INFLUENCE ELECTRICAL OF

STRONG M.

OF

ORGANIC

NONELECTROLYTES

CONDUCTIVITY

OF

AQUEOUS

ON T H E SOLUTIONS

ELECTROLYTES

M. K a r e l ' s o n

UDC 541.133

In a p r e v i o u s c o m m u n i c a t i o n [1], a model of d i s c r e t e s t a t e s was p r e s e n t e d for aqueous solutions of s t r o n g e l e c t r o l y t e s , making it p o s s i b l e to d e s c r i b e the t e m p e r a t u r e and c o n c e n t r a t i o n dependence of the e l e c t r i c a l c o n ductivity of the solution. According to this model, the m a j o r f a c t o r d e t e r m i n i n g the magnitude of the e l e c t r i c a l conductivity is the d e g r e e of s t r u c t u r i n g of the e l e c t r o l y t e solution. Obvious t h e o r e t i c a l and p r a c t i c a l i n t e r e s t is p r e s e n t e d by the v e r i f i c a t i o n of the model in the c a s e of nonaqueous media, and a l s o f o r mixed s o l v e n t s , w h e r e the influence of both components on the total s t r u c t u r i n g of the solution is an i m p o r t a n t f a c t o r . In this c o m m u n i c a t i o n , the influence of v a r i o u s organic n o n e l e c t r o l y t e s on the e l e c t r i c a l conductivity of aqueous s o l u tions of s t r o n g e l e c t r o l y t e s is e x a m i n e d f r o m the point of view of the model of d i s c r e t e s t a t e s of the solution p r o p o s e d e a r l i e r [1]. We shall e x a m i n e the s i m p l e s t model of c o n s i d e r i n g this influence. Let each molecule of the n o n e l e c t r o l y t e f o r m a cavity, c h a r a c t e r i z e d by the m o l a r volume V s , by m e a n s of changing the s t r u c t u r e of the s o l u tion. It is p r o p o s e d that the ions which e n t e r into this cavity stop taking p a r t in the e l e c t r i c a l conductivity of the solution. In o r d e r to be able to d i s r e g a r d the influence of the c h e m i c a l equilibria with participation by the ions of the e l e c t r o l y t e , we examine the value of the limiting equivalent conductivity h~o. To deduce the dependence of ~ o on the concentration c of the n o n e l e c t r o l y t e we take advantage of a p r o c e d u r e analogous to that p r e s e n t e d by Celeda [2]. F o r s i m p l i c i t y , we p r o p o s e that the exclusion of the ions f r o m p a r t i c i p a t i o n in e l e c t r i c a l conductivity m a y be viewed as a s e p a r a t e p r o c e s s ; i.e., the v o l u m e s V s for v a r i o u s m o l e c u l e s of the n o n e l e c t r o l y t e m a y o v e r l a p f r e e l y . Then f o r an i n c r e a s e in the concentration of the n o n e l e c t r o l y t e , the r a t i o of the effective d e c r e a s e of the nfreeW volume, dVf, to the i n c r e a s e of the v o l u m e V s c h a r a c t e r i s t i c f o r m o l e c u l e s of the given n o n e l e c t r o l y t e (able to o v e r l a p f r e e l y ) , Vsd(V0c), equals the r a t i o of the f r e e v o l u m e Vf to the total v o l u m e of the solution V 0 (see Fig. 1). In other w o r d s , upon addition to the solution, each molecule of the nonelectrolyte c a u s e s a d e c r e a s e in its v o l u m e p r o p o r t i o n a l to its c h a r a c t e r i s t i c v o l u m e V s and to the magnitude of the f r e e v o l u m e Vf in the solution. Hence, the following r e l a t i o n s h i p holds:

- - dV f = - ~ - V~d (Voc) vo

(1)

or

- - d In V I ~-

Vflc.

(2)

Integrating the l a t t e r e x p r e s s i o n in the l i m i t s c o r r e s p o n d i n g to the change in concentration of t h e s o l u tion f r o m 0 to c: vr

c

- - ~ dlnVl.-~Vs ~ dc, Vo

(3)

0

we obtain v~ In ~ ~---V~c.

(4)

F o r constant ionic mobility in the f r e e v o l u m e of the solution and c o n s e r v a t i o n of the spatial distribution of ions, the following r e l a t i o n s h i p holds: T a r t u State U n i v e r s i t y . T r a n s l a t e d f r o m T e o r e t i e h e s k a y a i l ~ k s p e r i m e n t a P n a y a Khimiya, Vol. 15, No. 1, pp. 80-85, J a n u a r y - F e b r u a r y , 1979. Original a r t i c l e s u b m i t t e d N o v e m b e r 10, 1978.

62

0040-5760/79/1501- 0062 $07.50 9 1979 Plenum Publishing C o r p o r a t i o n

2fl~t 7,75

"

V0

40 Cne,,'r

2,a

Fig. 1

Fig. 2

Fig~ 1. Relationship between the v o l u m e s of the v a r i o u s s t r u c t u r e s in a mixed solution of w a t e r and organic nonelectrolyte (definitions in the text). Fig. 2. E l e c t r i c a l conductivity of s e v e r a l e l e c t r o l y t e s in mixed solvents (25~ 1) KC1 ( d i o x a a e - H 2 0 [12]); 2) Me4NC1 ( t - b u t a n o l H20 [ l i D ; 3) C6HsCOOK (t-butanol-H~O [13]).

v ~ = ~,= (c) Vo

(5)

;~= (0) '

w h e r e X ~(c) and ~ oo(0) a r e the limiting equivalent e l e c t r i c a l conductivities of the e l e c t r o l y t e f o r c o r r e s p o n d i n g c o n c e n t r a t i o n s of the n o n e l e c t r o l y t e . Hence, f r o m Eq. (4) we have

~=, (c)

In ~

=

--

V,c,

(6)

or

Z,~o(c) = ~| (0) exp (-- V~c).

(7)

Analysis of n u m e r o u s l i t e r a t u r e data shows that the l a s t function is u n i v e r s a l for m a n y strong e l e c t r o l y t e s in v a r i o u s b i n a r y m i x t u r e s of w a t e r - o r g a n i c solvents (see, e~ F i g . 2}, o v e r a wide r a n g e of concentrations of the l a t t e r (0 < c < 7...10 m o l e s / l i t e r ) . The values Vs of the m o l a r v o l u m e s obtained f r o m the slopes of Eq. (6) a r e p r e s e n t e d in Table 1. It is noteworthy that the value of V s f o r the given n o n e l e c t r o l y t e p r a c t i c a l l y does not change if in the a n a l y s i s , instead of the value of k~o, that of ~-0 is used, i.e., the value ofthe equivalent e l e c t r i c a l conductivity of ions in the conducting a g g r e g a t e s in c o n c e n t r a t e d solutions of e l e c t r o l y t e s (see [1]). The model developed h e r e of the influence of n o n e l e c t r o l y t e s on the e l e c t r i c a l conductivity of solutions of s t r o n g e l e c t r o l y t e s m a y be independently v e r i f i e d , e.g~ by the data of d i f f e r e n t i a l - c o n d u c t i m e t r i c m e a s u r e m e n t s [3-7]. The d i f f e r e n t i a l - c o n d u c t i m c t r i c method is b a s i c a l l y a m e a s u r e m e n t of the influence of s m a l l additions of a b a s e on the specific e l e c t r i c a l conductivity of a solution of a strong acid, e x p r e s s e d by the value

y = A ~ ~o~, Co

(s}

w h e r e A>t is the change in the specific e l e c t r i c a l conductivity of the solution upon addition of an organic b a s e with concentration c o (considering also the c o r r e c t i o n for the dilution of the solution during the addition p r o c e s s ) . F o r all the w e a k organic b a s e s studied, a significant change in t h e value of Y with the concentration of the s t r o n g acid (I-I2SO4, HC104) was detected o v e r a concentration r a n g e of 0 to 20-25 wt.% [3-9]. A c c o r d i n g to our model, the addition of an organic nonelectrolyte (weak base) to a solution of a strong acid should p r o d u c e a p e r t u r b a t i o n in the s t r u c t u r e of that solution, which in turn is e x p r e s s e d by the change in the specific e l e c t r i c a l conductivity of the solution~ The concentration c n of ions of the e l e c t r o l y t e (g-ion/liter) excluded f r o m the conduction p r o c e s s upon addition of the w e a k organic b a s e to the solution is given b y the e x pression* * The f a c t o r 10 -3 is introduced to account f o r the change in s c a l e upon t r a n s i t i o n f r o m V s (cmS/mole) to c o (mole/liter).

63

TABLE 1. Molar Volumes V s Characterizing the Change in S t r u c t u r e of Solutions for Several Organic Compounds s..

v~(d.-c.) I

vs~

Electrolytes;[:

Methanol

75

73,74-1,2

Ethanol Acetone

124 160 175 180 185 210 220 235

121,44-4,0 146,04-1 i0

NaC1, KCI, Na2SO4, K2SO4. MgSO4, HC1, Ca[n'e(SO.~)2C6HJ, Sr[m-(SO3)2C6H4] KCI, KI, CsCI, UC14,NaOH, HCI, HCIO4 MnSO4, Mn[rnffSOa)2C6H4] NaCI, CHaCOONa, HCI NaCI, KCI, HCI

Compound

1

Propanol

2-Propanot Propionamido Ethylacetato Butanol tort -Butanol

10 11

Tetrahydrofuran

12 13 14 15 16 17 18

Tetrahydmpyran

155 167

Dioxane

Phenol Pivalic acid Nitrobenzeno

1,3 -Dinitr obenz~no 1,3,5-Trinitro-

bonm~ne

167,7.-1-2,7

i77,0:t:2,1 219,54-3,2 233,84-3,5

Kl, CsC1, KCIOa HCt, KBr, KCIO4, HCOOK, NaCI, NaBr, NaCIOa, KNOa, AgNO3, CsCI, LiBr, (CHa)4NCI, (CHa)~NBr, (CHa)~NI, (C4Hg)4NBr, HCI, HNOa MgBr2, ZnCI=, LiCI, KCI, KCIO4 KC1, KBr, NaCl, NaNOa, (CHa)4NCI, (CHa)4NBr

177,0=1=7,1

156,4:i=4,2

175 150 210 295 230 290 320

* Values of V s obtained from Eq. (11); magnitudes of Y calculated by data of [3-9]. t Values of V s obtained from Eq. (6); data on electrical conductivity taken from [10-13]. $ Electrolytes for which the applicability of Eq. (6) was verified.

r ~-00

200 Y .

2

!

I00

100

_

/

~

, 425

~5o

r

Fig, 3

2g

, x.RD

Fig. 4

Fig. 3. Satisfaction of Eq. (11) for several organic compounds (in aqueous solutions of H~SO4): 1) acetone [7]; 2) nitrobenzene [8]; 3) pivalic acid [9]. Fig. 4. Relationship of the molar volume V s to R D for several o r garlic compounds (numbering of points corresponds to Table 1). c. = V~c~Co.10=3,.

(9)

where c e is the concentration of the electrolyte (acid) in the solution in g - e q / l i t e r , c o is the concentration of additive (mole/liter), and Vs is the characteristic volume of the change in structure of the solution by the influence of the nonelectrolyte. The equivalent electrical conductivity )~ of a solution of a strong acid, for the c a s e of small additions (< 10-z%) of the nonelectrolyte, may be considered practically constant. The change in the specific electrical conductivity of the solution (the portion of ions corresponding to the concentration c n are excluded from the conduction p r o c e s s ) is A• 64

a __-~)~CeCoV ~ .t0-31

(10)

and the d i f f e r e n t i a l - c o n d u c t i m e t r i c effect caused by the change in s t r u c t u r e of the solution is given by the e x pression Y~ =

103A• -- ~.ceVs .i0 -3 =V~• Co

(II)

w h e r e ~t is the specific e l e c t r i c a l conductivity of the given solution. A v e r i f i c a t i o n of the adherence to the s i m ple p r o p o r t i o n a l i t y (11) shows (see Fig. 3) that it is m e t for v a r i o u s organic compounds in quite a wide r a n g e of changing c o n c e n t r a t i o n s of a strong acid (to 20-25%). The values of Vs obtained f o r s e v e r a l compounds a r e p r e s e n t e d in Table 1. The v a l u e s of V s found f r o m Eq. (11) f o r a s e r i e s of compounds p r a c t i c a l l y coincide with those values obtained independently b y data on e l e c t r i c a l conductivity in b i n a r y solvents. Hence, in m o d e r a t e l y concentrated solutions of s t r o n g acids, the main contribution to the d i f f e r e n t i a l - c o n d u e t i m e t r i c effect of organic compounds is introduced due to the change in s t r u c t u r e of the solution. Here the influence of the nonelectrolyte, c h a r a c t e r ized by the volume Vs, is independent of the type of conductive p a r t i c l e . Also to be noted is the existence of a l i n e a r dependence between the v a l u e s of Vs and file c h a r a c t e r i s t i c v o l u m e s of the m o l e c u l e s of aliphatic organic compounds which a r e e s t i m a t e d as the s u m s of t h e i r bond r e f r a c t i o n s Y~RD [14] (see Fig. 4): V, -----(-- 27.9 ___7.2) -}- (11.50 4- 0.32) Y,RD

(12)

(correlation coefficient r = 0.995). The observation of this relationship completely corresponds to the proposed model of the breakdown of electrical conductivity: the larger the molecules of the nonelectrolyte, the greater is the volume in which the structure of the solution is changed. We note that the intercept on the abscissa found from Eq. (12) practically coincides with the value of the characteristic volume of the water molecule (additional point). Falling outside function (12) (on the side of smaller values) are the Vs for alicyclie and aromatic compounds (see Fig. 4). The reason for this occurrence may consist in that cyclic molecules are m o r e condensed than the linear ones, and thus their active surfaces (making an influence on the structure of the solution possible) are smaller for equal sums of the bond refractions~

LITERATURE 1o 2.

3.

4.

5.

6.

7.

8.

9.

10.

CITED

Mo M. K a r e l ' s o n and V. A. P a l ' m , nA new model of e l e c t r i c a l conductivity of solutions of strong e l e c t r o l y ~ s , " T e o r . Eksp. Khim., 14, No= 6, 781-787 (1978). J. Celeda, " C h e m i s t r y of highly c o n c e n t r a t e d aqueous solutions. XI. Model of the hydration of ions and its u s e in the t h e o r y of the conductivity of c o n c e n t r a t e d e l e c t r o l y t e s , " Sb. Vys. Sk. C h e m . - T h e c h . P r a z ~ , B l l , 5-27 (1967}. Yu. L. Khaldna and Kho I. Kuura, "Conductime~ric method of studying the protonation of e l e c t r o n e u t r a l organic b a s e s in aqueous solutions of m i n e r a l acids~ Io Verification of the method," Reakts. Sposobn. Org~ Soedin., 3, No. I , l l 0 - 1 1 7 (1966). Yu. L. Khaldna and Kh~ I. Kuura, " C o n d u e t i m e t r i c method of studying the protonation of e l e e t r o n e u t r a l organic b a s e s in aqueous solutions of m i n e r a l acids~ If. Aliphatic alcohols," R e a ~ s o Sposobn. Org. Soedin., 3-, No. I , 199-205 (1966). Yu. L. Khaldna and Kh~ I. Kuura, " C o n d u c t i m e t r i c method of studying t he protonation of e l e c t r o n e u t r a l organic b a s e s in aqueous solutions of m i n e r a l acids. V~ ~ h e r s , " Real~s. Sposobn. Org. Soedin., 3, No. 4, 101-109 (1966). Yu. R~ Siigur and Yu. L. Khaldna, " C o n d u c t i m e t r i c method of studying the protonation of e l e e t r o n e u t r a l organic b a s e s in aqueous solutions of m i n e r a l acids. VI~ E s t e r s and c a r b o x y l i c acids, n R e a k t s . Sposobn. Org. Soedin~ 5, No. 2, 547-554 (1968)~ P. Ya. T a l ' t s and Yu. L. Khaldna, ~Conduetimetric method of studying the protonation of e l e c t r o n e u t r a l organic b a s e s in aqueous solutions of m i n e r a l acids. VIII. Acetone, benzene, and 1,2-dichloroethane," R e a k t s . Sposobn. O r g . Soedin., 1_O0,No. 1 , 1 0 7 - 1 1 8 (1973). M. Mo K a r e l ' s o n , V. A. P a l ' m , and Yuo L. Khaldna, " D i f f e r e n t i a l - c o n d u c t i m e t r i c investigation of c o m p l e x f o r m a t i o n of n i t r o s u b s t i t u t e d benzene with a proton in aqueous solutions of sulfuric acid," Reakts. Sposobn. O r g . Soedin., 1_~0,No. 1, 307-322 (1973). M . M . K a r e l ' s o n , V. A. P a l ' m , R. Khiob, and Yu. L. Khaldna, "Ionization m e c h a n i s m of s t r o n g acids. T r i c h l o r o a c e t i c , 2 , 4 , 6 - t r i n i t r o b e n z o i c , and p i c r i c acids in aqueous sulfuric acid," R e a k t s . Sposobn. Org. Soedin., l_j_l, No. 1, 239-256 (1974). L a n d o l t - B o r n s t e i n , Values and Functions f r o m P h y s i c s , C h e m i s t r y , A s t r o n o m y , Geophysics, and T e c h nology [in Russian], Vol. 2, Springer, Berlin. 65

11. 12. 13. 14.

T . L . B r o a d w a t e r and R. L. Kay, nSolvent s t r u c t u r e in aqueous m i x t u r e s . II. Ionic m o b i l i t i e s in t e r t - b u t y l a l c o h o l - w a t e r m i x t u r e s at 25~ ~ J. P h y s . Chem., 74, No. 21, 3802-3812 (1970). J . E . Lind and R. M. F u o s s , nConductance of alkali halides. I. P o t a s s i u m chloride in d i o x a n e - w a t e r m i x t u r e s , n J. P h y s . Chem., 6_~5,No. 13, 999-1065 (1961). J. J u i l l a r d , J. P. Morel, L. Avedikian, and C. L h e r m e t , n S o l v e n t - s o l u t e i n t e r a c t i o n s in w a t e r - t e r t - b u t y l alcohol m e d i a , ~ J. Chim. P h y s . P h y s i c o c h i m . Biol., 6__99,No. 7, 787-793 (1972). Handbook of C h e m i s t r y [in Russian], Vol. 1, GONTI, M o s c o w - L e n i n g r a d (1962).

SECONDARY OF

HYDROGEN V.

PERIODICITY

OF

THE

STRENGTH

BONDS

K. Pogorelyi

and

A. A. Yarmolinskii

UDC 541.571.9

The phenomenon of s e c o n d a r y (supplementary) p e r i o d i c i t y is included in the nonmonotonic c h a r a c t e r of the change of p r o p e r t i e s of c h e m i c a l compounds f o r m e d by e l e m e n t s of groups of t h e periodic s y s t e m . This nonmonotonicity is c l e a r l y shown during examination, f o r example, of the heats of f o r m a t i o n of compounds of e l e m e n t s of groups V - V I I with oxygen (P2Os > As~O5 < Sb205, SO 3 > SeO 3 < TeO3) o r fluorine (PF~ > A s F 5 < SbF5, SF 6 > SeF6) [1]. According to the hypothesis developed by Shchukarev [2], s o m e d i f f e r e n c e s in the p r o p e r t i e s of the valence e l e c t r o n s of a t o m s containing d o r f e l e c t r o n s in an inner o r b i t a l lie at the b a s i s of the s e c o n d a r y p e r i o d i c i t y . F o r e l e m e n t s of the m a i n s u b g r o u p s , s or p e l e c t r o n s , a c h a r a c t e r i s t i c f e a t u r e of which is the p r e s e n c e of e x t r a e l e c t r o n - d e n s i t y m a x i m a n e a r the nucleus, thanks to the p e n t r a t i n g capability of the s and p o r b i t a l s , s e r v e as v a l e n c e e l e c t r o n s . The overlapping of t h e s e m a x i m a with the main m a x i m a of the inner e l e c t r o n s c a u s e s an increa~se in the c o r r e l a t i o n a l repulsion f o r c e s , as the r e s u l t of which the e n e r g y of the valence e l e c t r o n s inc r e a s e s . On the other hand, on the s t r e n g t h of the p e n e t r a t i n g capability of t h e o r b i t a l s , the p r o b a b i l i t y i n c r e a s e s that the s and p e l e c t r o n s , which a r e s c r e e n e d b y d or f o r b i t a l s , will s t a y n e a r the nucleus, which r e s u l t s in f u r t h e r stabilization of the valence e l e c t r o n s . T h e s e two oppositely d i r e c t e d f o r c e s d e t e r m i n e the r e s u l t i n g change in energy. In the p r e s e n c e of internal s c r e e n i n g , the e n e r g y of the outer e l e c t r o n s would i n c r e a s e s y s t e m a t i c a l l y in keeping with the p r i n c i p a l quantum n u m b e r . However, beginning with p e r i o d IV, w h e r e d and then f o r b i t a l s a p p e a r , in a s e r i e s of c a s e s an o v e r a l l reduction of the e n e r g y of the outer e l e c t r o n s is o b s e r v e d . In this c a s e , nonmonotonicity a p p e a r s in the change of such c h a r a c t e r i s t i c s of isolated a t o m s as, f o r e x a m p l e , the r a d i u s of the orbitals of the v a l e n c e e l e c t r o n s o r the ionization potential [3], as the r e s u l t of which nonmonotonicity a p p e a r s in change of the c h e m i c a l p r o p e r t i e s of compounds f o r m e d by t h e s e a t o m s . Secondary p e r i o d i c i t y is shown m o s t c l e a r l y in the p r o p e r t i e s of compounds c o r r e s p o n d i n g to the highest oxidation state of e l e m e n t s of the main subgroup, since during the f o r m a t i o n of t h e s e compounds p as well as s e l e c t r o n s a r e used, the orbitals of which a r e c h a r a c t e r i z e d by m a x i m u m p e n e t r a t i n g capability. It should be noted that, up to the p r e s e n t time, s e c o n d a r y p e r i o d i c i t y has been o b s e r v e d only in the p r o p e r t i e s of e l e m e n t s (orbital r a d i u s , ionization potential) and t h e i r compounds (heat of f o r m a t i o n , o x i d a t i o n - r e d u c t i o n potential). Secondary p e r i o d i c i t y of the p r o p e r t i e s of m o l e c u l a r c o m p l e x e s ( c h a r g e - t r a n s f e r c o m p l e x e s or hydrogen bonding) has not been noted in the l i t e r a t u r e . In this w o r k , an a n a l y s i s is c a r r i e d out on data on the s t r e n g t h of hydrogen bonds f o r m e d by s t r u c t u r a l l y s i n g l e - t y p e compounds of e l e m e n t s of groups V-VII, with the a i m of detecting a p p e a r a n c e s of s e c o n d a r y p e r i o d icity. In this c a s e , hydrogen bonds of the type A - H . . . Y R n , which f o r m fixed proton donor A--H with a s e r i e s of e l e c t r o n donors YR n (Y being e l e m e n t s of the m a i n subgroup), a r e examined, since bonds of this type have been studied m o r e fully [4-10]. In addition, it is just for such bonds that the a p p e a r a n c e of s e c o n d a r y p e r i o d i c i t y is to be expected in the f i r s t instance, since the p e n e t r a t i n g ns and np o r b i t a l s of f r e e e l e c t r o n p a i r s of the Y a t o m s take p a r t in the f o r m a t i o n of the H...Y hydrogen b r i d g e . L. V. P i s a r z h e v s k i i Institute of P h y s i c a l C h e m i s t r y , A c a d e m y of Sciences of the Ukrainian SSR, Kiev. T r a n s l a t e d f r o m T e o r e t i c h e s k a y a i l ~ k s p e r i m e n t a l ' n a y a Khimiya, Vol. 15, No. 1, pp. 85-88, J a n u a r y - F e b r u a r y , 1979. Original a r t i c l e s u b m i t t e d F e b r u a r y 16, 1978.

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