Research: Science and Education
Factors That Influence Relative Acid Strength in Water: A Simple Model Michael J. Moran Department of Chemistry, West Chester University of Pennsylvania, West Chester, PA 19383;
[email protected] Teaching chemistry, especially general chemistry, requires explaining macroscopic phenomena (lab results) in terms of the properties of molecules. The relative strength of acids in water is a subject of some importance that is treated in many general chemistry textbooks (1). Unfortunately students are often left with explanations that may be nebulous and sometimes at odds with explanations for other phenomena, notably chemical bonding. Among the trends in acid strength that are cited in popular texts, we generally find (1): • For binary hydrides HnA across a period, acid strength is in order of increasing electronegativity of A, for example: NH3 < H2O < HF. • For binary acids within a group, acid strength increases as the electronegativity of A decreases. For example, in the hydrohalogenic acids the acid strength order is HF < HCl < HBr < HI. • For oxoacids (HO)nXOm with a given central atom (X), the stronger acid has the greater number of “extra” O atoms (m in the formula). • Among oxoacids with the same m and n and different central atoms (X), acid strength increases with increasing electronegativity of X.
The explanations found in these texts (1) for these phenomena generally involve H⫺A bond polarity and bond strength. On the one hand, students are led to expect that the more polar the bond, the stronger the acid. In other cases, especially with the hydrohalogenic acids, bond-dissociation en-
20 15
y = 0.0577x − 1.633 r 2 = 0.89 (other 30 acids)
10
pKa
5 0 -5
y = 0.058x − 11.031 r 2 = 0.99 (hydrohalogenic acids)
-10 -15 -20 -150
-100
-50
0
50
100
150
200
250
300
(BDE + EA) / (kJ/mol) Figure 1. The correlation of aqueous pKa‘s of a variety of 34 acids with the gas-phase (BDE + EA). The correlation coefficient for all 34 acids is r2 = 0.68. The lower line shows the correlation of the four hydrohalogenic acids (r2 = 0.99) and the upper line shows the correlation of the other 30 acids (r2 = 0.89).
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ergy trumps bond polarity: decreasing acid strength is attributed to increasing H⫺A bond energy. Sometimes these ideas of bond strength and bond polarity are mentioned together: to the electronegative groups is ascribed the property of withdrawing electron density from the H⫺A bond, thereby weakening it (1f, 1g). The notion of electronegative groups withdrawing electron density from the bond, thereby weakening it, is misleading. It is not unusual to see the opposite: molecules with more electron-withdrawing groups that have stronger H⫺O bonds (for example, 423 kJ兾mol in HNO3 versus 328 kJ兾mol in HNO2 and ∼443 kJ兾mol in halogenated acetic acids versus 440 kJ兾mol in acetic acid), although they are stronger acids. Also, inasmuch as the strength of a bond increases according to the square of the difference in electronegativity of the bonded atoms, and since the electron-withdrawing groups tend to make the O atom more electronegative, the increase in strength in the H⫺O bonds is to be expected. The idea that the increased acidity is attributable to an increased polarity of the bond is not easily squared with the facts that in the hydrohalogenic acids and the hydrochalcogenic acids the more polar bonds correspond to the weaker acids, and in transition-metal carbonyl hydrides, for example, HCo(CO)4, H 2Fe(CO) 4, and HMn(CO) 5 we find substances with hydridic H atoms (2) that are acids in water. HCo(CO)4 is a strong acid, albeit of low solubility (3)! An explanation of acid strength should be realistic enough to extend over a variety of acid types and remain consistent with sound ideas of chemical bonding. Yet it should be simple enough such that students can look to a few features of a molecule and predict with reasonable accuracy whether it will be a stronger or a weaker acid than another. This article suggests that it is advantageous to direct students’ attention to the sum of two properties: the gas-phase H⫺A bond dissociation energy (BDE) and the electron affinity (EA) of the A• radical. Neither of these properties alone correlates well with aqueous acidity, but their combination does. The data presented in Figure 1 and Table 1 show the correlation of the aqueous pKa to (BDE + EA) for 34 acids of a variety of types (r 2 = 0.68). The BDE values in the table are enthalpies (∆H ). The EA values are energies (∆U ), but in those cases where the standard enthalpies of formation of the gasphase anion and the gas-phase radical are available, it is found that the electron attachment enthalpy is within a few kJ兾mol of the EA value; the difference (∆U − ∆H ) has negligible effect. Perhaps surprisingly, the correlation is reasonably good even though entropy effects and hydration effects are neglected. It seems that relative acid strength can be explained to general chemistry students to a first approximation as the sum of these two effects, rather than either one alone. The correlation coefficients (r 2) for pKa versus BDE and EA separately are 0.01 and 0.37, respectively.
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Data
H +(g) + e− (g)
H • (g)
∆H = 1312 kJ/mol
The proton detachment enthalpy (PDE) is the enthalpy of the heterolytic dissociation of the proton from the acid, in the gas phase. HA(g)
A• (g) + e− (g)
(4)
∆H = EA
H +(g) + A−(g)
(1)
∆H = PDE
The data in Table 1 were taken primarily from the CRC Handbook of Chemistry and Physics (pKa values; ref 4 ) and NIST (gas-phase PDEs; ref 5 ). The ionization energy of hydrogen atoms, 1312 kJ兾mol, was subtracted from the PDE values to obtain the sum (BDE + EA). In many cases the NIST data included the electron affinity of the radical, and the bond dissociation enthalpy could be obtained by difference. In some cases BDEs so obtained could be checked
Equation 1 is the sum of eqs 2–4: the homolytic bond dissociation, the ionization of hydrogen, and the electron attachment to A•:
HA(g)
A− (g)
H • (g) + A• (g) ∆H = BDE
(3)
(2)
Table 1. Aqueous pKa and Gas-Phase (BDE + EA) Acid type
pKaa
Acid
Hydrochalcogenic acids
2.6
73
261
᎑188
3.89
117
329
᎑213 ᎑223
HF
156
378
184
365
᎑180
3.2
242
570
᎑328
73
422
᎑349
41
366
᎑325
3
298
᎑295
᎑14
---
---
284
436
᎑152
᎑9.5b
HBr
᎑10b
HI picric acid
0.42
CH3OH
15.5
C2H5OH
15.5
271
436
᎑165
phenol
9.99
151
368
᎑217
CH3CO2H
4.756
144
440
᎑296
FCH2CO2H
2.586
107
444
-337
ClCH2CO2H
2.82
96
443
᎑348
BrCH2CO2H
2.9
89
444
᎑355
ICH2CO2H
3.18
88
443
᎑355
F2CHCO2H
1.33c
73
443
᎑370
Cl2CHCO2H
1.35
62
443
᎑381
Br2CHCO2H
1.39c
62
444
᎑382
F3CCO2H
0.52
43
443
᎑400 ᎑193
HCO2H
3.75
133
439
C6H5CO2H
4.204
111
---
---
Miscellaneous
HN 3
4.6
127
393
᎑211
145
518
᎑373
Oxoacids
HClO4
᎑8c
᎑112
---
---
H2SO4
᎑3
᎑30
---
---
HCN
9.21
HIO4
1.64
᎑14
---
---
HNO3
᎑1.37c
46
423
᎑377
H3PO4
2.16
70
---
---
HNO2
3.25
111
328
᎑219
HOBr HOCl Ref 4 except where noted.
b
Ref 6.
c
Ref 7.
d
167
394
᎑227
10.5
168
397
᎑229
7.2
176
396
᎑220
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8.55
HOI a
7.05 10.33 ᎑7b
HCl
Carboxylic acids
EA/(kJ mol᎑1)d
H 2 Te H 2S
Alcohols
BDE/(kJ mol᎑1)
H2Se CH3SH Hydrohalogenic acids
BDE + EA/ (kJ mol᎑1)d
Ref 5.
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against the values calculated from enthalpies of formation of the neutral acid and the neutral radical; they were invariably found to be in agreement. In those few cases (some of the oxoacids and benzoic acid) where only the PDE data were available, separate BDE and EA values are not shown. Electron affinities in some tables (indeed, in NIST tables) are listed as positive values: they are understood to be the quantity of energy released when the electron is attached. In Table 1, the convention followed in many general chemistry texts was adopted to assign negative values to these exothermic processes. A stronger bond tends to make the acid weaker, and a more exothermic EA of the radical tends to make the acid stronger. Larger values of the sum (BDE + EA) tend toward weaker acids, with larger pKa’s.
of ionization, citing the work of Pitzer (10) for a variety of neutral weak acids in water that showed the entropy of ionization is roughly constant at ᎑88 J兾(mol K). Pitzer gave a plausible explanation that accounts for changes in rotational and vibrational degrees of freedom and the ordering of solvent water around the solute anion and arrived at the ∼ ᎑90 J兾(mol K) result that agrees with his data. There is precedent in the literature for a similar approach in studying acids in dimethylsulfoxide: Bordwell et al. (11) have related the BDE of acids to a simple two-parameter equation involving the pKa in DMSO and the oxidation potential of the anion in solution, in which they treat entropy effects as an empirical constant. They find BDEs within ± 8 kJ兾mol of the experimental gas-phase values.
Discussion
Hydration Effects Another point that must be addressed is hydration energy. The hydration steps are eqs 5, 6, and 7. Equation 6 is the hydration of the proton, which, like the ionization of hydrogen (eq 3) is common to all acids and hence sheds no light on relative strengths of different acids. Students should be aware that while the sum of (BDE + EA) is a reasonable predictor of relative acidity in solution, there will be exceptions, and these will usually be due to hydration effects. For example, Kebarle et al. (12) have found that in the XCH2CO2H series, X = F, Cl, Br, there is a reversal in order of acid strength in the gas phase compared to aqueous solution. When the acids in a chemically similar class are considered, the correlation of pKa with the sum (BDE + EA) improves significantly: for hydrohalogenic acids, r 2 = 0.99; for the hydrochalcogens, r 2 = 0.93; for oxoacids r 2 = 0.89; for alcohols and phenols, r 2 = 0.99; and for carboxylic acids, r 2 = 0.87. The approximation of ignoring the hydration effects is expected to be more reliable within a chemically similar class than between classes. In fact, it seems that only the hydrohalogenic acids are significantly different from the others: taken alone, they have an excellent correlation between gas phase PDE and pKa, and when they are excluded, the 30 remaining acids also have a strong correlation (r 2 = 0.89). As Figure 1 shows, the hydrohalogenic acids are offset approximately 150 kJ兾mol from the others. The reasons for this phenomenon are unknown to this author, but undoubtedly hydration effects play a role.
Hess’ Law Approach The strength of an acid in water (pKa) depends on the difference between the free energy of the molecules in solution and the free energies of the hydrated ions. The following equations illustrate acid dissociation (6): (5) HA(aq) HA(g) HA(g)
H • (g) + A• (g)
(2)
H • (g)
+ − H (g) + e (g)
(3)
A− (g)
(4)
H +(g)
H +(aq)
(6)
A− (g)
A− (aq)
(7)
A• (g) + e− (g)
(8) (net reaction) HA(aq) H +(aq) + A− (aq) A rigorous analysis that would yield a perfect correlation with pKa’s would require use of the enthalpies and entropies of reactions 5, 2, 4, and 7. Such an eight-parameter model, while accurate, would be unwieldy and bewildering to a beginning chemistry student. Students can readily get a qualitative feel for factors that affect the bond strength and the electron affinity. Substitution of a halogen atom in a carboxylic acid, for example, has a small effect (about 4 kJ兾mol) on the strength of the H⫺O bond, but it significantly increases the electron affinity of the carboxyl radical (by about 40 kJ兾mol). It is perhaps surprising and fortuitous that a reasonable correlation is found between the sum of these two effects and the pKa, without including entropy effects and solvation effects. The correlation of aqueous acidity to gas phase PDE has also been shown by Bartmess in 1979 for alcohols, thiols, nitroalkanes, and a few other very weak acids (8). This simple model is useful as an illustration that two parameters taken together, (BDE + EA), strongly influence the aqueous pKa’s of acids of a variety of types. Hydration effects and, to a lesser extent, entropy effects are evident in the deviation of the pKa of an acid from the value predicted from (BDE + EA), but they play minor roles.
Entropy Effects Jolly (9) has pointed out that the difference in acidity of protonic acids is primarily due to differences in enthalpy 802
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BDE versus EA A central idea of this work is that no one factor is a useful predictor of acid strength across several acid types, and while high accuracy can only be expected from a multiparameter model that also includes hydration and entropy effects, this simple model that employs only (BDE + EA) together can be useful. However, examination of Table 1 shows that within some classes of acids the BDE has a larger influence than EA; among other acids EA is more dominant. The hydrohalogenic acids (HX) and hydrochalcogenic acids (H2Y) each have a wider range of values of BDE than EA, and the correlation of pKa with BDE (r 2 = 0.93 for HX; r 2 = 0.65 for H2Y) is stronger than pKa with EA (r 2 = 0.09 for HX; r 2 = 0.05 for H2Y) . The wide range of BDE is due to the range in covalent bond energy of the halogen and chalcogen atoms and to the range in electronegativity (χ) of the atoms, with ionic resonance energy of the bond approximated
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by (100 kJ兾mol)(χX − χH)2 (13). The paradox is that more electronegative atoms tend to have large electron affinities, but they also tend to have stronger bonds to hydrogen. These work at cross purposes in their effects on relative acid strength. Among acids with ⫺OH groups (including carboxylic acids, oxoacids, alcohols, etc.) it is the EA that is the more dominant factor. Electronegative groups two or more bonds removed from the acidic H atom usually have only a modest effect on the O⫺H bond energy, but they can have a profound effect on the electron affinity of the O• radical, and in this way they influence the acidity of the parent molecule.
Oxoacids The rule of approximately ᎑5 units of pKa for each “extra” O atom beyond the (HO) groups in an oxoacid [m in the generic formula (HO)nXOm] is discussed in many texts (13). Rather than invoking the idea that the extra O atoms increase the H⫺O bond polarity or withdraw electron density from the bond, it is more instructive to focus on the electron affinity of the radical. This is equivalent to describing it as a stabilization of the negative charge on the conjugate base. Generally, the extra oxygen atoms are expected to increase the electron affinity. This has been attributed to the resonance delocalization of the negative charge in the anion (conjugate base) (14). For example, (HO)NO2, with 2 “extra” O atoms in the neutral acid, has 3 O atoms to share the negative charge in the NO3− conjugate base. This is a more stable situation than that of (HO)NO, in which there are only 2 O atoms to share the negative charge of the nitrite ion (conjugate base). The electron affinity of NO3•, ᎑377 kJ兾mol, is accordingly more exothermic than that of NO2•, ᎑219 kJ兾mol, and therefore HNO3 is the stronger acid even though its H–O bond is stronger by 95 kJ兾mol. The electron affinity of NO• is only ᎑2.5 kJ兾mol (15). Calculations of Xie et al. (16) have found that for the BrOn radicals, there is an increase in EA with additional O atoms: ᎑230, ᎑228, ᎑417, and ᎑509 kJ兾mol for n = 1 → 4. Experiments by Gilles et al. (17) have found ᎑229 kJ兾mol for IO and ᎑249 kJ兾mol for IO2. For chlorine oxides ClOn the electron affinities are ᎑220 , ᎑206, ᎑410, and ᎑506 kJ/mol for n = 1 → 4 (7, 18). Huheey et al. (19) show that the number of extra O atoms (m) and the electronegativity (χ) of the central atom can be included in a two-parameter equation that clearly shows that m has the greater influence: pKa = 10.5 − 5.0m − χ
(9)
Summary A useful guide to understanding relative acid strength in water is the combination of two parameters: the BDE of the H⫺A bond in the acid and the EA of the A• radical. In those cases in which the stronger acid is the molecule with the stronger bond, the greater EA compensates for the greater bond strength. The sum of the enthalpies of these two steps is a fairly good indicator of relative acidity, especially when comparison is made between acids of a given type. Electronegative groups attached elsewhere on the molecule have a greater effect on the acidity not in the weakening or polarization of the H⫺A bond, but rather in enhancing the electron affinity of the radical, or put another way, stabilizing the conjugate base. www.JCE.DivCHED.org
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Acknowledgment The author gratefully acknowledges helpful discussions with John Olmsted of Cal State–Fullerton and John Townsend and Jim Falcone of West Chester University of Pennsylvania. Literature Cited 1. (a) Kotz, John C.; Treichel, Paul M. Chemistry and Chemical Reactivity, 5th ed.; Thomson/Brooks–Cole: Pacific Grove, CA, 2003; Chapter 17. (b) Jones, Loretta; Atkins, Peter. Chemistry: Molecules, Matter and Change, 4th ed.; W. H. Freeman: New York, 2000; Chapter 15. (c) Munowitz, Michael. Principles of Chemistry; W. W. Norton: New York, 2000; Chapter 16. (d) Silberberg, Martin S. Chemistry: The Molecular Nature of Matter and Change, 2nd ed.; McGraw Hill: New York, 2000; Chapter 18. (e) McMurray, John; Fay, Robert C. Chemistry, 3rd ed.; Prentice Hall: Upper Saddle River, NJ, 2001; Chapter 15. (f ) Olmsted, John; Williams, Gregory. Chemistry, 3rd ed.; John Wiley: New York, 2002; Chapter 16. (g) Petrucci, Ralph; Harwood, William; Herring, F. Geoffrey. General Chemistry Principles and Modern Applications, 8th ed.; Prentice Hall: Upper Saddle River, NJ, 2002; Chapter 17. (h) Brown, Theodore; LeMay, H. Eugene, Jr.; Bursten, Bruce E.; Burdge Julia R. Chemistry: The Central Science, 9th ed.; Prentice Hall: Upper Saddle River, NJ, 2003; Chpater 16. (i) Chang, Raymond. Chemistry, 8th ed.; McGraw Hill: New York, 2005; Chapter 15. 2. Sweany, R. L.; Owens, J. W. J. Organomet. Chem. 1983, 225, 327–334. 3. Moore, E. J.; Sullivan, J. M.; Norton, J. R. J. Am. Chem. Soc. 1986, 108, 2257–2263 4. Handbook of Chemistry and Physics, 81st ed.; Lide, David R., Ed.; CRC Press: Boca Raton, FL, 2000–2001; pp 8.44–8.56. 5. NIST Chemistry Web book. http://webbook.nist.gov/Chemistry/ (accessed February 2004). 6. Cotton, F. A.; Wilkinson, Geoffrey; Murillo, Carlos A; Bochmann, Manfred. Advanced Inorganic Chemistry, 6th ed.; John Wiley: New York, 1999; p 63. 7. Lange’s Handbook of Chemistry, 14th ed.; Dean, John A., Ed.; McGraw-Hill: New York, 1992; pp 8.13–8.71. 8. Bartmess, John E.; Scott, Judith A.; McIver, Robert T., Jr., J. Am. Chem. Soc. 1979, 101, 6056–6063. 9. Jolly, William L. Modern Inorganic Chemistry; McGraw–Hill: New York, 1984; p 195. 10. Pitzer, K. S. J. Am. Chem. Soc. 1937, 59, 2365–2371. 11. Bordwell, F. G.; Cheng, Jin-Pei; Ji, Guo–Zhen; Satish, A. V.; Zhang, Xianman. J. Am. Chem. Soc. 1991, 113, 9790–9795. 12. Hiraoka, K.; Yamdagni, R.; Kebarle, P. J. Am. Chem. Soc. 1973, 95, 6833–6835. 13. See for example Pauling, L.; Pauling, P. Chemistry; Freeman: San Francisco, 1976; pp 402–405. 14. See for example Douglas, Bodie E.; McDaniel, Darl H.; Alexander, John J. Concepts and Models of Inorganic Chemistry, 3rd ed.; John Wiley: New York; 1994; pp 326–329. 15. Travers, M. J.; Cowles, D. C.; Ellison, G. B. Chem. Phys. Lett. 1989, 164, 449. 16. Xie, Y.; Schaefer, H. F., III; Wang, Y.; Fu, X.–X.; Liu, R.–Z. Molecular Physics, 2000, 98, 879–890; Chem. Abstr. 133:140554. 17. Gilles, M.; Polak, M.; Lineberger, W. C. J. Chem. Phys. 1992, 96, 8012–8020. 18. Wang, Xue–Bin; Wang, Lai–Sheng. J. Chem. Phys. 2000, 113, 10928–10933. 19. Huheey, James E.; Keiter, Ellen A.; Keiter, Richard L. Inorganic Chemistry: Principles of Structure and Reactivity, 4th ed.; Harper Collins: New York, 1993; p 329.
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