The Relation between the Ionization Potential and the Molecular Electronegativity of Organic Homologs Cao Chenzhong Xiangtan Teacher's College, Xiangtan, Hunan, 411100, People's Republic of China
Sanderson (1)first enunciated the principle of electmnegativity equalization and applied the principle (using his own electronegativities) to the calculation of atomic charges in both molecular and nonmolecular substances. He used these charges in calculations of polar-covalent bond energies (2-5).Bratseh (6, 7)outlined a somewhat different approach, based on Pauling electronegativities, for calculating equalized molecular electronegativity, atomic charges in molecular substances, and group electronegativity. By modifying Bratsch's procedure, Smith (8) proposed a new method for estimating atomic charges in a molecule. He correlated the core ionization energies with these atomic charges. The preceding works all explained the physical and chemical properties of compounds through the evaluation of the partial charges on the constituent atoms. However, the partial charge can be used to predict the electron activity of only the given atoms in a molecule. It does not predict the electron activity (such as the first ionization potential) of a molecule, especially the change rule of electron activity for organic homologs. Parr (9,101points out that electronegativity is the negative value of the chemical potential. Sanderson (4) considers that the princlple of electronegativity equalization corresponds to equalization of chemical potentials in a compound.
n" = 4); S,and 6 : are the partial charges on atom i of M and M+,respectively; and A& = 1.57(Si)m.
Molecular Electronegativity We can regard the molecular electmnegativity of a molecule as its chemical potential-and similarly for a molecular ion. Therefore, when a neutral molecule M losses its electron, forming a molecular ion M+(eq 11,
Then from eq 5, we get the following.
M+M'+e
(1)
its chemical potential increment is equal to the electronegativity difference between the molecular ion M+ and neutral molecule M. In Sanderson's (4,5) method of calculation, the neutral molecular electronegativity, or the partial charge on an atom of neutral molecule M or molecular ion M+, can be obtained by eqs 2 4 , respectively
n=
C ni = t h e total number of atoms in the species formula
Obviousl~,for M, L,
zSi=O ;=I
M+, n
C6;=+1 i=l
Thus, n n M-S; Z&;-Cs.-C-' - " SM*-S; i s -
i=l
i=l
As;
i=l
=f:%%Mi
i=l
Bi
-1
~ , t AsM+= SM+ - SM
1
As,+=--
-- 1
E L ELL i=lG
i = lh5,
ElectrOnegativity According to Bratsch's (6)approch, the equalized electronegativity can be expressed as x,e q
=
n+q
i=l
(3)
(6)
(7)
where Xeqis the neutral molecule or ionic electronegativity; Xi is the initial, prebonded electronegativity (Pauling scale) of a particular atom i; q is the integral charge of the polyatomic species. (For example, for neutral molecule M, q = 0; for molecular ion Mi, q = +I.) Let Xeq(M+) andX, (MI represent the electronegativities of M+and M. Then AX, (Mi)=Xeq(M3 - Xeq(MI
(4)
From eq 7, we get the following expression for AXeq(Mt).
Here SM and SM* are the electronegativity of M and M'; Si is the initial, prebonded electmnegativity (Sanderson scale) of a particular atom i; niis the number of atoms of element i in the species formula (e.g., for CH4, nc = 1and Volume 70 Number 1 January 1993
25
Ei = a + blLY,, (I@)
H
NH,
OH
SH
CI
Br
I
CHO
COCH,
CH=CH,
1
2
3
4
5
6
7
8
9
10
(~3s-)CH=CHMe (trans-)CH=CHMe 11 12 CECH 15
(trans-)CH=CHB
13
14
C=CEt
C=C--CMeCH,
17
18
16
19
20
K(CIC),H
22
23
X = (0.33S
Me3G(C=C)$Me3
26 27
+ 0.66)'
(11)
This implies that the molecular ionization potential Ei cannot be linearly related to both electronegativity scales. We must decide whether to use eq 9 or eq 10 to express the relation between the molecular ionization potential and the molecular electronegativity of an organic homolog.
Fk-(CH=CH)$il
25
(lo)
where a, a', b, and b' are empirical constant. In other words, we expect a linear correlation between Ei and AX, (Mt) or AS* for each homologous series. However, the Pauling and Sanderson electronegativity, as we know, are not related to one another. They are related as shown below (7).
21
H-(CH=CH)#
b&(CH=CHqHO
Ei = a' + b'As~*
(us-)CH=CHEt
CECMe
(9)
or
28
The Calculations for
30
29
a Homologous Series
31
We carried out the calculations of AX, (MI) and Figure 1. The molecular structure of the homologous series for HiCH$,-X showing X subtitutents 1 through ASw (by eqs 7 and 8) for 31. homologous series 1-31 (Fig. 11, respectively. Then we correlated their first ionization potentials Ei (11-14) with the values obtained for AX, (M+)and AS* Equations and are in but the value of using eqs 9 and 10.A set of a, b, r (correlation coefficient), +I& is not equal to that of AXeX,, (MI) due the different and v,r, are obtained for each of the 31 homologous electronegativity scale. For example, for the reaction series through regression analysis. The results are listed in Table 1, and the statistics of correlation coefficient r is CH, + C g + e listed in Table 2. According to Jaff6 (15), when r 2 0.99,the correlation is we get "excellent"; for r 2 0.95,"good"; and for r 2 0.90,"middling". By this standard, the r of this paper is "excellentn.AYgood" =0.4524 %,(Mi)= grade would be 93.55%, and a "middling" grade, 6.45%. Less than 0.90are 0.
G+z.zo
Comparing the Two Approaches to Electronegativity
and
Predicting Electron Activity Correlating Ionization Potential and Electmnegativity As said before, molecular electronegativity is the chemical potential of a molecule. Thus, hX., (Mf) or AS* is equal to the chemical potential increment from M to M+. Theoretically, the first ionization potential Ej of a homolog in a homol&ous series should be-directlypropotional to AXeX., (Mt) or AS*. That is, 26
Journal of Chemical Education
A s Table 2 shows, although the linear correlation of eq 10 is not as good as that of eq 9,it also has remarkably good correlation coefficients. This can be explained as follows. Comparing eqs 6 and 8, we can see the following. If
x , = cAsi or if xi --
mi-=
(wheree is a constant)
then
a,(m= C
~ M *
Table 2. Statistics of the Correlation Coefficient (for the Series of 31)
Table 1. The a, a', b, ff, r, and f of Regression Analysis Equations for the Homologous Series 1 to 31.
Series
n"
a
b
r
a
'
U
r
'
E,= a + Meq (M?
eq
E,=a'+UAW
Table 3. XiLASi Values for Various Elements 6 7
1-4 1-5
9.917 1.288 0.996 9.912 1.193 0.996 9.069 0.987 0.997 9.066 0.908 0.996
ele-
H
C
N
0
F
CI
Br
I
S
merit
Comparing the Two Equations
Now, we calculate the values of XjlAS; for different elements to see if they are equal to a constant. Some XiIAS; values are listed in Table 3. The values of X;lAS; for the main elements forming organic compounds are appmximately equal to 1, that is c = 1. Because X; = AS; and the homologous series each cover only a very small electronegativity range, a linear appmximation between molecular ionization potentials E; and ASS in eq 10 is acceptable. We expect that when the electmnegativity range of a homologous series increases, the linear correlation of eq 10 will decrease. For example, the following series CH3X
CHX3 HX where X = F, C1, Br, or I
has the following electronegativity ranges (Pauling scale). 27 28 29 30 31
0-3 1-5 0-3 0-3 0-3
5.249 26.735 5.220 22.351 4.600 41.569 5.226 30.647 5.060 27.351
0.991 0.998 0.997 0.936 0.998
5.270 24.662 0.992 5.240 20.595 0.998 4.618 38.550 0.996 5.278 27.874 0.922 5.067 25.488 0.998 ' The data for the ionization potential 6 of series 1,3. Wl, taken fmm ref
11, series 22-31, fmm ref 12; series 2.4, fmm refs 13and 14, respectively. '' "is the number of repeating units in series 1-31.
Thus, eq 9 will be equal to eq 10. E;=a+bAX,(t@)
CH3X: X,, (CH3F)-X, (CH31)= 2.491- 2.345= 0.146 CHX3: X,, (CHF,) -X., (CHI3) = 3.124 - 2.532 = 0.592
HX: X, (HF) - X,, (HI) = 2.832- 2.408= 0.426 The values ofXjlAS; for the elements vary from 0.91 (HI to 1.268 (F). In this case, the linear correlation of eq 10 is worse than that of eq g (see ~ ~ 4), and b the l ~ plots of E; versus ASM*are curved (Fig. 2) in the large electmnegativity range. It shows that eq 9 correctly expresses the correlation between the ionization potential and the chemical potential increment AX, (M9 of an organic homolog. Conclusion
This paper correlates the molecular electronegativity with the first ionization potential of organic homologs quantitatively. It is a great help to students (especially =a' + b'&SM+ those without quantum chemistry) in understanding the change rule of electron activity for organic homologs. which is just eq 10 again. Equation 9 also can be used Table 4. The Results of Regression Analysis to predict the ionization pofor the Series CH3X,CHX3, and HX. tential of a given molecule i n a homologous series Ei=a'+tfASM' Ei=a+MXeq(M3 whose ionization ~otential I SD.. has not been measured. a b r SLY series* a' Lf r' The calculation of hX., (M7 CH3X -41.815 109.669 0.995 0.169 -85.787 185.590 0.992 0.221 be carried out in a few minutes, using the most 97.059 0.966 0.535 0.119 -41.687 0.999 -15.075 47.744 CHX3 basic pocket calculator, so it 0.652 0.973 0.220 60.133 46.720 25.564 0.997 HX -20.745 is easy for students to use ' X F,CI, Br, I. Data for the first ionization potemial 6 of series C K X . CHX3,taken from ref 16: HX, from ref 14. " Standard Deviation. eq 9: = a + bcASM+
.
Volume 70 Number 1 January 1993
27
Literature Cited 1.Sanderson ' . R
& i e m lsJ1,114,670-672.
2. Sanderson R.T. Ckmlml Bands andBondsEnewies. 2nd ed.;Aeademie:NewYork, 1976. 3. Sanderson R. T. Polar Couolpnco; Academic: NewYorh, 1983.
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5. Sand.-n
R. T J Ckm. Edue IS@, 65,227.
6. Bratsch, S G. J. Chem Educ. 1984,61,588. 7. Bratsch, S G. J Chem Educ. 19S5,62,101. 8. Smith, D. W. J C h . Ed-.
1890,67,559662.
9. P m , R. C.; Donnelly, R. A; Ley, M.; Palke, W E. rl Chem. Phys. 1978,68,38013807.
B., 10. Pm,R.G.lnEkcfmnDrsfribullonondthsChomimlBond,Coppeae,P.:Hall.M. Ed%; Plan-: New York, 1982, pp 96100. 11. Sun Yukun: Xu Guangldan; Li h m i n Ckmiml J o v m d of Chinese Uniuemilks 1982.313). 389397. 12. Sun Yukun; Xu Guangian: Li Lemin Chemiml Journal of Chinese Uniuersitks 1982,3(11.119-129. 13. Wataoake, K;Mottl,J. R. J Ckm. Phys. 19S7,26,1773.
Figure 2. Plots of first ionization potential Ei versus AX, A*. 1.2:CH3X; 3,4: for CHX3: 5.6: for HX.
28
Journal of Chemical Education
(Mt) or
14. Weaat, R. C. Hondbwk of CkmisiryodPhysics, 58th ed.; CRC Press. 15. JaR'6,H.H. Chem. Reus. I953,5.3,191. 16. Zhu jikang; Li du; Li junqing; Pan yvgsng SCIENTIA SINICA (SCIENCE IN CHlN4L SEMESB ISsJ,5,4G3419.
