Ionics (2008) 14:541–543 DOI 10.1007/s11581-008-0214-3
ORIGINAL PAPER
A theoretical study on calculation of absolute hydration enthalpies for some univalent ions Hüseyin Yıldıran & Sevda Ayata & Sevgi Arzık & Tugba Nur Alp
Received: 1 October 2007 / Revised: 18 January 2008 / Accepted: 15 February 2008 / Published online: 12 March 2008 # Springer-Verlag 2008
Abstract Using the total radius of alkaline fluorides and sodium halides and their experimental total enthalpy values, absolute hydration enthalpies of sodium and fluoride ions ($HNaþ and $HF ) were previously calculated. Also, by the help of data of sodium and fluoride ions for all alkaline metal ions and halides absolute hydration enthalpies were determined. Keywords Absolute hydration enthalpies . Absolute hydration energies . Ionic radii
Introduction In general, hydration enthalpies (energies) are important in the determination of a number of chemical phenomena and they have been studied extensively for a long time. Since 1920, different approaches have been suggested by scientists. Some main works about this subject were listed in Table 1. However, no agreement has been reached between scientists on the values of hydration enthalpies [1, 2]. Therefore, in this work, this concept was examined. Due to the necessity of knowledge of absolute formation Gibbs free energy in aqueous medium and, consequently, calculation of absolute electrode potentials, the development of a
H. Yıldıran : S. Arzık : T. Nur Alp Faculty of Science, Department of Chemistry, University of Ege, 35100 Bornova, Izmir, Turkey S. Ayata (*) Faculty of Art and Science, Department of Chemistry, University of Dokuz Eylul, 35160 Buca, Izmir, Turkey e-mail:
[email protected]
novel method was considered because there are no difficulties for calculation of other parameters to reach this purpose to determine useful results from the criterion, the accurance, in suggested theoretical models for this subject. In 2007, Ayata [3] reported a procedure to estimate the radii of complex anions such as tetraborate in aqueous solutions using limiting equivalent conductivities. This method followed a study by Yıldıran and Tunçgenç [4] in 1981, which used limiting equivalent conductivities in a different procedure to obtain ionic radii values of alkaline metal cations and halides. Potassium chloride was initially selected to be the main ion investigated as it forms an isoelectronic ion pair. Both ions have an argon–argon electron configuration. However, as an aqueous solution of potassium chloride was used and as water molecules have a neon electron configuration, it was decided that sodium and fluoride ions, which both have a neon electron configuration, would be more advantageous as this way, solvent effects would be smaller. Moreover, both potassium and chloride ions have a soft spherical structure that makes the ions more prone to be affected by external factors. Both sodium and fluoride ions have a hard spherical structure, and they hardly get affected by external factors. Therefore, in this work, sodium and fluoride ions were selected to be the principle ions for investigation [5].1 1 In that work, we were interested to investigate whether it is possible to use a relationship between Δλ and Δr for metal halides to determine ionic radius values of Na+ and F− in aqueous solution. Δλ is the difference in the limiting equivalent conductivities between the anion and the cation, whereas Δr is the difference in ionic radius. The two results we obtained were identical, whether the calculation was made using the anion radius or on the cation radius. At least for the ions which we were interested in, identical results were obtained for the differences in limiting equivalent conductivity between any two ions, whether they were calculated from graph a or graph b depends on differences of total radii which are, in any case, identical, coming from either cation radius or anion radius.
542
Ionics (2008) 14:541–543
Table 1 Absolute hyration enthalpies (kcal/mol) for alkaline metal cations and halides found by some scientists [6–9]
[6, 7] [8, 9]
Li+
Na+
K+
Rb+
Cs+
F−
Cl−
Br−
I−
−132.1 −124.4
−106.0 −97.0
−85.8 −78.0
−79.8 −71.9
−72.0 −66.1
−113.3 −120.8
−81.3 −86.8
−77.9 −80.3
−64.1 −70.5
Table 2 Total radii of alkali halides ðrX þ rMþ Þa (Ǻ) [5, 10] versus their total hyration enthalpies (kcal/mol) [8, 9]
Total radii Experimental Enthalpy a
NaF
KF
RbF
CsF
NaCl
NaBr
NaI
2.31 −219.6
2.67 −199.6
2.82 −193.3
3.01 −189.1
2.81 −187.2
2.98 −179.7
3.23 −169.9
Distances between anions and cations nuclei in halide crystals
Hydration Enthalpy (kcal / mol)
230 ya = 50.289x3 - 368.94x2 + 846.43x - 387.41
220
R2 = 1
210 200
a 190 180
yb = -20,827x3 + 199,56x2 - 675,8x + 972,52 R2 = 1
170
b
160 2,00
2,20
2,40
2,60
2,80
3,00
3,20
3,40
´ Total radii of anion and cation (Å)*
Fig. 1 a Hydration enthalpies (Ǻ) of alkali metal fluorides (Na+, K+, Rb+, Cs+) versus total radii of anions and cations; b hydration enthalpies of sodium halides (F−, Cl−, Br−, I−) versus total radii of anions and cations. *The distance between anions and cations nuclei in crystals
Table 3 The enthalpies (kcal/mol) found for alkali metal cations and halides by proposed methods
Enthalpy
Na+
K+
Rb+
Cs+
F−
Cl−
Br−
I−
112.48
92.48
86.18
81.98
107.12
74.72
67.22
57.42
Ionics (2008) 14:541–543
543
Table 4 The enthalpies calculated for alkali halides by experimental (1) and by estimations (2) in kcal/mol F−
Na+ K+ Rb+ Cs+
Cl−
Br−
I−
1
2
1
2
1
2
1
2
−219.60 −199.66 −193.30 −189.10
−219.60 −199.60 −193.30 −189.10
−187.20 −167.20 −160.80 −156.60
−187.20 −167.20 −160.90 −156.70
−179.70 −159.60 −153.80 −149.10
−179.70 −159.70 −153.40 −150.20
−169.90 −149.80 −143.50 −139.30
−169.90 −149.90 −143.60 −140.40
Calculation of absolute hydration enthalpies By using the data in Table 2, curves a (for which the variation results only from the variation in the cation) and b (for which the variation results only from the variation in the anion) in Fig. 1 were drawn. By using data of ðrNaþ þ rF Þ þ ðrF rNaþ Þ ¼ 2:31 þ 0:07 (where rF ; rNaþ denote radius of fluoride and sodium ions, respectively), the hydration enthalpy of NaFð$HNaF Þ as 215.23 kcal/mol from curve a was found. Similarly, using data of ðrNaþ þ rF Þ ðrF rNaþ Þ ¼ 2:31 0:07, the hydration enthalpy of NaFð$HNaF Þ as 225.96 kcal/mol from curve b was found [5].1 By the help of the difference in anion hydration enthalpy (ΔΔHanion =4.37 kcal/mol) and difference in cation hydration enthalpy (ΔΔHcation =−6.36 kcal/mol) found from curve a and b, versus ðrF rNaþ Þ ¼ $r, the average absolute enthalpy value of ð$HNaþ $HF Þwere found as 5.36 kcal/ mol. By taking consideration of ð$HNaþ $HF Þ ¼ 5:36 kcal=mol and ð$HNaþ þ $HF Þ ¼ 219 kcal=mol, absolute enthalpy values of sodium $HNaþ ¼ 112:48 kcal=mol and fluoride ions $HF ¼ 107:12 kcal=mol were determined. By these values, total experimental enthalpy values of alkali halides are given in Table 2; absolute hydration enthalpies of other halides and alkali cations were calculated in Table 3.
Results and discussions First taking into account Stokes Laws 6πηrv=zeE [11] (where η, r, v, z, and E denote viscosity of solution, radius of ion, velocity of ion, charge of particle, and electric field strength, respectively.) and rF irNaþ , lF ilNaþ (where lF and lNaþ denote limiting equivalent conductivity of fluoride and sodium respectively), it can be seen that the viscosity of
the near environment of sodium ion is higher than the viscosity of fluoride ion environment [5]. It is known that the determining effect in the mentioned viscosity is ion–solvent effect. Depending on this phenomena, it can be said that absolute hydration enthalpy of Na+ is greater than fluoride ion. This result is also agreed with the proposed method. Also, the obtained results are in agreement with the experimental data in the diagonal direction indicated in Table 4. So, it can be concluded that the absolute hydration enthalpies of ions found by this novel method seems to be reasonable. The closeness of the softness or hardness of ions in the diagonal direction in Table 4 resembles the reliability of the novel method even though it meets the necessary, but insufficient, condition. Acknowledgement We would like to thank M. Merdivan from Dokuz Eylul University, Izmir for her helpful comments.
References 1. Bockris J’OM, Reddy AKN (1998) Modern electrochemistry, vol 1, 2nd edn. Plenum, New York 2. Conway BE (1981) Ionic hydration in chemistry and biophysics, 1st edn. Elsevier, Amsterdam 3. Ayata S (2007) Chem Eng Comm 194:893–900 4. Tunçgenç M (1981) MS thesis. Ege University, Izmir, Turkey 5. Yildiran H, Ayata S, Tunçgenç M (2007) Ionics 13:83–86 6. Desnoyer JE, Jolicoeur C (1969) In: Bockris JOM, Conway BE (eds) Modern aspects of electrochemistry, vol. 5. Plenum, New York 7. Rosseinsky DR (1965) Chem Rev 65:467–490 8. Bockris JO’M, Saluja PPS (1972a) J Phys Chem 76(16):2298– 2310 9. Bockris JO’M, Saluja PPS (1972b) J Phys Chem 76(15):2140– 2151 10. Pauling P (1960) The Nature of the Chemical Bond. Cornell Univ., Ithaca 11. Robinson RA, Stokes RH (1959) Electrolyte solutions. Butterworths, London
