Hydration Energies and Reactivity of the Hypohalite Anions

Nov 30, 2017 - to OI. − is seen to arise primarily from these differing trends in hydration energies rather than the gas-phase oxygen atom affinitie...
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Cite This: Inorg. Chem. 2018, 57, 1665−1669

Hydration Energies and Reactivity of the Hypohalite Anions David M. Stanbury* Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849, United States ABSTRACT: Herein is a dissection of the energetic contributions to a correlation between the rates and driving forces for oxygen atom transfer from three inorganic peroxides to the halides. Experimental data are used to calculate conventional and absolute hydration enthalpies for OCl−, OBr−, and OI−. It is found that the hydration enthalpies are more exothermic for the OX− species in comparison to their X− congeners, and it is found that the hydration enthalpies are approximately constant on progressing from OCl− to OI−. Both of these trends are contrary to expectations based on simple models of ionic hydration. Similar trends are seen in the Gibbs energies of hydration. The strong decrease in E° from OCl− to OI− is seen to arise primarily from these differing trends in hydration energies rather than the gas-phase oxygen atom affinities of the halides. These effects show that the Marcus-like driving-force dependence for oxygen atom transfer from peroxides to the halides arises from the differing trends in hydration energies rather than in the intrinsic O−X− bond strengths.

R

According to eq 1, one can calculate conventional hydration enthalpies of anions by eq 2:

eactions in aqueous solution that interconvert the halides (X−) and their corresponding hypohalites (OX−) can occur through oxygen atom transfer. Thus, halides can be oxidized by peroxides,1−3 and hypohalites may act as oxygen atom donors. It is reasonable to anticipate that the rates and driving forces of these reactions are closely related, and similarly one might anticipate a strong correlation between the rates and the gas-phase O−X− bond strengths. Alternatively, solvation effects may play an important role. In order to probe these issues, it is essential to have reliable hydration energies for the halides and the hypohalites. Such data have long been available for the halides,4−9 but to our knowledge corresponding data for the complete hypohalite series (OCl−, OBr−, OI−) have not been reported. (OF− is excluded because of its fleeting existence in aqueous solution.10) Here we report values for this series, identify some unexpected trends in the data, and show how they are the dominant contributions to the trend in the hypohalite E° values. We show that there is a strong correlation between the rate constants and ΔG° values for oxidation of the halides by three peroxides but that there is not a correlation with the O−X− bond energies, and we show that this difference is largely due to the hypohalite hydration energies. Conventional hydration enthalpies of anions are calculated unambiguously from standard thermochemical data and correspond to the process A−(g) + H+(g) → A−(aq) + H+(aq)

Δhyd H °(A−)con = Δf H °(A−, aq) − Δf H °(A−, g) − Δf H °(H+, g)

Such calculations for the halides are straightforward, since reliable values for the requisite data have long been available.11 For the complete hypohalite series, however, calculations according to eq 2 have not been published, presumably because reliable values of ΔfH°(A−,g) for the hypohalite series are not available in standard tabulations. This situation is no longer tenable, because accurate values of ΔfH°(A−,g) for OCl−, OBr−, and OI− can now be calculated from modern values for the enthalpies of formation12,13 and electron affinities14 of the corresponding neutral species. These values are given in Table 1 along with the derived values of ΔfH°(A−,g) for these species. The NBS (currently NIST) data for ΔfH° for the aqueous halide ions OCl− and OBr− appear to be based on firm experimental data, even for the somewhat unstable species OBr−.15 However, there seems to be no direct experimental basis for the ΔfH° value of OI−(aq). Bichowsky and Rossini obtained their estimate of ΔfH° for OI−(aq) by making the assumption that the enthalpy of acid ionization of HOI(aq) is the same as that of HOCl(aq).16 We presume that the same assumption underlies the NBS value. More recently, Schmitz assigned a ΔH° range of 18−28 kJ mol−1 for the acid ionization of HOI,17 but that was actually based on data for the ionization of HOBr obtained by Kelley and Tartar.18 The pKas of HOCl,

Δhyd H °(A−)con (1)

This process includes hydration of the proton so as to comply with the requirements for electroneutrality in both phases, and it yields a conventional enthalpy change when data are used according to the convention that ΔfH°(H+,aq) is zero. © 2018 American Chemical Society

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Received: November 30, 2017 Published: January 24, 2018 1665

DOI: 10.1021/acs.inorgchem.7b03031 Inorg. Chem. 2018, 57, 1665−1669

Article

Inorganic Chemistry Table 1. Thermochemical Data for the Gas-Phase Hypohalite Anions species −

OCl OBr− OI−

EA, eVa

ΔfH°(A,g), kJ mol−1 (298 K)

ΔfH°(A−,g), kJ mol−1 d

2.276 ± 0.006 2.353 ± 0.006 2.378 ± 0.006

101.6 ± 0.1 124.9 ± 1.7b 122.2 ± 1.7c

−118.0 ± 0.6 −102 ± 2 −107 ± 2

b

S°(A−,g), J K−1 mol−1

ΔfG°(A−,g), kJ mol−1 g −118.5 −116.5 −128.6

e

215.7 227.2e 233.1f

Reference 14. bReference 13. cReference 12. dCalculated as ΔfH°(X−,g) = ΔfH°(X,g) − EA. eReference 6. fCalculated at the PM3 level with Spartan ’08. gCalculated as ΔfG° = ΔfH° − T(S°(A−) − (S°(X2) + S°(O2))/2); values for S°(O2, g), S°(Cl2, g), S°(Br2, l), and S°(I2, s) are taken from ref 11.

a

Table 2. Anion Hydration Enthalpiesa species −

Cl Br− I− OCl− OBr− OI−

ΔfH°(A−,g)

ΔfH°(A−,aq)

ΔhydH°(A−)cond

ΔhydH°(A−)abse

−233 −219b −197b −118.0 ± 0.6c −102 ± 2c −107 ± 2c

−167 −122b −55b −107b −94b −93 ± 5f

−1470 −1439 −1394 −1525.1 ± 0.6 −1528 ± 2 −1522 ± 6

−356 −325 −280 −411.1 ± 0.6 −414 ± 2 −407 ± 6

b

b

All data are given in kJ mol−1. bReference 11. cFrom Table 1. dCalculated from eq 2 with ΔfH°(H+,g) = 1536 kJ mol−1.6 eCalculated from eq 4 with ΔhydH°(H+)abs = −1114 kJ mol−1. fThis work.

a

Table 3. Anion Hydration Gibbs Energiesa species −

Cl Br− I− OCl− OBr− OI−

ΔfG°(A−,g)

ΔfG°(A−,aq)d

ΔhydG°(A−)cone

ΔhydG°(A−)absf

ΔhydG°(A−)abs,calcg

−241.4 −245.1b −230.2b −118.5c −116.5c −128.6c

−131.228 −103.96 −51.57 −36.8 −33.4 −38.5

−1413 −1382 −1345 −1442 −1440 −1433

−349 −318 −281 −378 −376 −369

−323.2 −301.4 −264.5 −352.5 −342.6 −322.7

b

All data are given in kJ mol−1. bReference 6. cFrom Table 1. dReference 11. eCalculated from eq 6 with ΔfG°(H+,g) = 1523.2 kJ mol−1.6 fCalculated from eq 7 with ΔhydG°(H+)abs = −1064 kJ mol−1.6 gCalculated at the PM3/SM5.4 level with Spartan ’08. Note that these calculated values deviate systematically from the experimental values because the SM5.4 method is based on ΔhydG°(H+)abs = −1092 kJ mol−1. a

It is widely regarded that the Born solvation model captures much of the absolute Gibbs energy of hydration of ions, and a version optimized for the hydration enthalpies of polyatomic anions is expressed as8

HOBr, and HOI are 7.53, 8.59, and 10.64, respectively, while the ionization enthalpies for HOCl(aq) and HOBr(aq) are 13 and 29 kJ mol−1.19 It seems reasonable to extrapolate an acid ionization enthalpy of 45 ± 5 kJ mol−1 for HOI(aq). The NBS value of ΔfH° (=−138.1 kJ mol−1) for HOI(aq) seems to be based on firm experimental data.20,21 By combining this value with our extrapolated ionization enthalpy. we obtain ΔfH° = −93 ± 5 kJ mol−1 for OI−(aq). With the values of ΔfH°(A−,g) in Table 1, the corresponding values of ΔfH°(A−,aq) in Table 2, and the value of 1536 kJ mol−1 for ΔfH°(H+,g) we have obtained the values of ΔhydH°(A−)con that are given in Table 2. Table 2 also shows the corresponding results for the monatomic halide anions. Absolute single-ion hydration enthalpies of anions correspond to the process A−(g) → A−(aq)

Δhyd H °(A−)abs

Δhyd H ° = −700z 2/(rt + 0.3) kJ mol−1

In eq 5, z represents the ionic charge and rt is the thermochemical ionic radius (Å). Equation 5 does an admirable job in predicting the smooth increase in exothermicity of hydration across the lanthanide series (Ln3+) as the ionic radius decreases (lanthanide contraction).4 Equation 5 likewise leads to the expectation that the halide anion hydration enthalpies will become less exothermic on progressing from Cl− to I−, and Table 2 shows that this expectation is borne out. In opposition to these successes of the modified Born model mentioned above, the data for the hypohalite anions are quite unexpected. First, the absolute hydration enthalpies for each of the hypohalites are much more exothermic than those for their corresponding halides; eq 5 leads to the opposite expectation, since the hypohalite ions are larger than the corresponding halides. Second, the hydration enthalpies are relatively constant on progressing from OCl− to OI−, while the halides show the trend of strongly varying values noted above. Although the causes for this breakdown of eq 5 are not yet fully understood, there are at least three potential factors that should be considered. One is that the Born model is derived for spherical ions, while the hypohalites are certainly not spherical. Another is that the charge is not symmetrically distributed. The

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They can be calculated from the conventional values by the relationship Δhyd H °(A−)abs = Δhyd H °(A−)con − Δhyd H °(H+)abs

(5)

(4)

Note that these absolute enthalpies are extrathermodynamic, since they violate the principle of electroneutrality. There is widespread agreement that ΔhydH°(H+)abs is in the neighborhood of −1114 kJ mol−1;22 accordingly, Table 2 displays absolute hydration enthalpies calculated from eq 4 with this value for ΔhydH°(H+)abs. 1666

DOI: 10.1021/acs.inorgchem.7b03031 Inorg. Chem. 2018, 57, 1665−1669

Article

Inorganic Chemistry third is that hydrogen bonding between the water and the oxygen atoms of the OX− ions may have a significant effect; one might anticipate that this hydrogen bonding would become stronger with the decreasing electronegativity of the halogen atoms from Cl to I. Table 1 also shows values of S° and ΔfG° for the hypohalite gas-phase ions. The entropies are calculated by standard methods of statistical mechanics as described by Loewenschuss and Marcus,23 while the Gibbs energies of formation are calculated from the enthalpies of formation and the entropies. These values of ΔfG° are used in Table 3 to calculate conventional and absolute Gibbs energies of hydration of the hypohalites. The values of ΔhydG°con and ΔhydG°abs are calculated according to eqs 6 and 7:

oxidize the halides with rate laws having acid-independent terms:1−3 −d[X−] dt = k[X−][ROOH]

These reactions involve net oxygen atom transfer, and in the case of H2O2 there is good evidence that H2O is the leaving group and that the solvent mediates the proton transfer.28 Thus, the measured rate constants correspond to transition states where one of the peroxidic oxygen atoms is transferring to the halide:

Δhyd G°(A−)con = Δf G°(A−, aq) − Δf G°(A−, g) − +

Δf G°(H , g)

(6)

Δhyd G°(A−)abs = Δhyd G°(A−)con − Δhyd G°(H+)abs

(7)

These reactions display the typical increase in rate constant with increasing driving force, as illustrated by the reaction coordinate diagram for H2O2 in Figure 1.

For comparison, analogous ΔhydG° values for the halide anions are also shown in Table 3. The trends in these results are closely parallel to those of the enthalpies of hydration. It is possible that calculations with more sophisticated ionic hydration models will reveal the origins of these observations,22 and it is encouraging to note that hydration Gibbs energies calculated by the SM5.4 model24 as implemented in Spartan ’08 (Table 3) approximately track the experimental hydration Gibbs energies. With the results in Table 3 it is now possible to identify the origins of the trend of the strongly decreasing E°(OX−/X−) values on descending the group; Table 4 shows the relevant

Figure 1. Reaction coordinate diagram for oxidation of the halides by H2O2.

Table 4. Hypohalite Aqueous Standard Electrode (Reduction) Potentials and Halide Oxygen Affinities in Solution and the Gas Phase

OCl−/ Cl− OBr−/ Br− OI−/I− a

E°(basic), Va

ΔfG°(OX−,aq) − ΔfG°(X−,aq), kJ mol−1 b

ΔfG°(OX−,g) − ΔfG°(X−,g), kJ mol−1 c

0.890

−28.5

122.9

0.766

−58.1

128.6

0.48

−88.5

101.6

(8)

The driving-force dependence of these reactions is displayed more quantitatively in Figure 2, which shows plots of ΔG⧧ as a

Reference 27. bFrom data in Table 3. cFrom data in Table 1.

quantities. An equivalent function is the aqueous oxygen affinity of the halide, i.e. ΔG° for the reaction X−(aq) + 1/2O2(g) → OX − (aq), which is obtained as Δ f G°(OX − ,aq) − ΔfG°(X−,aq).25,26 These oxygen atom affinities become systematically more exoergic by 60 kJ/mol from Cl− to I−. However, the corresponding gas-phase oxygen affinities (defined as ΔfG°(OX−,g) − ΔfG°(X−,g)) are relatively invariant. It is clear that the difference in these trends arises from the different trends in hydration Gibbs energies: the halides become more weakly hydrated on descending the group while the hypohalites are similarly hydrated; therefore, OCl− is a stronger oxidant than OI−. Thus, the trend in E° values for the hypohalites is primarily a consequence of aspects of the hydration energies of the hypohalites that are not modeled properly by the Born equation. The above results provide some insight into the factors influencing the rates of oxygen atom transfer reactions. It is well established that the peroxides H2O2, HSO5−, and HOONO2

Figure 2. LFERs for oxidation of the halide ions by H2O2 (blue circles), by HSO5− (red triangles), and by HOONO2 (green diamonds). Note that the data for HSO5− and HOONO2 are so similar that they are overlapping. ΔfG° for HSO5− from Balej,36 ΔfG° for HOONO2 from Regimbal and Mozurkewich,37 and other ΔfG° values from Wagman et al.11 ΔG⧧ values are calculated from the rate constants in refs 1, 2, and 3. 1667

DOI: 10.1021/acs.inorgchem.7b03031 Inorg. Chem. 2018, 57, 1665−1669

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Inorganic Chemistry function of ΔG° for the three peroxides H2O2, HSO5−, and HOONO2. These plots demonstrate excellent linearity and have slopes of 0.47, 0.40, and 0.39, respectively. Marcus theory is well-known in electron-transfer chemistry, and it has also been applied to proton, hydride, hydrogen atom, and methyl transfer reactions.29−33 An important outcome of Marcus theory is that it predicts a slope of 0.5 for plots of ΔG⧧ against ΔG° for series of related reactions. The slopes of the lines in Figure 2 are close to the 0.5 value predicted by Marcus theory and thus are the first indication that Marcus theory can apply to oxygen atom transfer reactions. The driving-force dependence in these LFERs, however, is a consequence of the differential hydration energies of the halides and the hypohalites, since the gas-phase oxygen affinities of the halides are relatively invariant as noted above. Rate constants for oxygen atom transfer to chloride and bromide by compound 1 of myeloperoxidase and eosinophil peroxidase follow the same trends as for the peroxides,34,35 but the trends do not extend to iodide. Here, the trends are attenuated, possibly because access to the active site becomes rate limiting.

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AUTHOR INFORMATION

Corresponding Author

*E-mail for D.M.S.: [email protected]. ORCID

David M. Stanbury: 0000-0002-3892-9048 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS Professor Vince Cammarata (Auburn University) is thanked for his helpful comments. REFERENCES

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DOI: 10.1021/acs.inorgchem.7b03031 Inorg. Chem. 2018, 57, 1665−1669