ISSN 0036-0236, Russian Journal of Inorganic Chemistry, 2007, Vol. 52, No. 9, pp. 1359–1362. © Pleiades Publishing, Inc., 2007. Original Russian Text © G.S. Kuanysheva, K.U. Dzhamansarieva, G.Zh. Sdikova, 2007, published in Zhurnal Neorganicheskoi Khimii, 2007, Vol. 52, No. 9, pp. 1453–1456.
SYNTHESIS AND PROPERTIES OF INORGANIC COMPOUNDS
Stability of s-, p-, and d-Element Diphosphates in Water G. S. Kuanyshevaa, K. U. Dzhamansarievab, and G. Zh. Sdikovaa a
b
Al-Farabi State University of Kazakhstan, pr. al-Farabi 71, Almaty, 050038 Kazakhstan Satpaev State Technical University of Kazakhstan, ul. Satpaeva 23, Almaty, 050013 Kazakhstan Received March 1, 2007 0
Abstract—The mean atomic Gibbs energies of formation of (∆f G at ) of s-, p-, and d-element diphosphates have been calculated using ion increments of the Gibbs energy (∆fG0). The diphosphate hydrolysis kinetics is con0
sidered, and a correlation between the ∆fG at values and the hydrolysis rate constants is presented. DOI: 10.1134/S0036023607090082
The developing phosphorus industry in the Republic of Kazakhstan poses a variety of problems, including those of raising the phosphate mining output and creating new multifunctional materials. Water–salt systems in which hydrolysis and complex formation are in competition are frequent in practice, including commercial processes, various syntheses involving diphosphate ligands, and industrial and natural water. Nevertheless, there is only limited information concerning the physicochemical properties of phosphates. In particular, there has been no complete systematic analysis of the dependence of diphosphate hydrolysis kinetics on the properties (radius, ionization potential, polarizability, and polarizing power) of the cation of the polymer salt or on the phosphate structure. Gaining such information would provide a substantiated approach to predicting the stability of both individual and modified phosphorus polymers. Here, we report the hydrolysis kinetics of s-, p-, and d-element diphosphates in water and relate their thermodynamic functions of formation to kinetic parameters. In doing this, we use Kh.K. Ospanov’s general principles of predicting the solubility order of solids in terms of the approximate linear functions log W = 0
0
0
a∆f G at + b and log K = a∆f G at + b [1], where ∆f G at is the mean atomic Gibbs energy of formation of a compound (kJ/(mol at)). The former relationship is used in the quantitative prediction of unknown hydrolysis rates within one type of hydrolysis reactions; the latter, in the qualitative estimation of the hydrolytic stability order for a group of similar compounds. Furthermore, we present calculated thermodynamic 0
functions of formation (∆fG0, ∆f G at ) of diphosphates for series of elements in some columns and rows of the Periodic Table.
EXPERIMENTAL Thermodynamic calculations were carried out using the ion increment method [2]. The standard Gibbs energy of a solid salt was calculated as ∆f G0Mm(XαOβ)(s) = (m∆f G0M(sln, H2O, st)K + n∆f G0(XαOβ)m–, where M is the cation, X is the anion, m and n are the stoichiometric indices of the cation and the anion, and K is the proportionality factor between the thermodynamic function of the compound in the crystalline state and the same function of the compound in aqueous solution under standard conditions. Using reference data for alkali, alkaline-earth, s-, and p-metal cations in the standard aqueous solution of ion increments, it is possible to calculate the standard Gibbs energies of s-, p-, and d-element salts in the solid state. By comparing mean atomic Gibbs energy values, we established hydrolytic stability series for diphosphates in water. Calculated Gibbs energies of formation for the diphosphates examined are presented in Table 1. Below, we present hydrolysis rate constant data for s-, p-, and d-element diphosphates synthesized by standard procedures [3]. The resulting compounds were identified by X-ray powder diffraction, IR spectroscopy, atomic absorption spectrometry, and chemical analysis. The diphosphate identification data were in full agreement with reference data. Based on experimental data and the literature [4, 5], we determined hydrolysis rate constants for s-, p-, and d-element diphosphates from first-order equations. The order of the hydrolysis reactions was derived from the plot of –1 log cτ versus log c 0 . The hydrolysis rate constants thus determined are listed in Table 2.
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Table 1. Thermodynamic functions of formation (298 K) and stability series of diphosphates s2 elements Diphosphates
Mg2P2O7
Ca2P2O7
Sr2P2O7
2863
3052
3074
260
277
279
–∆fG0, kJ/mol 0
–∆f G at , kJ/mol
Sr2P2O7 > Ca2P2O7 > Mg2P2O7 p1 elements Diphosphates –∆fG0, kJ/mol 0
–∆f G at , kJ/mol
Al4(P2O7)3
Ga4(P2O7)3
In4(P2O7)3
Tl4(P2O7)3
7921
6478
6199
4821
255
208
199
155
Al4(P2O7)3 > Ga4(P2O7)3 > In4(P2O7)3 > Tl4(P2O7)3 d elements (row) Diphosphates
Mn2P2O7
Fe2P2O7
Co2P2O7
Ni2P2O7
Cu2P2O7
2506
2171
2115
2098
1853
227
197
192
190
168
–∆fG0, kJ/mol 0
–∆f G at , kJ/mol
Mn2P2O7 > Fe2P2O7 > Co2P2O7 > Ni2P2O7 > Cu2P2O7 d elements (column) Diphosphates –∆fG0, kJ/mol 0
–∆f G at , kJ/mol
Zn2P2O7
Cd2P2O7
Hg2P2O7
2321
2168
1635
211
197
148
Zn2P2O7 > Cd2P2O7 > Hg2P2O7
RESULTS AND DISCUSSION The mechanism of hydrolysis is complicated and often includes the formation of several intermediates. There are two approaches to the explanation of the hydrolysis principles. The first is “protolytic,” based on polarization theory. The second is based on complex formation. The diphosphate hydrolysis rate constant changes systematically as one goes from Mg2+ to Ba2+ in Group IIA. This is explained by the weak polarizing power (PP) of the cations and by the fact that, as goes down the Group IIA column, the ionic radius increases, the ionization potential decreases, and the basicity of the cation grows (the extent of hydrolysis decreases, and pKÒ increases):
PP
Mg2+
Ca2+
Sr2+
Ba2+
0.83
0.66
0.61
0.56
rion, nm I2, V
Mg2+
Ca2+
Sr2+
Ba2+
0.86 7.65
1.14 6.11
1.32 5.69
1.49 5.21
For the diphosphates of the Group IIB (zinc-family) elements, hydrolyzability increases from the top down. This is explained by the secondary periodicity effect and by the fact that polarizing power and the tendency to complex formation increase in the order Zn2+–Cd2+– Hg2+. This trend is consistent with the place of the zincfamily elements in the Periodic Table and with the chemical behaviors of these elements. An analysis of the correlation formula log K = 0
a∆f G at + b for T = 25°C and pH 7 (Fig. 1) demonstrates that, for the diphosphates of the Group IIB elements, the hydrolysis rate constant increases as the absolute 0 value of the mean atomic Gibbs energy ∆f G at decreases.
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STABILITY OF s-, p-, AND d-ELEMENT DIPHOSPHATES IN WATER
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Table 2. Hydrolysis rate constants and hydrolytic stability series for s-, p-, and d-element diphosphate s2 elements Diphosphates
Mg2P2O7
Ca2P2O7
Sr2P2O7
– log K
9.29
9.89
10.01
Sr2P2O7 > Ca2P2O7 > Mg2P2O7 p1 elements Diphosphates
Al4(P2O7)3
Ga4(P2O7)3
In4(P2O7)3
Tl4(P2O7)3
– log K
6.01
4.52
3.81
3.41
Al4(P2O7)3 > Ga4(P2O7)3 > In4(P2O7)3 > Tl4(P2O7)3 d elements (row) Diphosphates
Mn2P2O7
Fe2P2O7
Co2P2O7
Ni2P2O7
Cu2P2O7
– log K
7.11
7.29
7.89
7.95
9.09
Mn2P2O7 > Fe2P2O7 > Co2P2O7 > Ni2P2O7 > Cu2P2O7 d elements (column) Diphosphates
Zn2P2O7
Cd2P2O7
Hg2P2O7
– log K
8.01
6.65
6.29
Zn2P2O7 > Cd2P2O7 > Hg2P2O7
The hydrolytic stability of 3d-element diphosphates Cu2P2O7
>
9.09
– log Khydr. rate
Zn2P2O7 >
Ni2P2O7
8.01
According to a familiar theory of the hydrolysis mechanism [6], 3d-element diphosphates in water form stable intermediates, specifically, diphosphate com2– 2– 2– plexes, such as MnH2P2 O 7 , FeH2P2 O 7 , CoH2P2 O 7 , 2– ZnH2P2 O 7 ,
and
2– CuH2P2 O 7 .
According to stability constant ( log β ) data, the diphosphate complexes of divalent elements are very stable: 2–
NiP2 O 7 log β
5.82
2–
ZnP2 O 7 6.46
>
7.95
This trend of the hydrolysis rate constant can be explained in terms of crystal field theory; the Irving– Williams stability series of 3d-element complexes; Lewis acid and base theory, further developed by Usanovich; and Pearson’s concept of hard and soft acids and bases.
2– NiH2P2 O 7 ,
decreases in the following order:
2–
CuP2 O 7 6.97
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Co2P2O7
>
7.89
Fe2P2O7
>
7.29
Mn2P2O7. 7.11
These complexes are so stable that they hydrolyze only slightly. The smaller the radius of the central cation, the higher the stability of the diphosphate complex:
rion I2, V PP
Mn2+
Fe2+
Co2+
Cu2+
Zn2+
0.91 15.63 0.85
0.83 16.18 0.89
0.82 17.05 0.92
0.80 20.29 1.03
0.83 17.96 1.01
The increase in the stability constant of the diphosphate complex in going from Mn2+ to Cu2+ is due to the fact that the polarizing power of the cation increases progressively with increasing atomic number of the element and the coordination bond strengthens with increasing number of d electrons. According to acid and base theory, the 3d-metal cations are acids and the strength of such an acid is proportional to the second ionization potential of the metal. For the 3d-element diphosphates, log K was found to be linearly correlated with I2 (Fig. 2).
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–logK
–logK 9.5
Zn 8 Cd
9.0 8.5
7
Co
8.0 Hg 7.5 6
Fe
7.0
~ ~
~ ~
0 140
Mn
Zn
150
160
170
16
180 190 200 210 – –∆f Gat0 , kJ/(mol at)
17
18
19
20
21 I2, B
0
Fig. 1. Correlation between log K and ∆ f G at for Group IIB element diphosphates. 0
Thus, the above analysis of the calculated ∆f G at values and the experimental hydrolysis rate constants ( log K ) has demonstrated that these quantities are linearly correlated (with a correlation coefficient of r = 0.98) for the diphosphates of elements in any column of the Periodic Table, no matter what the nature of the elements (s, p, d). No linear correlation between these quantities is observed for rows of elements, including the 3d-series. REFERENCES 1. Kh. K. Ospanov, Theory of Monitoring Physicochemical Processes at Solid–Liquid Interfaces and Its Application Perspectives (Almaty, 2004) [in Russian].
Fig. 2. Hydrolysis rate constant versus the second ionization potential of the metal for 3d-element diphosphates.
2. A. S. Pashinkin, B. K. Kasenov, and M. K. Aldabergenov, Thermodynamics in Chemistry and Metallurgy (Rauan, Almaty, 1994) [in Russian]. 3. R. Ya. Mel’nikova, V. V. Pechkovskii, E. D. Dzyuba, and I. E. Malashonok, The Atlas of Infrared Spectra of Phosphates. Condensed Phosphates (Moscow, 1985) [in Russian]. 4. E. A. Prodan, Inorganic Topochemistry (Nauka i Tekhnika, Moscow, 1986) [in Russian]. 5. G. S. Kuanysheva, K. U. Dzhamansarieva, and G. R. Makasheva, Zh. Neorg. Khim. 42 (4), 567 (1997) [Russ. J. Inorg. Chem. 42 (4), 494 (1997)]. 6. V. I. Spitsyn and L. I. Martynenko, Inorganic Chemistry (Mosk. Gos. Univ., Moscow, 1991), Part 1 [in Russian].
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