Spectrochimica Acta, Vol. 38A, No. 3, pp. 383-387, 1982 0584-85391821030383-4)5503.00[0 Printed in Great Britain ~) 1982 Pergamon Press Ltd

Dimethylamine/n-hexane and dimethylamine/carbon tetrachloride systems. Infrared studies

SONIA MARTINEZ and Jose EDWARDS Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile

(Received 5 October 1981)

Abstract--The association constants for different conglomerates are calculated for the dimethyl/n- hexane and dimethyl/carbon tetracMoride systems at 253 K from a new infrared spectra method. The thermodynamics functions are calculated for these systems and checked with vapour pressure measurements as well as the kind of polymers formed.

INTRODUCTION

Hydrogen bonding of self-associated alcohols in solutions have been studied in a previous paper [ l ] with a new i.r. method. From this method, the association constants, the activity coefficient and other important thermodynamics functions can be calculated.

I t was of interest to extend the application of this new method to secondary aliphatic amines.

Numerous investigations have been made using i.r. spectroscopy for the identification of nitrogen bases hydrogen bonding and to study the equilibria be tween them [2, 3]. In these studies, the i.r. spec- tra of the dimethylamine in the fundamental and in the first overtone range of the NH stretching vibration have been investigated, but the asso- ciation constants have been evaluated in the first overtone range[2].

It this work, we study and evaluate the asso- ciation constants in the range of the fundamental NH stretching vibration for the self association of this amine in two different solvents.

MATERIALS AND METHODS

The spectra were measured on a Perkin-Elmer Model 621 instrument, in the range of frequency 3000 to 4000 cm -l.

The comercial compound used, dimethylamine (Fluka), carbon tetrachloride and n-hexane (both Uvasol Merk) were dried with conventional method.

Amine solutions concentrations were 0.05-0.2 M. All measurements were performed at 253 K. The experimental details followed in this work, are

similar to those described by WOLFF et aL [2, 4, 5].

Pa~SULTS AND DISCUSSION Interpretation of the spectra

The i.r. spectra of both diluted solutions at 253 K exhibit a characteristic shape corresponding to a mixture of different hydrogen bonding spe- cies.

(a) Free band v~ corresponding to amines monomers [2, 3]; the wavenumbers of v~ are 3357 +_ 10cm -~ in n-hexane and 3350_+ cm -I in carbon tetrachloride.

(b) Broad band 1'2 corresponding to associated molecules of amines[2, 3]; the wavenumbers of v2 are 3310_+ 10 c m - t in n-bexane and 3287 _+ 10 cm -1 in carbon tetrachloride. This band exhibits two shoulders ~'3 and ~'4 on the lower frequency band. These shoulders have a characteristic frequency at all the concentration ranges. The wavenumbers of ~'3 and z,4 are 3275 -+ 10 cm -1 and 3243 - 10 cm -1 in n-hexane and 3238-+ 10 cm -I and 3189-+ 10 cm -t in carbon tetrachloride respectively. The frequency of these bands do not differ from literature data [2, 3].

Association constant The optical densities of the v~ bands of amine

solutions have been measured and the values are reported in Figs. 1 and 2. In conveniently diluted solutions the Dr values are linear with molar con- centration which permits an assignment of the characteristic frequencies for dimers, trimers,

0.4

0.3

(3-

0.2

O.I

m

0.05 O. I

C. om ine , m o L / L

0.15 0.2

Fig. 1. Optical densities of assigned bands v~ for different polymers vs molar concentration in dimethyl-

amine/n-hexane system.

383

384 SONIA MARTINEZ and Jose EDWARDS

calculated: 0 9 _

0.4 --o7 - - 0 .

0 2 __025 oo5 075 o , / ~ , ' /

moL,L . . / / " Z ,

o , - 7 ,°`

0 0 . 0 5 0 1 O. 15 O 2

C, o m i n e , m o L / L

Fig. 2. Optical densities of assigned bands ~'i for different polymers vs molar concentration in dimethyl-

amine/carbon tetrachloride system.

tetramers [1], according to the equation

p = D, (D1) i

c, c, K - = (--C~,)., K,~=G.C,_,

These association constant values, the standard deviation cr and the linear correlation coefficient r are given in Table 1. For both systems, the Kn values are coincident with literature data[2].

These association constant values permit the assumption that polymers are formed from monomer, in agreement with HOFFMANN'S method [6].

Dimethylamine/n-hexane system (Table 1)"

(Kl2" K23"/(34) 1/3 = 0.92 and Kt41/3 = 0.92.

Dimethylamine/carbon tetrachloride:

(Ki2" K23" K34) 1/3= 0.77 and K14 I/3= 0.79.

On the other hand, we can determine polymers not only qualitatively but also quantitatively in a given concentration range. Both systems results are given in Table 2.

where D~ = optical density of polymers i and D, = optical density of monomer.

These results are shown in Figs. 1 and 2. With these results, the e~ values can be calculated from the systems of equations as described previously [ 1 ].

C = D---z~ + 2D2 + 3D3-~ 41)4 111 112 113 t[4

(length of cell = 1 cm).

The system of equations was evaluated at in- tervals of amine concentration of 0.005 M, permit- ting the calculation of the molar extinction coefficients ei for each range of concentration. From these data and the values of concentration extrapolated for optical density = 0 in Figs. 1 and 2, for each polymer, we can valorate the values of el, e2, e3 and e4. These results in both systems are in Table 1.

With the e~ and D~ values of the different poli- merle species, the association constants can be

Average association enthalpy per hydrogen bridge The enthalpy engaged in hydrogen bonds for

every conglomerate is proportional to the frequency difference (i 'm-I'~) between the ab- sorption bands of the polymers and monomers [1].

From the application of modified Van't Hoff's equation [ 1 ]:

_AH, i ASI ( vj) 4 R I N K . = R T +--~- = - k I'~ f T AS,

AHq AS1 I n K q = - R 2 6 ÷ R

-- ] ASI -- k (l ' m -~- I ' i)~(1/m I'j) - ] - - - R T t 1 R

for cyclic conglomerates or

AH,~ AS, In KiJ= - R T -~ R

_ k [ ( v m - v , ) ( ~ s _ _ ~ ) l AS, RTL (~-O " ( j - l ) J~- R

Table 1. The ei (mol/1. cm), Ki (l/mol), cr and r values for dimethyl- amine/n-hexane and dimethylamine/carbon tetrachloride at -20°C

cl E2 ~3 ¢ K K K K K o r 12 23 ]3 3w I k

dimethylamine in n-hexane 1.85 137 300 350 0.14 2.4 0.34 2.33 0.8 0.03 0.99

dimethylamine

in carbon

tetrachlor ide 4.65 80 250 5800.074 2.3 0.17 2.63 0.5 0.05 0.99

Dimethylamine/n-hexane and dimethylamine/carbon tetrachloride systems

Table 2. Monomeric and polymeric fractions for dimethylamine/n- hexane and dimethylamine/carbon tetrachloride systems at -20"C

ana ly t i ca l monomeric dlmeric t r imer i c tet ramer ic f r ac t i on f r ac t i on f r ac t i on f r a c t i o n f r ac t i on

d lmethy l - 0.075 0.879 0.0063 0.0013 - - - amine in n-hexane 0.1 0.865 0.010 0.0025 0.0004

0.15 0.847 0.016 0.0036 0.0016

0.2 0.83 0.019 0.0042 0,0022

d imethy l - 0.075 0.952 - - - 0.004 0.0022 amine in carbon 0.1 0.950 - - - 0.0041 0.0022 te t ra - ch lor ide 0.15 0.946 0.0067 0.0048 0.0023

0.2 0.935 0.015 0.0048 0.0023

385

for linear conglomerates; and by plotting In K , (in molar fraction unities) vs A v , (in J/mol) and or other similar equations, we obtain k = - 14 in n- hexane, k = - 1 0 in carbon tetrachloride and A S ; / R = - 4 . 1 in both systems (Fig. 3). By the substitution of these values we calculate AH;~ and A/-/~. As we do not know yet if we have linear or cyclic conglomerates, involving i or ( i - 1 ) hydrogen bonds (in this opportunity, the above linear conglomerate equations present better results than the cyclic conglomerates (Fig. 3), we replace the calculated AH~ in both cases in the equation

- R T In K~ =- AH~ - T A S i .

If we assume linear conglomerates, the mean values of A H are 6930J/mol in n-hexane and 6883 J/mol in carbon tetrachloride. On the other hand, considering cyclic conglomerates, the mean values of A H are 4367J/mol in n-hexane and 4348 J/mol in carbon tetrachloride. The first values show a more sat isfactory agreement with the lit- erature data[2]. In Fig. 4, the calculated mean

x,,

5

_

i K~,, ,2s~, r, z3, / K J K,3

0 4 0 0 / / 8 ( ) 0 1200 1600 2OO(: -2 ~ - (urn- uj), J/tooL

/ / " -4

- 6 -

Fig. 3. Ln K,~ as a function of Avz~. (O) Dimethylamine in n-hexane (O) dimethylamine in carbon tetrachloride.

<~

~c x \

O 2 5 4

i, polymers grade

Fig. 4. The calculated values of ASi vs/(polymer grade); (0) for linear polymers in n-hexane, (O) for cyclic polymers in n-hexane, ( x ) for linear polymers in carbon tetrachloride (A) for cyclic polymers in carbon tetra-

chloride.

values of AS~ for linear and cyclic conglomerates are shown. Both systems are coincident. Accord- ing to the equation[l] .

1 i2 S ( i ) = - ~ [AS(,+,, - AS,]

+ [(AS(;+~) - AS~) + AS,] i + AS,

the entropy for linear or cyclic conglomerates can be calculated as a function of polymer grade.

For linear conglomerate:

S ( i ) = - 5.4i 2 + 44.8i + 34.

For cyclic conglomerate:

S ( i ) = - 7.5i 2 + 49i + 34

(see Fig. 5). Again we found that linear con- glomerates are the most probable; in part- icular, the linear tetramers and the highest existent linear polymers appear to be i = 9 (Fig. 5).

386 SONIA MARTINEZ and Jos]~ EDWARDS

This figure also shows that the possible cyclic polymers formed are for i = 2 to i = 5, though the most probable are the trimers and the highest existent cyclic polymers appear to be for i = 7.

The average value of entropy of monomeric dimethylamine diluted in n-hexane or carbon tetrachloride is 74.5 j/Omol at -20°C.

S(i) might also be expressed as a function of P = K~-L/K12 and K12[1].

The value for the entropy of monomeric dimethylamine diluted in n-hexane at -20°C is 80 --- 10% J/*mol and diluted in carbon tetrachloride at -20*C is 81_+ 10% J/*mol. The coincidence of these values is not only good but expected, though carbon tetrachloride does not appear to be so inert a solvent as n-hexane. There is no literature data about the entropy of dimethylamine at -20°C.

1 S(i) = - ~(R In p • K,2)i 2 + (R In p • K , 2 + ASDi

+ AS,.

Activity coeDicients The fA and fB values were calculated from the

modified SAROLEA-MATHOT'S equations [7, 8].

e-2-xA+Ei°x'-e-2 ] p + 2 p + 2

+ 4 p - 2 -~

1/2(p/2+ t)

f . = p - 2 x + 4 ~ X i ( l p - 2 ( x B + P - 2 _ \ \

!12 (p12+ 1)

140

*20 -- /°~..o--. " N ,~ \

Bo / \ 'o ~" - \ \ = \ \ ~ 6o- ~ \

~ o - \ \ 2 0 - - ~

o I I I I I ~ I ~, 2 3 4 5 6 7 8 i

i, polymers grode Fig. 5. The entropy $(i) as a function of /(polymer

grade). (O) Linear polymer, (O) cyclic polymer.

where A = amine, B = solvent, with Y.i°X~ = 1.13, EXi =0.1, *Xl =0.05, p = 17, K12 = 1.I, g i _ l , i =

18.95 (arithmetic mean between K23 and K34) for the methylamine/n-hexane system and Ei°X~ = 1.10, ~X~ = 0.065, *X~ = 0.033, p = 33, Kt2 = 0.88, KH.~ = 29.42 (arithmetic mean between K23 and K34) in the methylamine/carbon tetrachloride system.

The association constant values were taken from Table 1 and transformed in molar fraction units. We obtain agreement between values cal- culated with our method and those calculated from vapor pressure measurement[9], as is shown in Table 3. The differences are not greater than 5 to 10% in the entire range of mole fraction. The obtained results with this method for the amine solutions are better than for alcohol solutions.

This method has proved to be very useful in the determination of the cyclic or linear molecular

Table 3. Activity coefficients for both systems at -20°C

Dimethylamine/n-hexane system Dimethylamine/carbon tetrachloride

Calculated Experl- Calculated Experi- values mental values mental

values values

Xamine fA fB fA fB Xamine fA fB fA fB

0.214 2.39 1.09 2 .05 1.06 0 .115 1 . 0 3 1.0 1.06 1.01

0.45 1 . 4 6 1 .44 1 .45 1.25 0 .306 0 . 9 6 1.0 0 .96 1.03

0.512 1 .38 1 .51 1 .35 1 .34 0.494 0.82 1.0 0.97 1.02

0.692 1 .26 1 .58 1.14 1.72 0 .751 0 . 9 6 1.0 0 .99 0.99

0.932 1.0 2 . 9 1 1 .00 3 .08 0.91 1.00 2.3 0 .99 0.98

Dimethylamine/n-hexane and dimethylamine/carbon tetrachloride systems 387

aggregates and in the determination of the size of these aggregates as mentioned above in the dis- cussion.

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(1953). [8] S. MAR~EZ and J. EDWARDS, Monatshefte fiir

Chemie. 112, 683 (1981). [9] H. WOLFF and H. E. HoFFeL, Ber. Bunsenges. Phys.

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