Acidities of Oxoacids Correlation with Charge Distribution Terry L. Meek University of the West Indies, Cave Hill, Barbados I t has long been recognized (1-5)that the strength of an oxoacid, as measured by its acid dissociation constant k,, depends primarily on the number of oxygen atoms doubly bonded to the central atom L in the molecule. This can be attributed to two effects: the inductive effect that highly electronegative oxygen atoms have on the polarity of the OH bond, and the stabilization of the coujugate base through increasing delocalizatiou of the negative charge. For oxoacids with the same number of L=O bonds, there is no obvious single factor which governs the acidity. Values of k . (or pk.) do not correlate well with, for example, the electronegativity of L or the number of OH groups in the molecule. Acidity does increase with increasing electmnegativity for acids with the same number of both L=O bonds and OH groups, but this is of limited usefulness. Calculation of Partial Charges In a n attempt to ascertain whether acidity can be correlated with some molecular parameter, the charge distribution within 24 oxoacid molecules and their coujugate base anions were examined by calculating the partial positive or negative charge on each atom. The basis of these calculations is Sanderson's principle of electronegativity equalization (61,according to which all the atoms in a molecule or ion have the same electmnegativity value. Those atoms whose electronegativities are ibwered &om the free-atom value acquire a partial negative charge, while those with increased elec&onegati;ities gain; partial positive charge. ~ u i n t i t a t i v e lSanderson ~, evaluated this molecular electronegativitv as the geometric mean of all the atomic electronegativiiies andassessed partial charge as equal to ~S11.57S" (71,where S is electronegativity in Pauling units. He used these partial charges to calculate (inter alia) bond energies and heats of atomization that agree very well with experimentally obtained values. An alternative method of calculating partial charges (8) uses the Mulliken a and b atomic parameters, where a is defmed by
Here the a and b parameters are in electron volts. Allen (11)has proposed a modified Lewis-Langmuir method for calculating partial charges. This treats the partial charge on an atom as resulting o d y from the effects of the other atom(s) bonded directly to it, without regard for the rest of the molecule. (Thus, the hydrogen atoms in all OH groups in every molecule would have the same partial charge.) In this paper the Bratsch method and eqs 1and 2 were used. The values of the Mulliken parameters were those compiled by Bratsch (12) from valence-state ionization potentials and electron affinities evaluated from spectroscopic data. Choice of Valence States Bratsch (12) points out that the electmnegativity of an atom will vary from one valence state to another, dependine on the t v ~ eof orbital used for bondine. However. it s h k ~ l dhe recognized that electronrgptivity is a measure of the electron-attractinrr ability of an atom on all the bondThus, all the bonding orbiting electrons in the m~lecule~ als, both o and n, should be taken into account. On this basis, all tetravalent carbon atoms, for example, would have the same eleetronegativity
-
a = 0.25 a, + 0.75 a,
inherent eledronegativity - ionizationqotential+eledmnaEnity 2
and b is defined by charge coefficient = ionization potential - electron affinity Reed (9)and Bratsch (10) have shown that, for a molecule or ion, equalized electronegativity is given by 1
I where V is the number of atoms of an element and q is the net charge of the species. The partial charge on atom Ais given by 270
Journal of Chemical Education
11
Ill IV v VI VII GROUP
Figure 1. The p orbital electronegativitiesfor second and third period elements. Closed circles indicate the a, values from Bratsch (12). Open circles indicate extrapolated values.
Table 1. Charge Distribution in Oxoaclds and Their Conjugate Bases Partial ChargeC
Partial ChargeC Acid (H0)2
HOi (H0)4SI (H0)sAs HOBr (H0)dGe (H0)eTe HOCl HOF
aa 12.55 10.26
ha 15.47
0
La
aeqb
-
9.61
-0.190
Anion
H +0.190
HOO-
4
La
5.70
-
H
0 4.443
-0.115
7.30 7.70 11.46 7.53 6.46 12.15 15.30
(H0)2CO 8.15 (H0)slO 8.00 HONO 10.29 (H0)zTeO 8.52 (H0)zSeO 9.48 (H0)sAsO 9.30 (H0)sPO 9.11 (H0)nSO 9.84 HOClO 12.15
because all use one s a n d three p orbitals (or some combination thereof) i n bonding. Nevertheless, t h e choice of valence s t a t e s for atoms with expanded octets remains a problem. For simplicity, t h e electronegativities assigned to t h e central atoms a n d t o oxygen were those tabulated b y
Bratsch for "tetrahedral" atoms, with the following exceptions. 1. In the periods with principal quantum number n > 2, p orbital electronegatinties of the elements in groups 5-7 are decreased due to shielding by the lonepair s electrons. When all of the valence electrons are used in bonding, this effect would not occur, and the p orbital eledmnegativities should be higher. More appropriate values were obtained by extrapolation of the p orbital electronegativitiesof Groups 2-4 elements of the same period (Fig. 1). They were used to calculate the valence state electronegatinties of the central atoms in H3P04, H3As04,HzS04,HzSe04,and HCIO1. 2. In H6Te06and H,IOs, the M bonds could be formed by combination of appropriate oxygen orbitals with sp3dZhybrids (full-hybridization model) or with unhybridized p orbitals (three-center-bondmodel) on the central atom. Since accurate d orbital electronegativities are not available, p orbital elmtronegativities were used. 3. For fluorine in HOF and oxygen in HzOz,Bratsch's (12) formula far assigning valence states was used. % s character =
'1
.5
.6
R
.7
.8
9
1.0I
Figure 2. The p& of oxoacids vs. the ratio of partial charges H'+ (acid)to 0" (conjugate base). Open circles indicate no L=O bonds. Closed circles indicate one L=O bond.
100
group number
For nitrogen in HN02, the bonding orbitals are two sp2hybrids and one p orbital, so that a valence state with 22.2%s character is appropriate.
Results The partial charges calculated for twenty-four oxoacids and their conjugate bases a r e listed i n Table 1.Inspection
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271
Table 2. Calculated vs. Experimental pka Values
FP
Acid
p
b
pkC
(HO)2 HOI (H0)nSi
0.429
11.70
11.65
0.457
11.01
10.64
0.542
8.92
9.66
(H0)3As
0.517
9.53
9.22
=
(~ka)~cak pkac
Acid
ti=
(H0)zCO (H0)dO HONO (H0)zTeO (H0)2SeO (H0)AO (H0)aPO (H0)nSO HOClO
0.684
5.42
3.58
0.798
2.62
3.30
0.764
3.46
3.15
0.687
5.35
2.48
I partial h a w e on hydrogen in acid I I partial charge on oxygen in conjugate base I (3)
Such a correlation i s logical, considering t h a t k, refers to a n equilibrium process and should be affected by both the acidity of the acid and the basicity of its conjugate base. Aplot of pk. vs. R is given in Figure 2. For the eighteen oxoacids with no L=O bonds (very weak acids) or one L=O bond (weak acids), fourteen lie close to a line whose equation i s given (by least-squares analysis) as pk. = 22.25 -24.60 R (4)
HOBr 0.554 8.62 8.74 0.782 2.91 2.27 8.40 8.63 2.30 2.24 (H0)4Ge 0.563 0.811 2.50 2.15 6.87 7.66 (H0)6Te 0.625 0.803 2.23 1.91 HOCl 0.596 7.59 7.53 0.814 HOF 0.711 4.76 ? 1.000 -2.15 1.32 ?Equation3: data in Table 1 q qua ti on 4 Values of pk, calculated from eq 4 show, for Cmostlyfmm Ref. 13 these fourteen acids, a n average deviation of of these values shows that none of the following correla0.36 log units from experimental values (Table 2). tions exist. Larger discrepancies a r e observed for HzC03 (1.84 units), H2Te03 (2.87 units), and HClO2 (3.47 units). The between the pk, and the partial charge on hydrogen, oxygen, pk, of HOF has not been determined, but is calculated from or thecentral atom in either the acid or the conjugate base eq 4 a s 4.76. Much better agreement is seen for H2C03if between the pk, and the OH bond polarity, or change in the = sp2 hybridization is used. Then R = 0.741 and (pk.),,, partial charge on oxygen or the eentral atom 4.03. For HC102 if the "Bratsch" valence state of 14.3% s i s between the pk. and the equalized eledronegativity of the acid or the conjugate base, or the change in aeq used, then R = 0.851 and (pk.),dc = 1.32. The relationship expressed by eq 3 does not hold for the following types of oxoacids. However, quite good correlation is seen to exist between pk. and the ratio R in the first column of Table 2, which is 1. Strong acids with two L O bonds, and the very strong perdefmed by chloric acid with three Table 3. Charge Distribution in Oxoacids and Anions with L 4 Bonds Partial ChargesC
Partial ChargesC aa
Acid
(H0)zCO 8.15 (H0)HCO 8.15
ha
aqb
0
L
H
Anion HOCW HCOz-
11.39
10.40
+0.198
4.233 +0.251
113 9
9.77
+0.142
-0.273 +0.202
(H0)sPO 9.11 9.53 10.48 +0.144 4.228 +0.257 (H0)zHPO 9.11 9.53 10.05 c0.098 -0.256 +0.233 c0.051 4.291 +0.181 (HOIHzPO 9.11 9.53 9.50 aL= central atom; values from Branch (12) 'Equation 1 'Equation 2 d~quation 3 'mostly fmm Ref. 13
0
L
aeqb
H
R~
pk2
8.31
+0.014
-0.367
+0.089
0.684
3.58
7.06
-0.095
-0.448
-0.009
0.451
3.75
(H0)zPOz- 9.04 (H0)HPOz- 8.33 HzPOY 7.39
-0.007
-0.320
c0.145
0.803
2.15
-0.081
4.366
+0.090
0.609
1.80
4.180
4.426
+0.017
0.425
1.23
Table 4. Charge Distribution in Oxoanions
Partial ChargeC Acid (H0)sTeO-
'L
=
a~' 6.46
ha 8.44
aqb 8.92
L +0.291
central $om: vatu? fmm Bratsch (12) Eq 2 Eq 3 'Mostly fmm Ref. 13
b ~ 1.q
272
Journal of Chemical Education
0 -0.328
H +0.136
I
Partial ChargeC Anion
I(HO)~T~&~-
amb 7.86
L
0
+0.166 -0.396
H +0.053
Rd 0.343
plhe 11.30
2. Adds in which one (or more) OH group is replaced by the less eledronegative hydrogen atom (Table 3) 3. Uninegative anions of di- and tribasic acids (Table 4)
Nevertheless, for neutral oxoacids with one or no L=O honds and no L H bonds, acidity does seem to be more direetly influenced by the calculated ratio of partial charges than bv. anv - other single - ~. a r a m e t e r . Rratsch (8)has pointed out two major difficulties in making such applications of Mulliken electronegativities: the assignment of valence states, and ascertaining the extent of d orbital participation in honding. Possibly, if these problems are ovwcome, partial eharge&ios codd be obtiined that give a better fit with experimental pk, values.
Literature Cited 1. Pauling, L.:O p ~ r nChzmiefry, l ht ed.;W. H.Freeman: San Franclsca 194T p 394. 2. Rieei. J. E. J Am. Cham. S a 1648.70.109. . . 3. Powell, P.;Timms,P.;The C h i 8 t r y o f t h z N o n Metals: Chapmanand H a l l : h d o n , 1974;pp1W-104. 4. Huheey, J. E.; Inorganic Chemiahy. 3rd ed; Harper and Ron: New Yo*, 1983: pp 29C297 m d ld9-1M . ..
5. Cotton. F A; W i k m , G.:Advonad Inogonic ChaMstry, 5th ed; Wiley: New Yo*, 1988; pp 10P105. 8. Sand8rsan.R. T Science 1951.214. 670. 7. Sandersan, R.T.;PdorCou&ncp; Academic: NenYmk, 1983:pp 37-40,
. .
8. Bratach, 8.0.J. Chem.Educ. 1988.65.223. 9. Reed, L.J. J. Phys. Chzm 1881.85,148 10 Brstaeh. S.G. J Chpm.Edue. 1%. . 61.588. . 11. Allen,L.C.J Am. Chzm. Sor. 1989,111,9115
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