Thermodynamic Constants for Association of Isomeric Chlorobenzoic and Toluic Acids With 1,3-Diphenyl-guanidine in Benzene

Abstract

This paper reports values of ΔF₂₅, ΔH, and ΔS₂₅ for the association of diphenylguanidine with the isomeric monochlorobenzoic acids and the isomeric toluic acids in benzene from spectrophotometric measurements at 25 and 30 °C, using bromophthalein magenta E (3′, 5′, 3″, 5″-tetrabromophenolphthalein ethyl ester) as the indicator. The results are compared with available data for other donor-acceptor associations in aprotic solvents which include the monomer-dimer equilibrium of benzoic acids, the association of tertiary amines with iodine, and the association of certain oxygen bases with phenols. The comparisons indicate that the value of the ratio ΔH/298ΔS is approximately constant in the following associations in aprotic solvents: (1) Association of phenolic or carboxylic acids with nitrogenous bases to form hydrogen bonded ion-pairs; (2) hydrogen bonding of weakly acidic phenols to nitrogenous bases; (3) association of tertiary amines with iodine. A somewhat smaller value for this ratio seems to apply to most associations of phenols with oxygen bases. Possible applications of these findings include estimation of other thermodynamic constants when one of the constants ΔF, ΔH, or ΔS is known, and clarification of the relative importance of ionic and covalent contributions in hydrogen bond formation.

1. Introduction

A spectrophotometric procedure was described earlier [1],2 by means of which the relative strengths of 40 carboxylic acids of the benzoic acid series were determined when in benzene solution at 25 °C. The strengths were expressed as values of K_assoc. or log K_assoc. for the reaction

$$\mathrm{B}\left(\text{base}\right)+\mathrm{HA}\left(\text{acid}\right)\rightleftarrows {\mathrm{BH}}_{\dots }^{+}{\mathrm{A}}^{-},$$ (1)

in which the base used was 1,3-diphenylguanidine. The phenolic acid, bromophthalein magenta E (3′,5′,3″, 5″- tetrabroinophenolphthalein ethyl ester) served as the indicator dye. An essential step was determining K for the association of diphenylguanidine with bromophthalein magenta E. After completion of the experimental work at 25 °C [1], analogous measurements at 30 °C were made for part of these acids, namely, bromophthalein magenta E, benzoic acid, the isomeric chlorobenzoic acids, and the isomeric toluic acids. This paper reports thermodynamic constants derived from the combined data at 25 and 30 °C, and discusses their significance.

2. Experimental Procedure and Results

Among the possible sources of error in studies of acid-base equilibria in benzene by spectrophotometry are the volatility of the solvent and effects of adventitious moisture or oxygen. Such errors can be minimized by making absorbance measurements very soon after the preparation of solutions.3 To facilitate speed in obtaining optical data, as well as to reduce errors arising from imprecise temperature control, the temperature in our laboratory is automatically controlled to match closely the temperature within the thermostated air bath which serves as the absorption cell compartment [3]. Throughout most of the year, a laboratory temperature of 25±0.5 °C can be maintained. During summer and winter weather, respectively, the laboratory temperature can be held as high as 30 °C or as low as 20 °C.

Qualitative observations of thermal effects on the extent of association of bromophthalein magenta E with bases [4] had made it seem likely that enthalpy and entropy changes involved in the kinds of acid-base associations which have been under study could be estimated from optical measurements covering the temperature range 20 to 30 °C, and plans were made to extend the measurements already made at 25 °C [1] to these two additional temperatures. In August and September of 1955 some of the experiments (see introduction) were repeated at 30 °C, using the same materials and following the same experimental technique as at 25 °C, but the work had to be interrupted without performance of the intended measurements at 20 °C.

The combined results of the experiments at 25 and 30 °C are summarized in table 1.4 The steps followed in calculating association constants corresponding to eq (1), and then applying a correction for the amount of carboxylic acid dimer presumed to be present, were the same as previously explained [1]. As noted in table 1, parallel studies of the association of diphenylguanidine with bromophthalein magenta E and with benzoic acid at 25 and 30 °C have been made in this laboratory [5], with very similar results.

Table 1.

Equilibrium constants for association of acids with 1,3-diphenylguanidine in benzene at 25 and 30 °C

Acid	t (°C)	No. expts.	Range of na	Range of n″a	103K21b	10−5Kcor.b	St. dev.	Coeff. var. %
Bromophthalein magenta E	$\{\begin{array}{c}25\\ 30\end{array}$	10	0.25 to 3	………………………………	………………………………	2.55   2.57c	0.098	3.8
		8	.75 to 3	………………………………	………………………………	1.649   1.66c	.070	4.3
Benzoic	$\{\begin{array}{c}25\\ 30\end{array}$	25	1 to 3	0.5 to 5	1.6	2.01   2.09c	.045	2.2
		8	0.5 to 3	.5 to 3	2.0	1.28   1.31c	.081	6.3
o-Chlorobenzoic	$\{\begin{array}{l}25\\ 30\end{array}$	9	.5 to 3	.5 to 4	3.7	12.5	.047	3.8
		8	.5 to 3	.5 to 4	4.7	7.42	.235	3.2
m-Chlorobenzoic	$\{\begin{array}{l}25\\ 30\end{array}$	16	.5 to 3	.5 to 5	2.4	12.1	.023	1.9
		8	.5 to 4	.5 to 4	3.0	7.13	.116	1.6
p-Chlorobenzoic	$\{\begin{array}{l}25\\ 30\end{array}$	8	.5 to 3	.5 to 4	(1.7)	6.94	.133	1.9
		9	.5 to 3	.5 to 4	(2.0)	4.20	.108	2.6
o-Toluic	$\{\begin{array}{l}25\\ 30\end{array}$	19	.5 to 3	.5 to 8	2.4	0.930	.179	1.9
		8	1 to 3	.25 to 4	3.0	.588	.112	1.9
m-Toluic	$\{\begin{array}{l}25\\ 30\end{array}$	11	1 to 3	1 to 8	1.4	1.50	.041	2.7
		9	0.5 to 3	0.5 to 4	1.8	0.948	.219	2.3
p-Toluic	$\{\begin{array}{l}25\\ 30\end{array}$	10	1 to 3	1 to 4	0.415	1.34	.084	6.3
		6	0.5 to 3	0.5 to 3	0.53	0.859	.288	3.4

^aThe molar concentration (C_a) of bromophthalein magenta E (3′, 5′, 3″, 5″-tetrabromophenolphthalein ethyl ester) was 5.0 × 10⁻⁵ throughout. The molar concentrations of 1,3-diphenylguanidine (nC_a) and of the aromatic carboxylic acid (n″C_a) varied within the ranges indicated. Experimental procedure and apparatus were as described in [1].

^bK₂₁ is the equilibrium constant for dissociation of dimeric carboxylic acid into the monomer in benzene, while K_cor. is the equilibrium constant for the association A (acid) +B (base)⇆S(salt) in benzene after the raw data have been corrected by taking into consideration the dimer-monomer equilibrium of the carboxylic acid; for method of calculating K_cor. see [1], especially sections 3.2 and 4.1. The values of K₂₁ used in correcting the association constants were based on data in the literature except in the cases of m- and p-chlorobenzoic acids, for which K₂₁ values have not been reported. In the case of m-chlorobenzoic acid, data for m-iodobenzoic acid were applied; in that of p-chlorobenzoic acid, K₂₁ values at 25 and 30 °C were estimated by trial and error. All equilibrium constants given in this table are in molar units.

^cReference [5].

The dimer-monomer data used in making the corrections are not known with certainty to be accurate. Self-association of diphenylguanidine, formation of complex anions (RCOOHOCOR)⁻, the “secondary” reaction of diphenylguanidine with bromophthalein magenta E [6], and adsorption of solutes on glass-or silicaware are additional possible causes of errors. However, it is believed that experimental uncertainties in the optical data are the main obstacle to the attainment of high accuracy; these have more effect when the association constants are relatively great in magnitude (10⁵ to 10⁶), as in the present work.5

Values for the thermodynamic constants ΔF₂₅, ΔH, and ΔS₂₅ were calculated in the conventional way from the K_assoc. values at the two temperatures. These results are summarized in table 2.6

Table 2.

Thermodynamic constants for association of acids with 1,3-diphenylguanidine in benzene^a

Acid	ΔF25	ΔH	ΔS25	$\frac{\mathrm{\Delta }H}{298\mathrm{\Delta }{S}_{25}}$
	kcal mole−1	kcal mole−1	cal mole−1 deg−1
Bromophthalein magenta E	−7.38	15.8	−28.2	1.9
Benzoic	−7.24	−16.2	−30.1	1.8
o-Chlorobenzoic	−8.32	−18.8	−35.1	1.8
m-Chlorobenzoic	−8.30	−19.0	−36.0	1.8
p-Chlorobenzoic	−7.97	−18.0	−33.7	1.8
o-Toluic	−6.78	−16.5	−32.5	1.7
m-Toluic	−7.06	−16.5	−31.5	1.8
p-Toluic	−7.00	−16.0	−30.1	1.8

^aCalculated from association constants expressed in liter mole⁻¹ units. See discussion in section 2 of the text.

3. Discussion

Two well-known thermodynamic equations,

$$-RT\ln K=\mathrm{\Delta }F$$ (2)

and

$$\mathrm{\Delta }F=\mathrm{\Delta }H-T\mathrm{\Delta }S,$$ (3)

are frequently utilized in efforts to develop generalizations about the effects of structural modifications on reaction rates and equilibria (for example, see [7 to 13]). The great majority of the attempts to assess relative contributions of changes in enthalpy and entropy to free energy changes have been made in connection with studies of reaction kinetics. In some instances, a structural change apparently leads to an increase in the energy of activation, with little or no effect on the entropy factor.7 In other cases, an increase in the energy of activation is accompanied by a parallel effect on the entropy factor.8

A class of chemical equilibria which is of major interest is the ionization of acids of the benzoic acid series in water, since this reaction series was adopted for evaluating substituent constants in the Hammett equation [8]. Thermodynamic constants for the aqueous ionization of some benzoic acids pertinent to this paper are compiled in table 3. The ΔH values for these acids, except in the case of o-toluic acid, are much less than one kcal mole⁻¹ in magnitude. Clearly, the values of ΔF₂₅ for aqueous ionization of the acids depend almost solely on the temperature-entropy term, TΔS.

Table 3.

Thermodynamic constants for ionic dissociation of selected benzoic acids in water

Acid	ΔF25	ΔH	ΔS25	298ΔS25
	kcal   mole−1	kcal mole−1	cal mole−1 deg−1	kcal   mole−1
Benzoic	5.74	0.11a 0.104c 0.09d	−18.9a c d	−5.64
m-Chlorobenzoic	5.22	.019b	−17.4b	−5.19
m-Iodobenzoic	5.26	.190b	−17.0b	−5.07
p-Chlorobenzoic	5.43	.226b	−17.5b	−5.22
o-Toluic	5.33	−1.50d	−22.9d	−6.83
m-Toluic	5.78	0.07b d	−19.2b d	−5.72
p-Toluic	5.92	0.30b 0.24d	−19.0d	−5.67

^aT. L. Cottrell, G. W. Drake, D. L. Levi, K. J. Tully, and J. H. Wolfenden, J. Chem. Soc. (London) 1948, 1016.

^bG. Briegleb and A. Bieber, Z. Elektrochem. 55, 250 (1951).

^cA. V. Jones and H. N. Parton, Trans. Faraday Soc. 48,8 (1952).

^dT. W. Zawidski, H. M. Papée, and K. J. Laidler, Trans. Faraday Soc. 55, 1743 (1959).

The thermodynamic constants obtained in this work for association of benzoic acids with 1,3-diphenylguanidine in benzene (table 2) contrast greatly with the corresponding constants for aqueous ionization.9 Values of ΔH are in the approximate range 16 to 19 kcal mole⁻¹, are all negative in sign, and the variations in numerical magnitude parallel those in the temperature-entropy term, the ratio ΔH/298ΔS₂₅ being 1.8, or very close to this value, in all cases. For five of the reactions ΔH/ΔF₂₅ is 2.3 the extreme values being 2.1 and 2.4.

For comparison, available values of ΔH and ΔS₂₅ for the monomer-dimer equilibrium of the same or closely related benzoic acids are presented in table 4. It is of considerable interest that the ratio ΔH/298ΔS₂₅ has practically the same value for the self-association of the benzoic acids in benzene as for their association with diphenylguanidine in this solvent.10 The enthalpy-entropy relationship for the two kinds of association reactions is also brought out in figure 1, in which −ΔS₂₅ is plotted against −ΔH. In this figure the equation for the solid line was calculated by the method of least squares, using data for all seven of the carboxylic acids.11 The dashed line is an extension of the solid line. For the monomer-dimer equilibrium, ΔH/ΔF₂₅ varies from 2.1 to 2.5, with the exception of p-toluic acid where the value is 1.9.12

Table 4.

Thermodynamic constants for self-association of aromatic acids in benzene^a

Acid	ΔF25	ΔHd	ΔS25d	$\frac{\mathrm{\Delta }H}{298\mathrm{\Delta }{S}_{25}}$d
	kcal   mole−1	kcal   mole−1	cal   mole−1   deg−1
Benzoic	−3.81	−8.37	−15.3	1.8
o-Chlorobenzoicb	−3.31	−8.31	−16.8	1.7
m-Iodobenzoicb	−3.57	−7.65	−13.7	1.9
o-Toluicc	−3.58	−8.39	−16.1	1.7
m-Toluicc	−3.91	−9.26	−17.9	1.7
p-Toluicb	−4.61	−8.72	−13.8	2.1

^aCalculated from monomer-dimer equilibrium constants (K₁₂) expressed in liter mole⁻¹ units.

^bComputed from data of G. Allen and E. F. Caldin (ref. [18]), after converting monomer-dimer constants from mole fraction units to liter mole⁻¹ units.

^cFrom data of F. T. Wall and F. W. Banes, J. Am. Chem. Soc. 67, 898 (1945).

^dDividing these values of ΔH and ΔS₂₅ by two, so as to obtain the average values per hydrogen bond has no effect, of course, on the ratio ΔH/TΔS.

Figure 1. −ΔS₂₅ versus −ΔH for association of some benzoic acids with 1,3-diphenylguanidine and for self-association (dimerization) of the same or analogous acids, in benzene.

H, Benzoic acid; o-, m-, and p-Me, the toluic acids; o-, m-, and p-Cl,themono-chlorobenzoic acids; BPM-E, bromophthalein magenta E; see table 2. The unlabeled symbols refer to the following associations (see table 5): open square, triethylamine with benzoic acid in benzene; filled square, tribenzylamine with picric acid in benzene; open diamond, triethylamine plus iodine in n-heptane.

A few additional investigations of thermodynamic properties of acid-base associations in aprotic solvents have been reported. Table 5 is a compilation of most of the published data. Several tentative conclusions may be drawn:

1. In most associations in which nitrogen is the proton acceptor (electron donor), the value of ΔH/298ΔS₂₅ is not far from 1.8.13

2. Statement (1) holds irrespective of whether the acid is a Brønsted acid (phenol, carboxylic acid) or the Lewis acid iodine.

3. In most associations in which oxygen is the proton acceptor (electron donor), the value of ΔH/298ΔS₂₅ is 1.4.14 Results with dioxane and methyl or ethyl acetate as the base indicate that the values of both −ΔH and −ΔS₂₅ increase on changing from carbon tetrachloride to a saturated hydrocarbon solvent, but without affecting the ratio of the two values.

4. With benzene as base (π-electron donor), the value of ΔH/298ΔS seems to be smaller.15

Table 5.

Thermodynamic constants for miscellaneous acid-base associations in aprotic solvents^a

Solvent	Base	Acid	ΔF25	ΔH	ΔS25	$\frac{\mathrm{\Delta }H}{298\mathrm{\Delta }{S}_{25}}$
			kcal mole−1	kcal mole−1	cal mole−1  deg−1
Benzeneb	Triethylamine	Bromophthalein magenta E	−6.1	−15.3	−30.9	1.7
Benzeneb	Triethylamine	Benzoic acid	−4.9	−11.0	−20.7	1.8
Benzenec	Tribenzylamine	Picric acid	−4.4	−11.2	−23.1	1.6
Carbon tetrachlorided	Benzene	Iodine	+1.1	−1.1	−7.4	0.5
Carbon tetrachloridee	Dioxane	Phenol	………………	−4.7	−11.5	1.4
Carbon tetrachloridef	Diethyl ether	Phenol	………………	−3.7	−7.6	1.6
Carbon tetrachlorideg	Ethyl acetate	Phenol	………………	−4.8	−11.9	1.4
Carbon tetrachloridef	Hexamethylenetetramine	Phenol	………………	−6.9	−13.6	1.7
Chlorobenzeneh	n-Butylamine	2,4-Dinitrophenol	−3.1	−12.2	−30.5	1.3
Chlorobenzeneh	Di-n-butylamine	2,4-Dinitrophenol	−4.6	−11.4	−22.8	1.7
Chlorobenzeneh	Tri-n-butylamine	2,4-Dinitrophenol	−5.1	−14.4	−31.3	1.5
Cyclohexanei	Trimethylamine	Phenol	−2.6	−5.8	−10	1.9
Cyclohexanei	Trimethylamine	p-Chlorophenol	−3.1	−7.0	−13	1.8
Cyclohexanei	Trimethylamine	p-Cresol	−2.4	−3.8	−5	2.6
n-Heptanej o	Pyridine	Iodine	−3.3j	−7.8	−15.5j	1.7j
n-Heptanek o	Triethylamine	Iodine	−5.0	−12.0	−23.5	1.7
n-Heptanel	Methyl acetate	Phenol	………………	−5.3	−12.8	1.4
Isooctanem	N,N- Dimethylacetamide	Phenol	………………	−7.7	−14.8	1.8
Petroleumethere	Dioxane	Phenol	………………	−5.4	−13.1	1.4
Petroleumetherg	Ethyl acetate	Phenol	………………	−5.7	−13.7	1.4
Nitrobenzenen	Pyridine	Methanesulfonicacid	………………	−17.1	………………	………………

^aFrom thermodynamic constants or association constants (converted where necessary to liter mole⁻¹ units) given in the references cited below.

^bReference [5].

^cA. A. Maryott, J. Research NBS 41, 7 (1948); M. M. Davis and E. A. McDonald, J. Research NBS 42, 595 (1949).

^dBee reference [5], table II, footnote f.

^eS. Nagakura, J. Chem. Soc. Japan, Pure Chem. Sect. 74, 153 (1953), through reference [17], appendix B.

^fM. Tsuboi, Bull. Chem. Soc. Japan 25, 60 (1952).

^gS. Nagakura, J. Am. Chem. Soc. 76, 3070 (1954).

^hSee reference [5], table II, footnote d.

ⁱR. L. Denyer, A. Gilchrist, J. A. Pegg, J. Smith, T. E. Tomlinson, and L. E. Sutton, J. Chem. Soc. (London) 1955, 3889; see table 5.

^jC. Reid and R. S. Mulliken, J. Am. Chem. Soc. 76, 3869 (1954). ΔF and ΔS are for 17 °C instead of 25 °C.

^kS. Nagakura, J. Am. Chem. Soc. 80, 520 (1958).

^lS. Nagakura, J. Chem. Soc. Japan, Pure Chem. Sect. 75, 734 (1954), through reference [17], appendix B.

^mS. Mizushima, M. Tsuboi, T. Shimanouchi, and Y. Tsuda, Spectrochim. Acta 7, 100 (1955).

ⁿH. C. Brown and R. R. Holmes, J. Am. Chem. Soc. 77, 1727 (1955).

^oThe method used in calculating K_assoc. values has been criticized (see R. S. Drago and N. J. Rose, J. Am. Chem. Soc. 81, 6141 (1959).

A linear relationship of −ΔH and −ΔS in a related series of association reactions has been interpreted as signifying that with increasing strength of the bond between donor and acceptor there is increased restraint on motions of the component parts.16 Perhaps the different values which ΔH/298ΔS₂₅ seems to have (see table 5) for bases with nitrogen as the electron donor atom and those with oxygen as the electron donor (approximately 1.8 and 1.4, respectively) result chiefly from variations in −ΔH.

The existent thermodynamic data for donor-acceptor reactions in aprotic solvents are not extensive enough to determine the scope of the relationships indicated above, or accurate enough to detect possible small effects resulting from variations in structure as, for example, isomerism in the toluic acids or the chlorobenzoic acids. Two important areas of possible application may be suggested, however.

(1) If one of the three constants ΔF, ΔH, and ΔS is known, it should be possible to estimate values for the other two. To illustrate, from the value of ΔH which has been determined for association of pyridine with methanesulfonic acid in nitrobenzene (see table 5), estimated values for ΔS₂₅, ΔF, and K_assoc., in the units used above, are −32, −7.6, and 3.7×10⁵, respectively. The assumption must be made that nitrobenzene does not affect the association differently from other solvents listed in the table. A further example concerns association of triethylamine with phenol in n-heptane. The reported value of K_assoc. at 25 °C is 83.8 [21]. This leads to the following approximate values for ΔF, ΔH, and ΔS₂₅, respectively: −2.6, −5.9, and −11. These agree well with the constants reported for association of trimethylamine with phenol in cyclohexane (see table 5).

(2) The theory of hydrogen bond formation still needs clarification (see [17], chs. 7 and 8). Evidence for hydrogen bonding in ion-pairs of salts that are formed by union of nitrogenous bases with hydrogen acids (and therefore have one or more protons attached to the nitrogen of the cation) has been pointed out ([4,2,5] and references cited), but has not received wide consideration in discussions of hydrogen bonding. The thermodynamic data in tables 2, 4, and 5 point to a relationship of such systems with the more weakly bonded systems which so far have been the basis for speculations about the nature of hydrogen bonding and the relative importance of ionic and covalent contributions.