for checkup after every five measurements, m/mol·kg1 the electrode recalibrated if the deviation ı0.5%. In all the pH and conductivity measurements, a thermo- 0.0010 9.733 9.425 stat (GDH-1015W, Sayfo Analytical Instrument Fac- 0.0040 10.123 9.792 tory, Ningbo, China) was used to maintain the tem- 0.0063 10.283 9.914 perature of the solutions within ±0.01 K uncertainty. 0.0101 10.349 9.926 Viscosity, , was measured with a single Ubbelohde 0.0725 10.852 10.362 viscometer (Jingliang Precise Instrument Co., Shang-hai, China), which was placed in a well-stirred con- 0.1715 11.084 10.576 stant temperature water bath and the temperature of 0.4003 11.352 10.771 the solutions was kept within ±0.05K uncertainty. The 0.6102 11.507 10.903 flow time was measured with an accurate 0.01 s stop- 0.8159 11.621 11.008 watch and the double-distilled was used for calibration. Measurements were repeated at least 4 times for each 1.0520 11.734 11.070 solution and temperature. The uncertainty of the vis- 1.4565 11.916 11.249 cosity measurements was estimated to be 0.5%. Ra- 1.9218 11.982 11.348 man spectra of solid and liquid samples were recorded 2.3792 12.107 11.395 in the ranges of 3004000 cm1, respectively, with a Nicolet Almega Dispersive Raman spectrometer (laser: 2.8476 12.231 11.492 532 nm, exposure time: 8 s) at room temperature. The 3.3676 12.323 11.55 solid samples were put in the microscope slide (num- 3.8549 12.412 11.624 ber of exposures: 1). The liquid samples were held in 4.3318 12.489 11.721 a quartz glass tube (number of exposures: 32). *4.9404 12.589 11.768 *5.4909 12.678 11.810 3 RESULTS AND DISCUSSION
*6.0737 12.783 11.904 3.1 Chemical species in solutions
* Samples for Raman spectra measurement Measured pH of aqueous NaB(OH)4 solutions were collected in Table 1 as functions of molality (m), at 298.15 and 323.15 K. pH of aqueous NaB(OH)4 solutions raises with concentration increasing, but at different concentration range different increasing rate can be found. In extreme low concentration (m<0.07 mol·kg1), pH rises sharply with concentration increase. This maybe because the polyborates do not show any significant extent of polymerization, and the dominant species are B(OH) and B(OH)3 in the extremely dilute solution. The de-hydration and polymerization make pH changes com-plicated with concentration increase in moderate con- Figure 1 Raman spectra of aqueous NaB(OH)4 solutions
centration (0.07<m<1.46 mol·kg1). A good linear and characteristic peak of the B(OH) at room temperature
relationship between pH and concentration can be aü4.94 mol·L1; bü5.49 mol·L1; cü6.07 mol·L1; dü seen in high concentration (m>1.46 mol·kg1), which microcrystals;ƽcharacteristic peak may be due to the low acidity makes B(OH) become the dominant borate. Raman spectrum is an effective method for Polyborate distributions in aqueous NaB(OH)4 polyborate study . In order to get a clear picture of solution at 298.15 and 323.15 K were calculated using the main polyborates and their equilibria in aqueous measured pH values and the literature equilibrium NaB(OH)4 solutions, Raman spectra of the labeled constants  by Newton iteration algorithm, as solutions in Table 1 were recorded and displayed in Fig. 2 shown. is the moles of boron for individual Fig. 1. Range of 5001200 cm1 is the most favorable polyborate divided by the moles of total boron. As Fig. 2 zone for the investigation of borate solution, which shown, the dominating borate anions is B(OH) , the might be considered as the characteristic absorption bands of polyborates other polyborates (H . The only obvious band near 741 cm1 in Raman spectra of aqueous NaB(OH) B O (OH) and B O (OH) are less than 5% in solutions is the characteristic peak of the B(OH) . Chin. J. Chem. Eng., Vol. 21, No. 9, September 2013
(a) 298.15 K (b) 323.15 K Figure 2 Variation in the distribution of boron species with concentration in aqueous NaB(OH)4 solutions at 298.15 and
Ƶ H3BO3;ƽB(OH) ; Table 2 Density and v of aqueous NaB(OH)4 solutions at various temperatures
m/mol·kg1 0.0307 1.00067 22.1884 0.99947 23.4299 0.99805 24.3370 0.99461 24.4818 0.99041 24.9200 0.0612 1.00305 22.8853 1.00183 23.8027 1.00038 24.7124 0.99688 25.6877 0.99259 27.3060 0.0921 1.00546 23.0420 1.00418 24.2819 1.00273 24.8619 0.99915 26.3281 0.99479 28.1111 0.1232 1.00788 23.1695 1.00654 24.5656 1.00508 25.0620 1.00140 26.9320 0.99698 28.7116 0.1545 1.01030 23.3013 1.0089 24.7881 1.0074 25.4286 1.00355 27.9945 0.99908 29.7095 0.3170 1.02210 25.8230 1.02061 26.7977 1.01912 27.0458 1.01510 28.7478 1.01011 31.1458 0.6504 1.04574 27.4018 1.04366 28.7341 1.04212 28.9026 1.03754 30.5086 1.03199 32.4506 0.9963 1.06938 28.3239 1.06653 29.9166 1.06471 30.2832 1.06012 31.2942 1.05390 33.1696 1.3888 1.09399 29.9393 1.09104 31.1314 1.08885 31.6384 1.08445 32.2011 1.07766 33.9063 1.7200 1.11370 31.0442 1.11084 31.9461 1.10870 32.3193 1.10351 33.1991 1.09681 34.5024 2.2405 1.14357 32.2168 1.14006 33.1724 1.13753 33.6169 1.13183 34.4942 1.12507 35.5012 2.7166 1.16885 33.2884 1.16517 34.1292 1.16254 34.5263 1.15689 35.2225 1.14931 36.3321 2.9647 1.18171 33.7061 1.17765 34.5941 1.17511 34.9278 1.16870 35.8063 1.16139 36.7332 3.7917 1.22073 35.2605 1.21667 35.9524 1.21369 36.3209 1.20724 37.0145 1.19934 37.8847 4.4038 1.24758 36.1549 1.24333 36.7914 1.23992 37.2010 1.23336 37.8235 1.22533 38.6030 Note: The densities are in units of g·cm3, and v are in units of cm3·mol1 So the sodium metaborate [NaB(OH)42H2O] was the solution, as a function of concentration and tem- assumed to dissociate in aqueous NaB(OH)4 solution perature are shown in Table 2. The apparent molar volumes v for these solutions, given in Table 2 were calculated from the equation Therefore, all our results reported for sodium metaborate were denoted as NaB(OH) ates into Na+ and B(OH) in aqueous solution. where 0 is the density of water at corresponding temperatures, 0 0.99823, 0.99707, 0.99568, 0.99225 3.2 Volumetric properties
and 0.98807 g·cm3 at 293.15, 298.15, 303.15, 313.15 and 323.15 K, respectively; m is the molality (mol·kg1) of solution and M2 is the molecular weight The densities of aqueous NaB(OH)4 solutions of the compounds, 101.828 for NaB(OH)4 here. were measured at 293.15, 298.15, 303.15, 313.15 and Most of the equations reported in the literature 323.15 K. The density and apparent molar volume of  with only two variables, i.e. the density and the Chin. J. Chem. Eng., Vol. 21, No. 9, September 2013
concentration or temperature. Here we proposed a new 3.2.2 Apparent molar volumes
expression, Eq. (3), which takes the density as a func- The concentration dependence of the v of tion of both concentration and temperature. NaB(OH)4 is shown in Fig. 4. Correspondingly, we A Bm Cmt Dmt2 Em1.5 Fm1.5t Gm1.5t2 (3) tted the experimental data to a three constant poly-nomial of concentration (mol·kg1) where A, B, C, D, E, F, G are empirical constant de- termined by least-squares fit; m is the concentration in M A ( v ) A m A m (4) units of mol·kg1; t is the temperature in units of °C. where A ( v f ) , A , and A are empirical constant Herein, for the aqueous NaB(OH) 4 solution, an em- determined by least-squares fit, v f is the apparent pirical equation molar volume at infinite dilution which is also equal 0.99618 0.07451m 2.0135×104mt to the limited partial molar volume. The least-squares 2.2871×106mt2 0.00158m1.5 parameters together with the correlation coefficient of 5.50018×106m1.5t 2.46203×107m1.5t2 ts are reported in Table 4. with R2 0.9988 was deduced in temperature range from 20 to 50 °C. Fig. 3 displays the measurements and the empirical density correlation of aqueous NaB(OH)4 solutions vs. concentration at 293.15, 298.15, 303.15, 313.15 and 323.15 K. As shown in Fig. 3, our experi-mental data are also in good agreement with the lit-erature . Figure 4 Plot of apparent molar volume ( v) against molality
of aqueous NaB(OH)4 solutions at different temperatures
Ƶ313.15 K;ƽ323.15 K;Ʒ303.15 K;ͩ298.15 K; 293.15 K
The temperature dependence of the v f of NaB(OH)4, shown in Fig. 5, can be expressed by the equation 09.71 27.65T 0.087T 9.21u10 T (5) with an average deviation of 0.4 cm3·mol1. The in-crease in the v f of NaB(OH) 4 with increasing of tem- perature (Table 3) could be attributed to the form of a tight hydration sphere, and the behavior of the first layer hydrated water molecules interacting with bulk water region. The apparent molar expansibilities, w , calculated from Eq. (5) between 293.15 Figure 3 Density vs. concentration plots for aqueous
and 323.15 K (Table 3) indicate that NaB(OH)4 be- 4 solutions at various temperatures
ƻexperimental values;Ʒliterature data for NaB(OH) haves like most common electrolytes with decreasing calculated data from nonlinear fitting I with increasing temperature. Table 3 Least-squares parameters of Eq. (5) [ I and w(v ) /wT for aqueous NaB(OH)
w(v ) / T 293.15 20.50 8.7662 0.6211 0.9965 0.2250 0.00461 298.15 21.63 9.2237 0.9703 0.9986 0.2020 0.00696 303.15 22.53 8.3561 0.6493 0.9984 0.1555 0.00616 313.15 23.85 8.5864 0.9613 0.9900 0.1253 0.00185 323.15 25.03 10.037 1.8221 0.9661 0.1185 Chin. J. Chem. Eng., Vol. 21, No. 9, September 2013
Table 4 Viscosity of aqueous NaB(OH)4 solutions at as
functions of concentration at 298.15 and 323.15 K
m/mol·kg1 0.0010 0.8996 0.5529 0.0050 0.9010 0.5546 0.0105 0.9027 0.5581 0.0498 0.9138 0.5702 0.0972 0.9299 0.5918 Figure 5 Partial molar volumes at infinite dilution of
0.1965 0.9604 0.6277 NaB(OH)4 as a function of temperature
0.4032 1.0309 0.7116 Ƶpresent work;ƽWard et al.;ƷCorit et al. 0.6117 1.1041 0.7788 As Fig. 5 shown, the agreement among the dif- 0.8214 1.1912 0.8625 ferent data sources is satisfactory. Using Hepler's  1.0318 1.2910 0.9362 reasoning, NaB(OH) 1.4639 1.5067 1.1177 4 would be classified as a "struc- ture breaking" solute between 298.15 and 323.15 K 1.9061 1.7771 1.2960 (that is, if v f w(v ) / T 2.3861 2.1276 1.5155 ute has the hydrophilic character, while if the behavior 2.8709 2.5957 1.7919 shows that v f w(v ) / T 3.3606 3.0945 2.1461 solute has hydrophobic character) , this may due to the 3.8623 3.7088 2.4701 unique structure of B(OH) anion (four tetrahedrons 4.4012 4.5922 2.9699 OH groups) . 5.1494 6.1484 3.8338 3.3 Transport properties
Measured viscosities for aqueous NaB(OH) least-squares fitted parameters in Eq. (6) are summa- solutions were collected in Table 4. The viscosity rized in Table 5. data are plotted in Fig. 6 at two temperatures. A The viscosity data of concentration less than 0.1 semi-empirical equation : mol·L1 were analyzed in terms of the extended Jones-Dole viscosity equation: b m c m K 1 A c B c Dc (7) has been shown to be useful for data tting over wide concentration range, where a0, b0, and c0 are the where r /0·r, and 0 are the relative viscosity, adjustable temperature dependent parameters. The viscosity of the solution and viscosity of the solvent, calculated data from nonlinear fitting calculated data from the extended Jones-Dole equation Figure 6 (a) Viscosity vs. concentration plots for solutions at 298.15 K and 333.15K and (b) relative viscosity vs. concentration
ƽexperimental values at 298.15 K;Ƶexperimental values at 333.15 K
Chin. J. Chem. Eng., Vol. 21, No. 9, September 2013
Table 5 Coefficients for Eqs. (6) and (7) and the hydration number
298.15 0.8937 0.3569 0.0034 0.3660 3.2923 0.98137 20.9 323.15 0.5895 0.4211 0.0115 0.9987 0.1704 0.2579 5.2630 0.99768 13.5 respectively, and c is the molar concentration. Coeffi- Table 6 Electrical conductivity of aqueous NaB(OH)4
solutions at as functions of concentration
) is a measure of ion-ion interactions and may be calculated from equilibrium theory, as summed by at 298.15 and 323.15 K
Jenkins and Marcus . Coefficient (B), also called /mS·cm1 m/mol·kg1 the Jones-Dole coefficient, is an empirical constant, qualitatively correlating on the size of solute particle 0.0005 0.04254 0.06552 and on ion-solvent interaction characteristic for elec- 0.0010 0.08336 0.128 trolyte and solvent . B of B(OH) were calcu- 0.0040 0.3234 0.4909 lated by subtracting the B of Na+ ion  from the 0.0063 0.5058 0.7523 values of NaB(OH)4 at 298.15 and 323.15 K, respec- 0.0101 0.7842 1.143 tively, that is B 0.0725 5.267 7.713 L·mol1, which are well con- 0.1715 10.34 16.14 sistent with the literature values of dilute aqueous 0.4003 19.16 31.57 NaB(OH)4 solutions at 298.15 K . The calculated 0.6102 26.00 42.61 B of B(OH) (B <0) indicated it behaves as a struc- ture disordering ion between 298.15 to 323.15 K, 1.0520 36.52 60.45 which is consistent with our study on volumetric 1.4565 43.34 73.01 properties of aqueous NaB(OH)4 solution. 1.9218 47.25 83.31 For a dilute solution of spherical colloidal sus- pensions, Einstein derived the relation 2.3792 49.55 90.31 2.8476 51.7 94.44 3.3676 52.31 97.54 where is the volume fraction of the solute. For 1Ή1 3.8549 51.92 100.4 type electrolyte, Eq. (9) becomes 4.3318 50.99 99.92 K 1 2.5V c (9) 4.9404 48.42 99.73 where Vh is the hydrodynamic volume. Where Vh is 5.4909 44.57 98.52 the partial molar volume ( v f ) of the unsolvated sol- 6.0737 42.01 95.64 ute particle in a continuum solvent. Thus, the value of the hydration number (Hn) can be calculated as H B /V (10) equation [30, 34]: Hn lies between 0 and 2.5 for unsolvated species and has higher values for solvated species. The calcu- (m / ) exp[b(m lated Hn of B(OH) are 20.9 and 13.5 at 298.15 and where is the concentration corresponding to the 323.15 K indicated the B(OH) maximum conductivity max at a given temperature; a aqueous solution . It's maybe another evidence for and b are empirical parameters; m is molality in units a tight hydration sphere is formed around B(OH) in of mol·kg1. In all the concentration range a function aqueous solutions. between conductivity and concentration can be given though nonlinear fitting. 3.3.2 Electrical conductivity
The decrease of molar conductivity with increas- The experimental electrical conductivities of ing concentration must be due to the increase of vis- aqueous NaB(OH)4 solutions are listed in Table 6. cosity of the aqueous solution and polymerization. Figure 7 (a) shows that a break can be found, the The polymerization makes charge carriers in unit vol- conductivity increases as concentration and tempera- ume decrease, and higher polyborate anions and their ture. The conductivity data over the whole concentra- hydration also means the charge carriers are large in tion range studied were tted to the Casteel-Amis size, and the increasing viscosity make migration rate Chin. J. Chem. Eng., Vol. 21, No. 9, September 2013
Figure 7 (a) Conductivity vs. concentration plots for solutions at 298.15 and 323.15 K and (b) molar conductivity vs. con-
centration (<0.01 mol·L1) to zero
ƽexperimental values at 298.15 K;Ƶexperimental values at 323.15 K;
calculated data from nonlinear fitting Table 7 Values of kmax, u, a and b coefficients for Eq. (11) and the transport properties of aqueous NaB(OH)4 solutions
298.15 52.37 3.2297 0.00208 3.72×104 9.5646 0.2526 323.15 100.11 4.3081 0.00475 5.82×104 16.2050 0.1640 slower. In extremely dilute solution (smaller than 0.01 mol·L1), it can be ensure that polyborates do not exist to any significant extent polymerization so the main species are B(OH) and B(OH) where B(OH) is limiting conductivity (S·m2·s1); F is 3 with an equilibrium the Faraday constant (9.64846×104 C·mol1); e the elementary charge (1.6022×1019 C); zi the charge number of the ion; 0 the viscosity of water Limiting molar conductivity ( /f ) of NaB(OH) 0 8.903 and 5.494×104 Pa·s at 298.15 and 323.15 can be gotten by extrapolate to c 0 mol·L1 through K, respective); R is the universal gas constant (8.314 the Kohlrausch correlations. As Fig. 7 (b) shown, the J·mol1·K1); T is the absolute temperature (K). The conductivity of an ion in pure water, which is the lim- plot of / against c1/2 is a line with /f as intercept iting ionic conductivity, is related to the water viscos- to slope A at concentration (c<0.01 mol·L1) where ity by the Stokes-Einstein equation [Eq. (14)], where 136.05 S·cm2·mol1. rs is the Stokes radius or hydrodynamic radius [35, 36]. The limiting ionic conductivities for the B(OH) ion The rs, the ionic mobility ( P ), the diffusion co- were calculated by subtracting the limiting ionic con- ) and the transference number ductivities of Na+ ion  from the limiting molar conductivity of NaB(OH) ) for B(OH) anion can be calculated as Eqs. (14)(17), respectively, and list in Table 7. 56.15 S·cm2·mol1 which are well consistent with Corti's conclusion at 298.15 K . 4 CONCLUSIONS
pH of aqueous NaB(OH) 4 solutions were pre- S r (14) cisely measured as functions of concentration from dilute to saturation at 298.15 and 323.15 K. Coupling z u F (15) with Raman spectra of some concentrated samples, polyborate distribution calculated using measured pH values and literature equilibrium constants of aqueous Chin. J. Chem. Eng., Vol. 21, No. 9, September 2013
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