Standard enthalpy of formation of disodium hydrogen phosphate hexahydrate and sodium diphosphate

J. Chem. Thermodynamics 43 (2011) 521–526

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Standard enthalpy of formation of disodium hydrogen phosphate hexahydrate and sodium diphosphate H. Gmati-Ben Khaled, I. Khattech, M. Jemal ⇑ Faculty of Science, Chemistry Department, Applied Thermodynamics Laboratory, Tunis El Manar University, 2092 Tunis El Manar, Tunisia

a r t i c l e

i n f o

Article history: Received 4 July 2010 Received in revised form 23 October 2010 Accepted 8 November 2010 Available online 20 November 2010 Keywords: Calorimetry Thermochemistry Heat of formation Disodium hydrogen phosphate Sodium diphosphate

a b s t r a c t Commercial disodium hydrogen phosphate dodecahydrate (Na2HPO412H2O) was used as a precursor for synthesizing disodium hydrogen phosphate hexahydrate (Na2HPO46H2O) and sodium diphosphate (Na4P2O7). The purity of the synthesized products was checked up by IR spectroscopy and X-ray diffraction. The heat of dissolution of these compounds, in acid solutions of several concentrations (w/w) of H3PO4 was measured in a C-80 SETARAM calorimeter. Many dilution and mixing processes were also realized in the calorimeter in order to get the standard enthalpy of formation of these products. The values obtained for the enthalpies of formation are: (3210.5) and (3516.5) kJ  mol1 for sodium diphosphate (Na4P2O7) and disodium hydrogen phosphate hexahydrate (Na2HPO46H2O), respectively. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Disodium hydrogen phosphate (Na2HPO4) is used as a saline cathartic, in water treatment and in ceramics, animal food, shampoos, detergents, and medicinal production. This compound exists in many hydrated forms. Ghule et al. [1], Duval [2], Hammick et al. [3] and Wendrow and Kobe [4] showed that disodium hydrogen phosphate dodecahydrate (Na2HPO412H2O) decomposes into (Na2HPO48H2O), (Na2HPO47H2O), (Na2HPO42H2O), (Na2HPO41H2O) and into the anhydrous form. Sodium diphosphate (Na4P2O7) is used in the food industry as an additive to the preparation of products such as hamburgers, or in the form of solutions for the immersion-treatments of seafoods to control yield and modify texture. Its incorporation in soap powders and synthetic detergents stabilizes sodium perborate and minimizes the risk of damages of clothes by oxidation. Synthesis of sodium diphosphate has been reported by several authors [1,2,5–7]. The synthesis was carried out by heating different precursors at various temperatures. According to Gangadharam et al. [5] this product could be obtained by heating sodium diphosphate decahydrate (Na4P2O710H2O) up to 150 °C with a heating rate of 1 °C  min1. Then the product is maintained at that temperature for a long time. Borisova et al. [6] synthesized sodium diphosphate from the dihydrate (Na4P2O72H2O) by heating at 200 °C. Edwards [7] heated also the dihydrate at the same temperature.

⇑ Corresponding author. Tel.: +216 98 902 771; fax: +216 71 883 424. E-mail address: [email protected] (M. Jemal). 0021-9614/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2010.11.008

Ghule et al. [1] and Duval [2] used disodium hydrogen phosphate dodecahydrate (Na2HPO412H2O) but both of them used a temperature range to get the sodium diphosphate. In this work we used the commercial disodium hydrogen phosphate dodecahydrate as a precursor for the synthesis of sodium diphosphate (Na4P2O7) and that of disodium hydrogen phosphate hexahydrate (Na2HPO46H2O) which has not been previously reported. Dehydration of (Na2HPO412H2O) was carried out thermogravimetrically in order to determine the synthesis temperature range of each product. The enthalpies of dissolution of these compounds in appropriate solvents were determined by using a calorimeter. Sodium diphosphate is found in two crystal systems [8,9]: the orthorhombic system with cell parameters as a = 9.367  1010 m, b = 5.390  1010 m and c = 13.480  1010 m and the hexagonal system with a = 10.79  1010 m, b = 10.79  1010 m, and c = 13.49  1010 m. Enthalpy of formation of disodium hydrogen phosphate hexahydrate (Na2HPO46H2O) is unknown, however that of sodium diphosphate was determined by three authors [6,10,11] but one of the published values [10] differs considerably from the other values. In order to get the formation enthalpies of these compounds, many processes such as dissolution, dilution and mixing were carried out in phosphoric acid aqueous solution with varying weight percentages of H3PO4. This difference in composition was necessary in order to get the same final state in the thermochemical cycles. The used percentages were 3.85, 3.93, and 4.00 (w/w) H3PO4.

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tion of Na2HPO4 into Na4P2O7 and water according to the following reaction:

2. Preliminary experiments Commercial disodium hydrogen phosphate, ‘Na2HPO412H2O’, of a purity higher than 99% (Fluka) was used. The product was checked up by XR diffraction using a SEIFERT-XRD 3000 TT diffractometer, and the diffractogram is in good agreement with the database [12] at least in the domain 2h < 30° for which data are given. IR spectroscopy has been carried out between (4000 and 500) cm1 using a Perkin-Elmer 8400 FTIR spectrometer and the spectrum shows characteristic bands of the product. Preliminary experiments carried out in air at room temperature showed that the commercial hydrated product decomposes spontaneously as time goes by. Consequently the compound has been followed during several days using a B60 SETARAM thermobalance. The TG curve is showed in figure 1. It is seen a continuous weight loss which stops after about 60 h under room temperature. Then, the final product was heated from room temperature to 750 °C at a heating rate of 150 °C  h1 and a nitrogen gas flow of 2 L  h1. Figure 2 shows successive dehydration steps. X-ray diffraction performed on the final product and on the intermediate product appearing at about 150 °C and the weight loss recorded show that the last transformation corresponds to the decomposi-

Na2 HPO4 (s) ! 1/2Na4 P2 O7 (s) + 1/2H2 O(g). Taking into account the proportionality between the distance separating two plateaux and the corresponding weight loss, the formulas of the starting and intermediary compounds have been determined as Na2HPO46H2O and Na2HPO45H2O respectively. So the two first decompositions correspond to the following successive reactions: 58—85  C

Na2 HPO4  6H2 OðsÞ ƒƒƒƒ! Na2 HPO4  5H2 OðsÞ þ 1H2 OðgÞ 90—120  C

Na2 HPO4  5H2 OðsÞ ƒƒƒƒ! Na2 HPO4 ðsÞ þ 5H2 OðgÞ Pentahydrate and hexahydrate have not been previously reported in the literature despite the fact the latter is more stable than the commercial ‘‘dodecahydrate’’ at room temperature. 2.1. Synthesis of the samples Taking into account the results of the thermogravimetric analysis, Na2HPO4 was synthesized by heating commercial ‘‘dodecahydrate’’ at temperature up to 230 °C followed by the maintenance of that temperature during one night. Synthesis of sodium diphosphate was carried out according to the same procedure except that the heating temperature was 350 °C. Purity of the synthesized products was checked by X-ray diffraction [12] and infrared spectroscopy [13,14]. X-ray profiles recorded on Na2HPO4 (figure 3) and Na4P2O7 (figure 4) show a good agreement with the ICSD 37142 and 10370 files of these products. IR spectra show bands in the ranges (1150 to 1060, 950 to 860, and 550 to 520) cm1 characterizing HPO2 in disodium 4 hydrogen phosphate [13] and in the ranges (1170 to 1000, 970 to 930, and 780 to 760) cm1 characterizing P2 O4 7 group in sodium diphosphates [14]. 2.2. Calorimetric study

FIGURE 1. Isothermal TG curve of commercial Na2HPO412H2O in air at room temperature.

2.2.1. General consideration In order to determine the enthalpy of formation of any compound from the values of the dissolution enthalpies, it is used a procedure in which the species or compounds existing in solution

FIGURE 2. TG curve of Na2HPO46H2O.

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Intensity

λ=1,54Å

10

20

30

40

2θ/°

50

60

70

FIGURE 3. Diffractogram of Na2HPO4.

FIGURE 4. Diffractogram of Na4P2O7.

are involved in other processes to get successive reactions which sum leads to the reaction of formation of the considered compound. In this way, it was possible to determine the enthalpies of formation and mixing of several hydroxyl-, chloro-, carbonateand fluoro-apatites [15–17]. An alternative way consists in considering a particular reaction involving the compound to be studied and other solid reactants and products for which the formation enthalpies are reported in the literature. Measurements of the dissolution of the whole constituents in the same solvent enable to derive the enthalpy of the reaction. This is true only when reactants and products are solids and dissolution leads to the same final state. When one or more reactant or product is a solvent constituent, here is water, the mixing process leads to a solution more diluted than the starting solvent. Consequently the composition of the latter has to be modified in order to lead, on dissolution or dilution, to a common solution composition. In addition complementary experiments have to be done in order to close the thermochemical cycle.

For example, the formation enthalpy of Na2HPO46H2O can be deduced from the enthalpy of the following reaction: Dr Hl

Na2 HPO4 ðsÞ þ 6H2 OðlÞ ! Na2 HPO4  6H2 OðsÞ

ðR1Þ

In this reaction the enthalpies of formation of Na2HPO4(s) and H2O(l) are picked from the literature [18] and the following thermochemical cycle can be considered (cycle1).

Na2HPO4(s) + 6H2O(l) + + Slv1 (3,85%) Slv1 ΔdilH1 ΔsolH1 E1

+

ΔrH1

Na2HPO4.6H2O(s) + Slv2 (3,93%) ΔsolH2

E2

ΔmixH1 E3

E4

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Slv1 is a 3.85% (w/w) phosphoric acid solution noted as [H3PO4135.96H2O]. Dissolution of Na2HPO4 and dilution of H2O in Slv1 lead to E1 and E2 solutions, respectively. The latter process is schematized as:

[H3 PO4 135.96H2 O] + 6H2 OðlÞ ! [H3 PO4 141.96H2 O] The final solution is a 3.69% (w/w) of H3PO4 composition (E2). Enthalpy of this process was calculated from the literature data [19]. Mixing volumes of E1 and E2 containing the same amount of H3PO4 moles leads to a solution having the mean value acid composition (E3 with 3.77% (w/w) of H3PO4 or [H3PO4138.96H2O]). That composition is the same as the one resulting from dissolution of Na2HPO46H2O in 3.93% (w/w) of H3PO4 or [H3PO4132.96H2O] taking into account the added water molecules, and so the thermochemical cycle is balanced. For sodium diphosphate, the following reaction was considered:

Ddil H1

Dr H2

2Na2 HPO4  6H2 OðsÞ ! Na4 P2 O7 ðsÞ þ 13H2 OðlÞ

ðR2Þ

And the corresponding cycle is given below (cycle2):

2Na2HPO4,6H2O(s) + Slv3 (4,00%)

value differs from the standard ones 29.7447 [20], 29.773 [21], and 29.765 [22], by 1.2%. The dissolutions of phosphate products were carried out by dissolving from (14 to 55) mg of a solid in 4.5 mL of the calorimetric solvent. The drawing of the heat (DHmes) determined by integrating the rough thermogram as a function of the moles number of solid gives a straight line which slope equals the molar dissolution enthalpy (DsolH) of the compound. As indicated previously mixing processes (E1 + E2), (E6 + E7) were realized by considering volumes of solutions having the same amount of H3PO4. This was also so for (E5 + E8). One of the two solutions to be mixed, E1, E6, or E8 contains variable amounts of dissolved salt. Enthalpies of dilution processes were calculated by linear interpolation of literature data considering the interval to which belongs each of the solutions [19]. These processes correspond to the following reactions:

½H3 PO4  135:96H2 O þ 6H2 OðlÞ ! ½H3 PO4  141:96H2 O Ddil H2

½H3 PO4  135:96H2 O þ 13H2 Oð1Þ ! ½H3 PO4  148:96H2 O

ðR3Þ ðR4Þ

ΔrH2

Na4P2O7(s) + 13H2O(l) + + Slv1 Slv1 ΔsolH4 ΔdilH2

ΔsolH3

E6

+

3.1. Dissolution processes

E7 ΔmixH2

E5

3. Results

E8 ΔmixH3

Tables 1 to 3 show the values measured for the heats (Qr) of dissolution of increasing number of moles (n) of various solids in several calorimetric solvents. Plotting the values of the measured heats (Qr) versus the number of moles (n) for a specific solid, it is obtained a straight line which slope is equal to the enthalpy of dissolution of the solid in the used solvent. Equations of the lines are as follows:

Qr ¼ 8:1n þ 0:0026; In this cycle, the starting compound is the disodium phosphate hexahydrate, the formation enthalpy of which has been determined previously. However dissolution of this compound leads to a solution containing monophosphate species (E5) whereas the final solution resulting from dissolution of diphosphate (E8) should contain diphosphate ions and so closing the cycle needs determination of the enthalpy resulting from mixing E5 and E8 solutions. Sodium diphosphate was added to Slv1 (3.85% (w/w) H3PO4) leading to the solution E6. Addition of water to Slv1 leads to solution E7 having 3.52% (w/w) H3PO4 or [H3PO4148.96H2O]. The mixing of the resulting solutions (E6 and E7) is made as was made the mixing of solutions (E1 and E2), with volumes of them containing the same quantity of phosphoric acid. This leads to a solution having 3.68% (w/w) H3PO4 or [H3PO4142.46H2O], consequently the concentration of Slv3 was fixed as 4.00% (w/w) H3PO4 or [H3PO4130.46H2O] in order to get, on dissolution of hexahydrate, the same final composition. 2.2.2. Experimental A C-80 SETARAM calorimeter operating at 25 °C was used in the reversal cell mode. This device is suitable for dissolution, dilution and mixing processes to be performed in a wide range of various proportions of reactants or solutions. The reliability of the device has been checked up by measuring the heat, Q, resulting from the dissolution of various amounts ‘m’ (10 to 50) mg of tri(hydroxymethyl) aminomethane, or ‘TRIS’ in 5 mL of a 0.1 molal HCl solution. Least square processing of the linear expression of Q over ‘m’ gave a value of the slope leading to a molar enthalpy value of solution as 30.14 ± 0.27 kJ  mol1. This

R2 ¼ 0:9841 for Na2 HPO4 in Slv1 ð3:85%Þ

ð1Þ

Qr ¼ 63:9n þ 0:0014; R2 ¼ 0:9989 for Na2 HPO4  6H2 O in Slv2 ð3:93%Þ;

ð2Þ

Qr ¼ 74:9n þ 0:0009; R2 ¼ 0:9992 for Na2 HPO4  6H2 O in Slv3 ð4:00%Þ;

ð3Þ

Qr ¼ 39:9n þ 0:0001; R2 ¼ 0:9991 for Na4 P2 O7 in Slv1 ð3:85%Þ:

ð4Þ

Table 4 summarizes the values of the molar enthalpies of solution with the corresponding errors determined statistically taking into account the scatter of the experimental values around the least square lines.

TABLE 1 Enthalpy of solution of Na2HPO4(s) in Slv1. Na2HPO4(s) in ‘‘Slv1’’ 3.85% (mmol)

Qr (J)

0.1063 0.1305 0.1756 0.2294 0.2576 0.2762 0.3583

3.3693 3.5323 4.1287 4.3797 4.7530 4.7802 5.3903

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H. Gmati-Ben Khaled et al. / J. Chem. Thermodynamics 43 (2011) 521–526 TABLE 2 Enthalpy of solution of Na2HPO46H2O(s) in Slv2 and Slv3.

TABLE 5 Enthalpy of mixing DmixH1.

Na2HPO46H2O Slv2 (3.93%)

Slv3 (4.00%)

(mmol)

Qr (J)

(mmol)

Qr (J)

0.07292 0.09844 0.12116 0.14792 0.17252 0.24028

6.068 7.739 9.199 10.702 12.227 16.865

0.07444 0.09992 0.131 0.15508 0.1824 0.20176

6.396 8.392 10.668 12.623 14.646 15.843

mmol of (Na2HPO4)

Qr (J)

0.0341 0.0484 0.0717 0.0951

0.0229 0.0416 0.0937 0.1550

TABLE 6 Enthalpy of mixing DmixH2.

TABLE 3 Enthalpy of solution of Na4P2O7(s) in Slv1.

mmol of (Na4P2O7)

Qr (J)

0.0196 0.0270 0.0391 0.0998

0.0259 0.0509 0.0903 0.2602

Na4P2O7(s) in ‘‘Slv1’’ 3.85% (mmol)

Qr (J)

0.0552 0.0578 0.0610 0.0674 0.0700 0.0780 0.1003 0.1460

2.3508 2.3606 2.5892 2.8375 2.9547 3.2471 4.1700 5.9397

TABLE 7 Enthalpy of mixing DmixH.

DmixH1/(kJ/mol) (E1 + E2) 2.2 ± 0.4

DmixH2/(kJ/mol) (E6 + E7)

DmixH3/(kJ/mol) (E5 + E8)

2.9 ± 0.1

0

TABLE 8 Enthalpy of dilution DdilH.

3.2. Mixing processes 3.2.1. Cycle1 Volumes of about 1 mL of E1 and E2 containing the same amount of phosphoric acid were mixed to lead to E3 solution. Various amounts of Na2HPO4 were previously dissolved in E1 volume and thus the variation of the measured enthalpy results from the dilution of HPO2 ions and not from that of the phosphoric acid. 4 The results are reported in table 5 and could be expressed as DmixH1 = 2.2n  6E05, (R2 = 0.9877) (5) leading to a value of 2.2 kJ per Na2HPO4 mole.

DdilH1/(kJ/mol) 6H2O + Slv1

DdilH2/(kJ/mol) 13H2O + Slv1

0.031

0.066

TABLE 9 Enthalpy of reactions equations (R1) and (R2).

DRH1/(kJ/mol)

DRH2/(kJ/mol)

53.63

107.06

TABLE 10 Standard molar enthalpy of formation of the phosphate compounds at 25 °C.

3.2.2. Cycle2 Mixing E6 and E7 solutions was performed after dissolving various amounts of Na4P2O7 in E6. The results are reported in table 6 and allowed to express DmixH2 as: DmixH2 = 2.9n  3E05; (R2 = 0.9990) (6) leading to a value of 2.9 kJ per Na4P2O7 mole. Solutions E5 and E8 have the same acid concentration (3.68%) but HPO2 and P2 O4 ions respectively. Mixing E5 and E8 led to 4 7 an undetectable thermal effect suggesting a possible hydrolysis 2 of P2 O4 7 to HPO4 in a previous process, according to the following reaction:

DfH°(Na2HPO46H2O)/(kJ/mol)

DfH°(Na4P2O7)/(kJ/mol)

3516.5

3210.5

3.3. Dilution processes Enthalpies of formation of Slv1, E2 and E7 were picked up from the literature [19] and listed below together with the enthalpies of dilution in kJ/mol at 25 °C, table 8

Df H ð½H3 PO4  135:96H2 OÞ ¼ 1288:358 ðH3 PO4 3:85%Þ; Df H ð½H3 PO4  141:96H2 OÞ ¼ 1288:389 ðH3 PO4 3:69%Þ;

2 P2 O4 7 þ H2 O ! 2HPO4

This may also result from the very large dilution of the corresponding solutions in phosphate entities (0.02 M). Table 7 shows the molar enthalpies of mixing at 25 °C.

Df H ð½H3 PO4  148:96H2 OÞ ¼ 1288:424 ðH3 PO4 3:52%Þ: Table 8 gives the calculated enthalpies of various dilutions.

TABLE 4 Enthalpies of solution of salts in different percentages (w/w) of H3PO4. Compound

Na2HPO46H2O(s)

Na2HPO46H2O(s)

Na2HPO4(s)

Solvent

Slv2 (3.93%)

Slv3 (4.00%)

Slv1 (3.85%)

Na4P2O7(s) Slv1 (3.85%)

DsolH (kJ/mol)

DsolH2 63.9 ± 1.9

DsolH3 74.9 ± 2.0

DsolH1 8.1 ± 0.6

DsolH4 39.9 ± 0.6

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The whole results enable to derive the enthalpies of (R1) and (R2) reactions at 25 °C. Table 9 presents the values of these enthalpies. Taking into account the enthalpies of formation of Na2HPO4 and H2O [18] it is possible to estimate the values of the enthalpy of formation of disodium hydrogen phosphate hexahydrate (Na2HPO46H2O) and thus that of sodium diphosphate (Na4P2O7), at 25 °C. Table 10 presents the values calculated for these enthalpies. Because of the lack of errors on the literature values, accuracy of these quantities cannot be evaluated. 4. Discussion and conclusion As mentioned above, the heat of formation of Na2HPO46H2O has never been previously determined but that of Na4P2O7 has been determined by Borisova et al. [6] in 1996 (876.0 ± 4.0 kJ/mol) by using HNO3 3 mol  dm3 as a solvent, Irving and McKerrell [10] in 1968 (3192.3 ± 4.1 kJ/mol) using a 60% perchloric acid solution and Meadowcroft and Richardson [11] in 1963 (880.3 ± 10.0 kJ/ mol) using a HCl 6N solution. A considerable divergence is observed but the papers published in 1968 and 1996 reported erroneous values from that of 1963 and 1968, respectively. The value obtained here is close to the value published in 1968.

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JCT 10-226