Ultraviolet absorption spectra of monomer and dimer of benzoic acid

JOURNALOF MOLECULAR SPECTROSCOPY 8, 257-275 (1962)

Ultraviolet Absorption Spectra of Monomer and Dimer of Benzoic Acid HARUO HOSOYA, JIRO The Institute

TANAKA, AKD SABURO NAGAKURA

for Solid State Physics,

The University

of Tokyo,

Minato-ku,

Tokyo,

Japan

Ultraviolet and infrared absorption spectra of benzoic acid and methyl benzoate were measured under various conditions. It was found experimentally that, while the C=O (6~) and O-H (3~) stretching bands of benzoic acid are changed either by chain-like hydrogen bonding or ring dimer formation, the CT band of benzoic acid (230 rnp) is not changed unless the ring dimer is formed. The CT band of benzoic acid in inert solvents shifts from 229 to 233 rnr and increases considerably its intensity by the ring dimer formation. The cause of this spectral change was explained by the exciton-type dipolar interaction, the magnitudes of the red shift and intensity increment being calculated theoretically. The pK value of the monomer-dimer equilibrium of benzoic acid was obtained by the proposed method. INTRODUCTION In the previous derivatives

paper

in sulfuric

(1) , we reported

acid solutions

and Raman

spectra.

Protonation

occurs at the carbonyl

sulfuric

Important

on behaviors

of benzoic

acid and its

which were studied by the use of ultraviolet

conclusions oxygen

obtained

there

were as follows:

atom of benzoic

(i)

acid in concentrated

acid giving the ion (2) OH

OH In this case, the intramolecular band of benzoic

charge-transfer

acid which appears

rnp. (ii) Mesitoic acid in concentrated verted into the ion

sulfuric

/ Me-

(abbreviated

at 228 rnp in aqueous

/

Me

‘\__c(j+

0 -‘Me 257

hereafter

solution

acid, on the other

to CT)

shifts to 262 hand,

is con-

“58

HOSOYA,

TANAKA

AND

NA(+ABURA

in two steps via the ion

I’urt,her, in the course of the st’udy, it was found that in n-hrptane or chloroform solut,ion t’he CT band of benzoic arid shifts toward longer wavelengths compared wit.h that in aqueous solution’. The direction of t,he shift is quit’e opposite to t,hat, expect’ed from the polarit’y of solvents. Since this phenomenon is eonceivably in an intimate relation with the monomer-dimer equilibrium of benzoit acid, it, is undertaken t’o study the equilibrium with some det,ails by ultraviolet and infrared absorpt’ion measurements and t,o clarify the effect, of the dimer formation upon the CT band of benzoic arid. The monomer-dimer equilibrium of benzoic acid has already been studied by many authors from both spectroscopical (,5-Q) and thermochemical (10, 11) points of view. In part,icular, Forbes ef al. (4)) and also Ito et al. (5, 6) studied this problem from the change of the &raviolet absorption spectra. HoweTTer. the present work is essentially different from the previous works in the following two point’s : ( 1 ) It’ is experimentSally confirmed t,hat’ t.he CT band of bcnzoic arid remains unaltered by chain-like hydrogen bonding such as .H-

0..

0

,,m--

‘\ -_c4 \

’

and

‘OH..

but shifts toward dimrr formation

longer

wavelengths

alld increases

.A-

its intensity

by the ring

O...HO u\

\

j--c

4’

\

\

//

OH..

.O

c;_-.” “; ‘,-/

(2) The bathochromism and hyperchromism caused by t,he dimer formation are explained by the dipolar int#eraction in the excited sbate as t,he simplest case of the Davydov splitting in cryst,al spectra (12-18). l’urther a new analytical method convenient’ for evaluating the equilibrium constant for monomer-dimer equilibrium is proposed. This method is shown to bc> useful for evaluating the accurate value of t#he equilibrium constant. 1This phenomenon tailed

discussion

was previously on the mechanism.

reported

by

ITngnade

and

Lamb

(3) without

de-

MONOMER

AND

DIMER

EXPERIMENTAL

OF BENZOIC

ACID

2.59

DETAILS

MATERIALS Benzoic acid (99.98 %) especially purified for analytical purpose by the Osaka Industrial Research Institute was used without further purification. Commercial methyl benzoate of G.R. grade was purified by distillation. n-Heptane from Enjay Product Co. was purified by the same method as described in the previous paper (19). Dioxane and tetrahydrofuran were dried with sodium metal and distilled over it. Ethanol was dried with Molecular Sieve and was carefully distilled over magnesium ribbon catalyzed with iodine. Commercial methanol and see-butanol were purified by distillation. Phenol of E.P. grade was used without further purification. Carbon tetrachloride was dried with calcium chloride and was distilled over phosphorus pentoxide. Glacial acetic acid of G.R. grade was refluxed over phosphorus pentoxide and was distilled over it. MEASUREMENTS A Cary recording spectrophotometer model 14 M was used for the measurement of ultraviolet absorption spectra of various solutions. Quartz cells with ground glass stoppers of O.l-mm, l-mm, l-cm, and IO-cm pathlengths were used2. For the measurement of equilibrium constants the sample cells were placed in a brass holder regulated at a constant temperature of 3O.O”C. The monomerdimer equilibrium of benzoic acid in n-heptane was studied by measuring absorption spectra of the benzoic acid solutions with seven different concentrations ranging from 1.04 X lo-’ to 1.04 X lob5 M. An equilibrium between benzoic acid and dioxane in n-heptane was studied with the solutions of a fixed concent)ration (4.895 X low3 M) of the proton donor and various concentrations ( 1.40 X 1O-2-O.6.56 X lo-* n/r) of the proton acceptor. The method for evaluating the values of K, cD , and eMwill be described in a later part of this paper. For measurements of ultraviolet absorption spectra at low temperature, a stainless steel Dewar vessel containing liquid nitrogen was used at the bottom of which a quartz cell of l-cm lightpath was mounted through a thin Teflon ring. As for chloroform, tetrahydrofuran, dioxane, and pure acetic acid solut’ions of benzoic acid and methyl benzoate, absorption measurements were carried out by using cells of O.l-mm lightpath, since t,he solvents exhibit considerably strong absorption in the wavelength region below 240 rnp. A Hitachi EPI-2 infrared spectrophotometer attached with a lithium fluoride or rocksalt prism was used for measurements of infrared absorption spectra. Fused quartz cells of l-cm pathlength and 5-cm cells with sapphire windows were used for the measurements in the 3-~ wavelength region, and a cell of 0.1032The authors wish to thank Dr. A. Kuboyama for using the quartz cells of 0.1.mm lightpath.

for his kindness in giving them a chance

260

HOSOYA,

lightpath with XaCl region longer than 3 I*.

TAXAKA

ASI)

SAGAKURA

windows for the measurements

mm

in the wavelength

RESULTS

The ultraviolet absorpt’ion spectra of benzoic acid and methyl benzoat,e measured with the n-heptane solut8ions are shown in Fig. 1. As is clearly seen in this figure, each of these spectra consists of three bands which appear near 280, 230, and 200 mp. In the present paper, a special attention is paid to t,he 230-mp band which was int,erpreted by us as the int,ramolecular charge-transfer band

FIG.

1. Cltraviolet

1, Benzoic

acid.

II

I

I

I

I

I

I I 200

I

I

I

absorptionspectra

2, Methyl

benzoat,e.

[

I

11

I

(

I I 250

I

of benzoic

acid and ruethy

I’ll1

11

I

300

1

I

I

my benzonte

in rr-heptnrle.

MONOMER

AND

THE OBSERVEDCT BANDS AND C=O

DIMER

OF BENZOIC

TABLE

Ia

ACID

BANDS OF BENZOICACID AND METHYL BENZOATE

i

Benzoic acid

Methyl benzoate

Solvent

I

Y;f’

v(C=O)

m

n-Heptane n-Heptane (dilute solution) ccl, CHC13 Dioxane Tetrahydrofuran MeOH EtOH set-BuOH PhOHe

233 229

1700 (vs)

1701 (s) 1700 (s) 1701 (s) 1701

(cm-l)

“(C=O)

1740 (VW)

-

1700 (vs) 232 228 228 226 228 228

261

228 228

-

1743 (w)

-

-

1725 1723 1720 (s) 1721 (s) 1720 (m)

228 228 228 228 228 -

1709 (s) 1711 (s) 1712 (s) 1711 (s)

I

(cm-‘)

1732

1731 1730 1730 1727 (s) 1730 (s) 1731 (m) 1734 (s)

a n-Heptane containing 1 vol. y0 of phenol. TABLE

Ib

THE ASSIGNMENTOF THE CT BANDS ANT) C=O BANDS OF BENZOICACID BENZOATE

IN VARIOUS

AND METHYL

SOLVENTS

Benzoic acid

Methyl benzoate

i

I Hydrogen-bonded monomer

Free monomer

___. 0

0

state OH I

O...HO

0.,.x

.$-c”

‘\

OH...X III

\

+cT

OH...X VII

\

OH...0 II

x (CT) (md Y (C=O)

.$-c”

d

I

0.

0

\ C-ti

\

OMe

IV

\

...-c

OMt! V

(-__

229

226-228

226-228

232-233

228

228

1740-1743

1720-1725

1700-1701

1700

1727.-1734

1709-1712

(cm-l)

from the observed

direction

of the transition

moment

(20).

intensity of this band and of the carbonyl stretching (C=O)

The location and band at about 6 p

were measured with benzoic acid and methyl benzoate under various conditions. The results on the locations of these bands are listed in Table Ia. Besides them, the intensities of t,he OH stretching band of benzoic acid measured under various conditions are shown in Table II.

HOWYA,

2(2

TASAKA

A&l)

TABLE APPARENT

~~.~SIMAL

ABSORPTION

Concentration 1.805 I ,805 1.805 1.805 1.805 1 ,805

ITLTRAVIOLET Siwe

benzoic

of benzoic X x X X X X

TETRACHLORIUE Concentration

acid

IO-2M 10-3 lo-’ 1O-3 1O-3 10-a

ABS~RPTIOX

II

COEFFICIENTS

CARBON

4.54 2.27 2.27

XAGAKURA

OF THE OH

BAXD

OY BENZOI(' .%(.IDIN

AT 3545 cnlr* of diosane 0 0 0 X lo-2111 X 10-l X 10-l

Apparent

e,,,:,* 15 43 103 10 :jo 0

SpEcm.4

there exists a monomer-dimer equilibriunl acid in inert’ solvent’s such as n-heptane, 0

rcprrsenkd

by Eq.

( 1) for

O...HO

(II) h expected that t,he CT band of benzok acid changes with the co~l~nt&ion of the solution, as was observed by It’o rt a/. (5, 6) with the 280~mc( band of benzoic acid. As is seen in Fig. 2, the CT band of benzoic acid which appears at 233 mp in the n-heptane solution of the concentration higher t’han 1O-3 Al continuously shifts t>oward shorter wavelengths with the decrease of bcnzoic acid conrent,ration and finally reaches 229 rnp for the solution of the concentration below lo-’ A/. At the same t,ime the intensit#y of t!his band increases wit,h the increment of the caoncentration of benzoic acid. The same blue-shift phenomenon was also observed eit’her by elevating temperature of t,he solution it,he conc*entrat,ion of henzoic acid, lo-’ A/) from the freezing point of the solvent ( -9O”Cj up t,o room temperature, or by the gradual addition of prot’on acceptors such as diosane, diethyl ether, and tetrahydrofuran. l;urt~hrrmore, t,he CT band of benzoic Cd wa,s found to appear at 228-226 ml in pure ethanol and methanol which (~1 act, as proton donors as well as proton acceptors. On the ot,her hand, the (1T hand of methyl benzoate incapable of forming a hydrogen bridged dimrr rcmains unaltered both in its wavelengt#h and intcnsit,y by changing t,he solvent ( SW Icig. 3 and Table I). In view of t,he above-mentioned fact)s, the 2-X3-rnp band of benzoic acid can safely be assigned to the CT band of t,he acid dimrr 11, while t,he 229-226 rnp baud of benzoic: acid and methyl benzoat,e is due to thr frccl molecules and various t#ypes of hydrogrn bridged acid monomers. it may

MONOMER

AND

DIMER

OF BENZOIC

ou . cm-l

ACID

263

1

40,000

FIG. 2. Concentration effect of the CT band of benzoic acid in n-heptane (30°C). Concentration of benzoic acid are (1) 1.04 X 10~%; (2) 1.04 X lo-3M; (3) 1.04 X lo-“M; (4) 1.04 X 10-5M. The circles are E’S at 232.5 mp, which are plotted against log C to give Fig. G. INFRARED

ABSORPTION

SPECTRA

OF C=O

AND

O-H

STRETCHING

BA?;DS

The OH stretching band is observed at 354.5 cm-l for benzoic acid in carbon tetrachloride, apparent, maximal molar extinction coefficients increasing with the decrease of concentration as shown in Table II. This change suggests that the observed OH band is due to the free monomer the fraction of which increases with the decreasing concentration of benzoic acid. Table II also shows that, the OH stretching band at X545 cm-’ of benzoic acid utterly disappears in t,he carbon tetrachloride solution containing 4 % (vol.) dioxane. With the decrease of dioxane concentration, the OH band of the free monomer appears gradually. Therefore, in dioxane and ot’her proton accepting solvents, hydrogen bonding is formed between the acidic proton of benzoic acid and the oxygen atom of prot,on acceptor with a structure like III”: 3The similar type of hydrogen bonding was found to exist, in the ternary solution con-

HOSOYA,

TAXAKA

AND

NAGAKCRA

mP

220

1

1

250

I

cm-l Fro. 3. Ultraviolet absorption spectra (CT bands) of methyl benzoate under conditions. (1) in n-heptane 10-2-10-5Lll; (2) in ethanol 1W3M; 13) in tetrahydrofuran

various lo-“M.

R I

O-H...0

\ ‘R’

(III)

The

C=O band of methyl bpnzoate appears at, an almost constant, ~a\‘(: 1730 cm-‘, in the solutions of n-heptane, carbon t8etrachloridc, and t~et,rahydrofuran, while in pure alcohols (met,hanol, ct8hanol, set-butanol, etc.) and in wheptane containing a small amount of phenol (1 vol. Yl) or ethanol ( 10 vol. T), a new additional peak appears at lower wave numbers, 1712-1709 numhcr,

taining small amounts of to the result of ultraviolet constant for the benzoic than the corresponding acid is :i stronger proton

phenol and proton acceptors like dioxane in n-heptane. ilrcording absorption measurements, it was concluded that the equilibrium acid-dioxane system is 102-103. This value is lo-100 times larger value for the phenol-dioxane system. This means that benzoic donor t.h:tn phenol.

MONOMER

AND

DIMER

OF BENZOIC

TABLE MAXIMALABSORPTION

III

COEFFICIENTS AND RELATIVE INTENSITIES OF HYDROGEN AND FREE C=O BANDS rmar

state

O...H-OR //

0 /

4-C

MeOH EtOH see-BuOH PhOH”

333 318 358 -

B Extrapolated

431 434 324

4-C

%/?v

\ OCHI IV (1730 cm')

OCHa

V (1711 cm-')

Solvent

O...H-OR /T

4-C \

265

ACID

BONDED

kw.x

0 /?

4-C \ \ OH...OR'R" OH...OR'R" VII III' (1723 cm-l) (1700 cm-11

0.773 0.733 1.105 Too large

392 399 470

278 257 171

%I/CIII~

1.41 1.55 2.75 Too large

to pure solution.

cm-l (see Table Ia). From the concentration dependency of the intensity of the 1711~cm-’ band, it is sure that the following equilibrium is present: 0 / 0

\_CY

+

H-OR’

\

$

0 ’

-

O-R

(IV) (1730 cm-l)

//

O...H-OR’

“-C

\

O-R

(2)

(V) (1711 cm-l)

As shown in Table III, relative intensities of two bands eV/~rVfor the methanol and ethanol solutions are almost equal to each other and are smaller than the value for the set-butanol solution. The value for the phenol solution will be very large, as is expected from the value observed with the ternary solution containing a small amount of phenol as a proton donor in n-heptane. The order of this quantity seems to be in an intimate relation with the relative proton donating power of these solvents. Besides structure V, structure VI may be considered as a possible st’ructure of hydrogen bridged methyl benzoate in alcohols: 0

k-OR’ (VI)

However, structure VI may be excluded on the basis of the fact that the carbony1 oxygen atom is stronger in proton accepting power than the hydroxyl oxygen atom is, as is seen from the previously obtained result by the present authors on the protonation of benzoic acid in strong acidic media (1, 2).

HOSOYA,

‘36 The kd.

&u&ion

is more

The skong

bcnzoic

TAKAKA

csomplicated

1700-cm-’

AN11 NAC:AKCRB

for t,he C=O

st,retching

and very weak 1710~cm-’

acid in n-heptane

or carbon

tetrachloride

garded as due to dimer II and monomer

C=O

band of henzoic

bands observed

solution

may

safely

for

be rc-

I, respectively.

In view of t,he fact t#hat the free OH band at 3545 cm-l of henzoic acid utterly disappears

in diosane,

hydrofuran

solut’ions can he ascribed

also observed

the

C=O

in tbe alcohol

band appearing

band

solutions

at 1700 cm-‘.

near

1720 cm-’

t,o t,he species III. of henzok

in dioxane

The

arid distinrt

This fact strongly

supports

and tjetra-

liWcm-' hand was from a stronger

that, t’here exists

the

hydrogen hridged benzok acid (III’) with a skucture completely similar to III in the alcohol solutions. In t,his case benzoics arid acts as a proton donor and nkohol

as proton

acceptor.

hand in the alcohol bridged

specimen

structure,

On t,he other hand, the appearance

solut8ions suggesk wit*h a structure

we can take structure

with two alcohol

molecules,

which as proton

the cxisttncc similar

VII

of t,he 1700-cnlP’

of unot)her type of hydrogen

to the dimrr.

where the benzoic

As the most acid molecule

one of which acts as proton

possible combines

dollor and t,he other of

acceptor: 0

0

-CT

+

\

H--OR

2

f ’

..-C4

R

:tllIlOSt

13 ( romplet~ > ’

OH-. .O ’

OH

I1 (III’) 0

-c:

-H-OR

0..

9

/

\ OH...0

R

.:’ +

H-OR

;-’

It

~~~~

i-1)

‘OH.-.0

-1 ‘H

~\ H (VII’)

l
(1)

is essentially

donating

observed supports

charact’er

wit’h t,he proton skongly

the same as cquilibrim~l

of alcohol. donating

and set-butanol Table

powers

this interpretat,ion.

the two bands due to the specimens

The parallelism

(2) w&h regard to the between

of t)he three

these

alcohols

That, is to say, the relative VII and III’,

phenol

intensities

~~~~~~~~~~~ for met,hanol,

are quit,e similar to t’hose for the values

two VBSPS

and

of

ethanol,

t\,/eTV , as is evident

in

III.

The assignment acid and methyl the experimental for the purpose

of the C=O benzoate results

stretching

is summarized

band to t#he various in Tahle

on t#he CT bands of benzoic

of comparison.

From

t,his table

st,at,es of beuzoia

Ib. This t,able also contains acid and methyl

henzoat,r

it is clear that, t,he appreciable

MONOMER

AND

DIMER

OF BENZOIC

267

ACID

red shift of the CT band occurs only in the case of the ring formation like O...H-0 R-C

/

\

‘\

//

O-H..

and that the other hydrogen-bridged

R-C

2 \

R-C 0-H..

.X

.O

C-R

st’ates like // \

o...x

0-H..

o...x

.X

’

and

R-C

4

\

O--Me

give no predominant effect on the band position. In the following part of the paper, a theoretical approach will be done to the bathochromism phenomenon as well as to the hyperchromism caused by the ring dimer formation. CALCULATIONS

OF THE

BAND SHIFT AND INTENSITY BY THE DIMER FORMATION

INCREMENT

CAUSED

Several authors have recently studied the spectral changes in band positions and intensities caused by the formation of dimer or polymer; Levinson et al. (13) on pyridocyanine dyes, Bayoumi and Kasha (1.4) on N-heterocyclic compounds, Witkowski and Moffitt (Iti) on vibronic problems, and Tinoco (16, 17) and Rhodes (18) on polynucleotides. The cause of these changes comes from the exciton-type dipole-dipole interaction between the component molecules regularly oriented with each other. The change of the CT band of benzoic acid observed in the case of ring dimer formation may be understood from the same point, of view,4 and may be regarded as the simplest rase of the Davydov split,t’ings in crystal spectra. In a dimer system, even if electronic overlapping and exchange between the two component molecules (A, B) are negligibly small, an elect’ronic excitation in one molecule (4 ) can not be independent of that of the part’ner molecule (B) . This is because the two component molecules correlate with each other mainly through electrostatic interact#ions between electric dipoles. These int’eractions which cause the band shift and splitting, and also the increment or decrement of the absorption intensity, are sensitive to directions and magnitudes of t,he permanent dipole moments and of the transition moments. In the previous studies (16-18) lack of det)ailed knowledge about the electronic structure and the spatial configuration has made discussion somewhat ambiguous. Fortunately, however, in the case of benzoic acid the elertronic structure has been studied extensively (90) and the spatial arrangement of the dimer has been very likely postulat,ed from the x-ray analysis data of the crystal (21). Thus we 4 In the course of the preparation of this paper, the authors have known that ElBayoumi and Kasha interpret,ed the spectral change observed with the naphthoic acid dimer from the same point of view- (unpuhlished result).

38

HOSOYA,

succeeded

in treating

chromism

of henzoic

TAXAKA

r&her

AXI> S.4C:AKLlRA

quantitatively

the

acid on dimer formation

hyperchromivm

hy applying

and

hat,ho-

t,he first-order

per-

turbation theory. AIwording to the notatjions adopted by Tinoco ( 16, 17) , the wave fmwt~ions of the ground and excited states of bcnzoic acid dimw can be espresscd as follows 1)~ the first-order

Transition O-‘,I o-

perturbation

theory:

[Wavelength maximum xi,,,

Oscillator strength iII,/

J? I.!

0”

2815 .4

1

0-‘2(C’T) O-3 O-41

~)

o-+I(,) Ok+0

1950 1700 1700 Gfwlnd st at>r dillole moment

ii (Jhserved

values. lJ Estimated values. r Distance between t,he centers of t,he transition nlomenk p.ton and haoa_ ri Angle det.ermined by the transition rnoment pboa and the line (z-axis) connecting centers of the two transition moments ~LAO~ and ~CLIU~.

the

MOKOMER

G~~,,~~, =

AND

ei.ej

DIMER

_

OF BENZOIC

269

1

3(ei-rij)l(ej.rzj)+ rij

rij

= l/r$(sin

ACID

ix.sin jz -

2 cos iz.cos jz) :

z-axis being chosen as the line connecting the cent’ers of the transition moments pioa and VjOal , angle ix being determined by the z-axis and the PiOa

7

ei : unit vector in the direction of the FiOa, rij : distance between the centers of the pioo and vjoar . Oscillator strength for the transition 0 -+ a is obtained by using these wave functions #t and +i, and evaluating the integral values. The ratio of t’he perturbed oscillator strength to the unperturbed one is thus obtained to be

$ J$Gioa;joo(

-

%

+

$L $8

paa eioa

(Giaa;joopa,

POO -

(6) .

eiaa

-

poo eioa.

eioo)

Gioo;joc $o)eioa.eioa

of which the last two terms are of minor importance, and where K = 3e2/8?r:m2 = 1.08 x 1O-6 A, L = he/e’ = 0.853 X 103, N = 2(i = A, B), X and ~1in A unit, and G in AP3 unit. For the actual evaluation the lowest four excited states and the ground state were taken into account. The numerical values used in the calculation are summarized in Table IV, and the geometry of the dimer was taken from the x-ray crystal analysis data determined by Sim et al. (WI) (Fig. 4). The direction of the dipole moment of benzoic acid in the ground state was assumed by Smyth (22) t’o be inclined away from the C-C axis by 74” toward the carbonyl group. The locations of transition moments necessary for evaluating the magnitudes of the band shift and intensity increment were calculated from the wave functions obtained previously (20)‘. Their magnitudes, however, were taken from 5The directions of the transition moments of benzoic acid were measured with a single crystal by one of the present authors (20) for the CT and the ‘280 rnr (lowest) bands, in accordance with the predicted values.

270

HOSOYA,

FIG.

4. Geometry

and

TAXAKA

ANI)

coordinate

SAGAKURA

system

of the henzoic

acid

dimer.

the ohscrved oscillat,or skengths for the CT, I%-nm, and 280-ml bands. The evaluated FOzT/fOCTvalue was 1.375 ( = 1 + 0.306 - 0.008 - 0.001) . ,Agrerment between the calculated and observed (1.42 = 0.27/0.19) values is fairly good. The largest contribution to this value arises from t.he interaction bctwcn the t’ransition moment’ of the CT transition in *4 and that of the nearest, shorter wavelength transition (19T, rnF) in B which are linearly parallel t,o each other. This means that, owing to t#he special arrangement of t’he transition moments in t’he diner, t,he CT band is intensified by borrowing t,hc intensit,y from the nearest short,er wavelength st#rong band in the neighboring molecule. Sest, let us calculat,e t)he band shift on the dimer formation. Since it, is easilv shown that cont,ributions of the perturhat,ion terms in the wave functions &,’ and $k are negligibly small, the following simplified wave functions may tw adopted $0 = F.UPFec 3&

= I:fi(IF_4CT(FBc

+ (FA,!(FBCT)

&iT

=

-

lid~(~.m(FBO

(7)

pFAO$%CT) .

whrre the + and - signs mean the symmetrical and antisymmetrical comI)inatiorw of tbe CT states of the two component molecules. The change in t,hc t,ransition energy (AI&) on dimer formation can be represent,ed as follows: Ai&

=

[

c&T

)*I’,,

=

/

p;CT

PACT

&

~‘A,

dl’

-

j+O*

(P*B” (mu” f/l’

v-4,

-

s

#O dl’

a:”

(FAO ~‘A,

Pf”

CFrcOdl) (8)

MOPiOMER

AXD

DIMER

OF BENZOIC

ACID

271

By using the above equation, the values of AIS& and AE& were obtained to be +202 and -281 cm-‘, respectively. The transition to the upper state & is prohibited as is clearly seen from the consideration of the symmetry of the wave function, whereas t.he t,ransition to t,he GCT is allowed. From this fact it may be expected that the CT band shifts toward longer wavelengths by the ring dimer formation. This expectation is qualitatively in agreement with the observed red shift phenomenon. However, the calculated value is only 37 Y%of the observed shift ( -750 cm-‘). This fact seems to suggest that some other factors other than the dipole-dipole interaction may contribute t.o t,he observed red shift phenomenon. The contribut’ion of additional electronir configurat’ions such as

(j___H...o-C

//

‘\

‘\

/

0 . ..H--0

pertinent to t.he hydrogen-bridged possible factors. DETAILED

ANALYSIS

i,--H...OC-

and -C

/

‘\

‘\

/

O--H.,.

0

ring dimer may be considered as one of the

OF THE MONOMER-DIMER

EQUILIBRIUM

For the sake of convenience, the term “dimer fraction” ratio of the number of “molecules” in the dimeric form to the “molecules” present. The equilibrium constant K for equilibrium of benzoic acid in inert solvents like n-heptane

K = P(l

C-

X cx/2 - X)2 = 2C(l -

X)2’

X is defined as the the total number of the monomer-dimer is then expressed by

(9)

where C is the total concentration of the benaoic acid molecules. Let the observed apparent molar extinction coefficient and the molar extinction coefficient of the monomer be E and eM, at a fixed wavelength, respectively. A dimer is regarded here as composed of the two molecules, each with molar extinction coefficient of cD. Then E, cM, and Q, are related to each other by the following equation : E = t.+f(1 -

X) + t,,X.

(IO)

Inserting Eq. (10) into Eq. (9)) one can finally obtain

6M)(b -

K = (e -

2C(ED c’

=

cc-

,I2

G) ’

taf)(QJ- EM)

2K(Eo -

6)”

.

(11) (12)

It is difficult to obtain the accurate value K, since one can not det,ermine exactly the values of tD and eM from the absorption measurements. De Maine et al.

HOSOYA, T,4?iAKA AKD NAGAKURA

272

TABLE MONOMER-DIMER

log C (C in M) -1.983

1.56

-2.381 -2.682 -2.983 -3.682 -3.983 -4.983

1.55 1.51 1.-K 1.30 1.21

proposed

,og (S--B~)(eu-eM) 2(eo-42

c at 232.5111~

x

10”

an accurate

0.920 0.907 0.854 0.787 0.574 0.455 0.136

1.859

0.X

but

are the

somewhat

observed

SOLUTIUN

Dimer fraction X=(v-,,)/(,,-,,j

1.719 1.300 0.939 0.307 0.011 -1.042

FIG. 5. Plots of C against E. The circles region is physically meaningless. (~3)

V

EQITLIBRIUM OF BENZOIC ACID IN CHEPTANE

values

troublesome

in Fig. 2. The shnded

met,hod

of obtaining

equilibrium of nitromethane. K, cD , and eM for the monomer-dimer assumed that benzoic acid is almost completely dimeric in n-hexane

Ito

(6)

solution

with the concentration of 6.7.5 X lo-” ~11. Ikwussion on this assumpt,ion will be made later. In the present paper, we measured the E’S of t,he solut’ions with a wide range of concentrations,

10-‘-10-5A/,

by the

USP

of O.l-mm,

l-mm,

I-cm,

and lo-cm cells (see Pig. 2 and Table V) and succeeded in evaluating t.hr K value by applying t,he analysis method similar to t.hat described in the preriow paper (1). Since K, Ed , and e.$, are related to Eq. (11) as shown in Fig. 5, in which the shaded region has no physical meaning, t)he point’s in it are the observed \-nlues

MONOMER

FIG. 6. Plots of observed acid in n-heptane solutions among C, X, and PK.

AND

DIMER

OF BENZOIC

273

ACID

E at 232.5 rnM (3O.O”C) versus the concentration of benzoic (C in M), showing the diagram representing the relations

with beneoic acid concentrations of lo-’ to lop5 M which cluster about the point A. On the other hand, the almost equidistant points shown in Fig. 6 are just those in Fig. 5 transformed into the coordinate system log C-e, of which the physically meaningless parts of the curve C-c in Fig. 5 are excluded automatically. The two dotted lines are the asymptotes for the curve log C-e and represent the values of cD and cM . According to Eq. (11) or (12)) the logarithm of the C value at E = (ED + cM)/2, is equal to the pK ( = -log K). n’amely, log c,

= PK.

(13)

A simple calculation showed that at this concentration 0.5. Further, the pK value is also expressed as6

the dimer fraction is

pK = log Ci + 0.220, 6 Successive differentiation

of t,he logarithm

(14)

of Eq. (12) with respect to E gives the result

of 2

~ 8

303

By equating this equation solved to be

log de”

c=

9 + 2(e, -

2eM)’ + (2CM2 -

(En -

e)(E -

to be zero, E at the point

e =

(3 -

4)EM

+

Ed4)2

of inflexion

(,1/z -

En*)

. of the curve

log C--E is

l)erJ

= 0.586~~ + 0.414~~ By inserting this Evalue into Eq. (12) and taking the logarithms obtain Eq. (14).

of the both sides, one can

HOSO‘TTA, TANAKA

“74

FIG. 7. Plots of log equilibrium of benzoic

AND

NAGAKURA

log c {(B - E,W)(ED - c~)/Z(cg - e)‘} against log C: for the monomer-tlimer acid,

e at 232.5 mu (30°C) in wheptane

where C; is the value for C’ at t’he point of inflexion of t,hese simple relations value. l:or obtaining we adopted

is sufficient~ enough

more accurate

t’he least squares

as adopt,ed in t,he previous The virtual

evaluation

scluarcs calculation

knowledge method.

paper,

much

of the curve log C’--6. Either

for a rough estimation

concerning

Since

solution.

t)he K, erJ , and c.+, \-altws,

the procedures

is not mentioned

are quite

cD , and c.,, was Carried out by applying to the following equation.

By the use of the observed

t.\f) ieD -

seven couples

t,) :A( eD -

t)‘l

the same

here repeatedly

of K,

log C’ = log 1ic -

of the pli

+ PK.

of data representing

( 1).

the kast

j 1.i)

the relation

he-

tween C’ and E Cat, 232.5 rnp, SOT), calculations were successi\-ely executed three times until t’hc K, cD , and c,~ converged t,o definite values. Thew \*;dr~es arci :

t,v = 16.2 X 103, K = 7.95

x

10”

c,,, = 8.68 or

pk’ =

X lo:‘,

-:<.
and

at 30°C’.

i This value is a littale different from that previously obtained by Tto (6). -J.% room temperature) by the change of the 280 mw hand in ,a-hesane solution. Other clata infrared ahsorption measurements in rarbon tetrachloride solutions are -4.15 125°C’) Harris and Hobbs (7), -3.65 (Zl”C) by Wenograd and Spurr (8). and - 3.92 i21iY’) Lindberg (9).

(at b! by 1)~

MONOMER

AND

DIMER

OF BEXZOIC

ACID

27.5

Using these CDand tM values, log c’ was plotted against

and all the points were found, as expected from Eq. (1.5)) to lie just on the line with a unit slope (see Fig. 7). This fact shows that there exists the monomerdimer equilibrium of benzoic acid in n-heptane and the quantities related to it can be evaluated accurately by the present authors’ method. Finally, we add a note on the relation between E and X. The relation X = (c - Q)/(ED - tM) tells us that z linearly changes with X, and X becomes equal to 0 and 1 at the points of t = eM and c = Ed, respectively. Therefore, the curve plotting e against log C turns out to represent at the same time the ordinate as shown in Fig. 6. According to this result, the dimer fraction is found t’o be about ten per cent in the solution with the benzoic acid concentration of 6.75 x IO-” M (6). RECEIVED:

June 15, 1961 REFEREXCES

1. H. H~SOYA AND S. ~YAGAKURA, Spectrochint. Acta 17, 324 (1961). 2. R. STEWART AND Ii. YATES, J. Am. C’hena. Sot. 82, 4059 (19600). 3. H. E. UNGNADE AND R. W. LAMB, J. iZnl. Chem. Sot. 74, 3789 (1952). 4. W. E. FORBES, A. R. KNIGHT, AND D. L. COBFEN, Can. J. Chenz. 38, 728 (1960). 6. M. ITO, H. TSUKIOKA, AND S. IMANISHI, J. Am. C’hena.Sot. 82, 1559 (1960). 6. M. ITO, J. Mol. Spectroscopy 4, 144 (1960). 7. J. T. HARRIS, JR., AND M. E. HOBBS, J. Am. Chem. Sot. 76, 1419 (1954). 8. S. WENOGRADAND R. A. RPURR,J. Am. Chew Sot. 79, 5844 (1957). 3. J. T. LINDBERG, Sot. Scientiarium Fennica 20, 5 (1957). 10. E. N. LASSETTRE,Chew Revs. 20, 259 (1937). 11. G. AI,LEN AND E. F. CALDIN, Trans. Faraday Sot. 49, 895 (1953). 12. A. S. DAVYDOV, J. Erptl. Theoret. Phys. (1J.S.S.R.) 18, 210 (1948). 18. G. S. LEVINSON, W. T. SIMPSON, AND W. CURTIS, J. Am. Chena. Sot. 79, 4314 (1957). 14. M. A. EL BAYOVMI AND M. KASHA, presented at the Symposium on Molecular Structure and Spectroscopy, Columbus, Ohio, 1959. 16. A. WITKOWSKI AND W. MOFFITT, J. Chem. Phys. 33, 872 (1960). 16. I. TINOCO, JR., J. dna. Chem. Sot. 82, 4785 (1960). 17. I. TINOVO, JR., J. Chew. Phys. 33, 1332 (1960); 34, 1067 (1961). 18. W. RHODES, Florida State University (unpublished). 19. H. YADA, J. TANAKA, AND R. YAGAK~RA, BlcZl. Chew Sot. Japan 33, 1660 (1960). 20. J. TANAKA, J. Chem. Sot. Japan 79, 1114, 1379 (1958) (in Japanese). 21. G. A. RIM, J. M. ROBERTSON,AND T. H. GOODWIN, Acla Cry&. 8, 157 (1955). 22. C. P. SMYTH, in “Dielect,ric Behavior and Structure,” p. 308. McGrawHill, Sew York, 1955. 23. P. A. D. DE MAINE, M. M. DE MAINE, A. A. BRIGGS, AND G. E. MCALONIE, J. Mol. Spectroscopy 4, 398 (1960).