Electronegativity and the Acid-Base Character of Binary Oxides Steven G. Bratsch Southwest Texas State University, San Marcos. TX 78666 o
The Pauling electronegativity scale (1,2) can be used to predict standard enthalpies of formation of binary compounds a t 25 O C via the equation
-
AH"f -96.5.
n.
[XA- XBI2
10
00/
8
(1)
In eq 1, AH% is the standard enthalpy of formation in kiloioules Der mole. n is the number of eauivalents in the compoundformuln,and X . and XI, are the Paulingelectronegarivities for the two elements under consideration. Pnulinr's electronegativities have units of (electron volts)'B; the conversion factor between electron volts and kilojoules per mole is 96.5 (the Faraday constant). As discussed by Allred (2), eq 1is on1 reliable within about f20%and fails for compounds - X B is~ greater than about 1.8 (eV)'I2. Still, it is where remarkably successful in view of the fact that no consideration is given to structural changes or physical states of reactants or products. Smith (3)has recently com~iledanumerical scale of acidbase character for b i n a h oxides by analogy with the Pauling electronegativitv scale. For each oxide. he bas evaluated an acid-basiparameter a, which can be k e d to predict standard enthalpies of combination a t 25 OC of binary oxides to form oxo-salts via the equation
LA
In eq 2, b,,,,@ is the standard enthalpy change in kilojoules per mole of oxide ion transferred from basic oxide B to acidic oxide A, and a(A) and a(B) are Smith's acid-base parameters for the two oxides under consideration. Smith has arbitrarily referenced his acid-base parameters to a(H20) = 0;oxides witha < 0 tend to be basic or amphoteric, while oxides with a > 0 tend to be acidic. Smith's acid-base parameters have units of (kilojo~les/mole)~/~. Equation 2 is more reliable than eq 1,generally well within +lo%,perhaps because it is more specific in its application. I t is of interest to investigate Smith's acid-base parameters within the framework of the Pauling electronegativity system and modern electronegativity theory. Sanderson's
5 0
a -
-5 - 10 -15
y
I
I
I
I
Plot of Smith's acid-base parameters a (3) versus equalized electronegativities Xeq(eq 3). Pauling elechonegativitiss from ref 1 and 2. The line drawn corre~pondsto eq 5.
principle of electronegativity equalization (4a) states that two or more atoms of different initial (prebouded) electronegativities equalize their electronegativities on combination. It has been suggested ( 5 , 6 ) that the equalized electronegativity X,,in an oxide may be estimated by
In eq 3, X, is the equalized electronegativity of the oxide, N
Volume 65
Number 10 October 1988
877
is the numher of atoms in the oxide formula, u is the number of atoms of each element in the oxide formula, and X is the initial, prebonded electronegativity of each element on the Pauling scale (1,2). A possible relationship between Smith's oxide acid-base scale and the Pauling electronegativity scale is
where m and b are a slope and an intercept, respectively. Considering the units of the Smith and Pauling scales as given above, the theoretical slope m should he the square root of the Faraday constant, 9.8 [kJ/(mol eV)I1l2. The theoretical intercept b should he that which gives a(H2O) = 0;usingX,(H20) = 2.50 (eq 3), b = -24.5 (kJ/rn~l)~". Thus, eq 4 can be rewritten as
.
a
= 9.8. X,,
- 24.5
Relatlonshlp between Acid-Base Character of Blnary Oxldes and Partial Charge on Combined Oxygen
The partial charge on comhined oxygen may he estimated by ( 5 6 )
(5)
A plot of Smith's acid-base parameters a (3)versus equalized electronerativitv X,, (ea 3) is provided in the ficure. Solid points r G r e s e k oxaes forkhiih the electronegat&ity of the other element is available for the oxidation state under consideration; open points represent oxides for which it is not. The line drawn corresponds to eq 5 and is not a statistically derived best fit. I t is seen that the solid points obey eq 5 reasonably well; deviations from the line drawn may be attributed to uncertainties in both X., and a. Open points in the figure represent oxides for which the electroneeativitv of the other element is not available for the oxidation state under consideration. For example, the electroneeativitv of maneanese(VI1) is unavailable, and MnzO7 is representkd in the figure by an open point, estimating X.,(Mn207) = 2.71 by using XM. = 1.55, which is the value given by Allred (6) for manganese(I1). Because the electronegativity of manganese(VI1) is probably much greater than 1.55, the actual X,,(Mn2O7) is probably much greater than 2.71, and the point for Mn207 should he displaced toward the right, i.e., closer to the line given by eq 5. A similar argument applies to other oxides represented in the figure by open points. Relationship between Standard Enthalples of Combination of Blnary Oxldes and Electronegalivity
Comhination of eqs 2 and 5 gives
Equation 6 can he used to estimate standard enthalpies of combination of binary oxides (in kilojoules per mole of oxide ion transferred) in cases where experimentally determined acid-base parameters are unavailahle. I t is the first quantitative application of the author's ( 5 6 )proposed adaptation of Sanderson's principle of electronegativity equilization (4a) to the Pauling electronegativity scale. Equation 6 is about as reliable as eq 1, i.e., within about f20%. It is significant that eq 6 requires no adjustable parameters, thereby providing support for the calculation of X, via eq 3.
In eq 7,do is the partial charge on comhined oxygen, X,, is the equalized electronegativity of the oxide (eq 3), and Xo is the initial, prehonded electronegativity of oxygen, 3.44 (2). Solving eqs 5 and 7 for X,, and setting them equal to one another gives
Sanderson (46) has qualitatively discussed the relationship between oxide acid-base character and partial charge on comhined oxygen, noting that oxides with very negative 60 tend to he basic, oxides with moderately negative 60 tend to he amphoteric, and oxides with only slightly negative 60 tend to he acidic. Equation 8 puts Sanderson's ideas on a quantitative basis. Literature Cited
1. Pauling, L. TheNofur. of the Chsmicol Bond, 3rd ed.: Cornell University Ithsca, NY. 1960: PP SS95. 2. Ai1red.A. L. J.Inorg.Nue1.Chsm. 1961.17.215. 9. Smith, D. W. J Chem. Edue i987.64.480. 4. Smder8on.R. T.Polor Couo1ence:Academic:NewYork. 1983:(a) pp3739. (b)pp 19% """
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