Spectrochimica Acta, Vol. 42A, No. 4, pp. 531-536, 1986. 0584-8539/86 $3.00+0.00 Printed in Great Britain. ~) 1986 Pergamon Press Ltd.

Methanol/n-hexane system--l . Infrared studies

SONIA MARTiNEZ Departamento de Quhnica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile

(Received 8 January 1985; in final form 29 July 1985; accepted 25 September 1985)

Abstract--The association constants for different conglomerates of the methanol/n-liexane system are calculated at 303 K from a new i.r. spectra method. The thermodynamic functions, as well as the kind of polymers formed, are calculated for this system and checked with vapour pressure measurements.

I N T R O D U C T I O N

In previous communications a new method to calcu- late the association constants of conglomerates of alcohol and amine molecules has been described [1, 2]. With this method, the association constant of all conglomerates formed can be exactly calculated. It is important to emphasize that as with this method a relative value of the extinction coefficients is calcu- lated, the error which could be introduced in the absorbance measurements of the overlapped bands of the different molecular species is avoided. Hence, this possible error does not interfere with the final result.

It was of interest to extend the application of this method to methanol/n-hexane solution because of the difficulty of obtaining the association constants of methanol with other methods.

Virtually all investigators agree that a solution of an alcohol in a non-polar solvent consists of a variety of hydrogen-bonded species[3-5], as well as non- associated monomers. However, there is controversy over the sizes, shapes and relative number of hydrogen- bonded molecules. We believe that this method will be useful in the determination of the size of the aggregates.

E X P E R I M E N T A L

The i.r. spectra were measured on a Perkin-Elmer Model 621 instrument, in the frequency range 3000-4000 cm-1.

Methanol and n-hexane (both Uvasoi Merck) were dried with conventional methods.

Alcoholic solution concentrations in the range 0.001-0.3 M were measured at 303 K with concentration intervals of 0.0025 M.

The length of the cell was 1 ram.

R E S U L T S A N D D I S C U S S I O N

Interpretation of the spectra

The i.r. spectra of a dilute solution at 303 K exhibit a characteristic shape corresponding to a mixture of different hydrogen bonding species: (a) A sharp band 7,, corresponding to alcoholic mono- mers [3, 4]; the wavenumber o f ~ , is 3660 cm-1. This band exhibits two shoulders ~z~ and ~3t on the lower frequency band. These shoulders have a characteristic frequency at all concentration ranges. The wavenum-

hers of Vzl and ~31 are 3640 and 3628cm -1, respectively. (b) A broad hand v~ corresponding to associated molecules of alcohol [3, 4]. This hand exhibits several shoulders vzc, v3c, Vsc and -v6,- These shoulders also have a characteristic frequency at all concentration ranges.

The wavenumber of V~ is 3350cm -1 and the wavenumbers of v2c, v3c, vsc and V6c are 3550, 3450, 3280 and 3205 cm - 1, respectively 1-3-5]. The subscript numbers denote the number of monomers which compose the oligomer chain and I represents the linear and c the cyclic species.

Association constant

The optical densities of the ~ hand of the alcoholic solution were measured and the values are reported in Fig. 1.

For conveniently diluted solutions, the Dr values are linear with molar concentration (linear correlation

0.~

0.2

c

~ o

~ 0 . 2

Broad bond

3350 : / 32.°,,7 / ~ 3~.5o

3550

Sharp band

3660

0.02 0.08 0.14 0.21 C, Alcoholic mo l / I

Fig. 1. Optical densities of the v o band assigned for different polymers vs molar concentration in the methanol/n-hexane system. (+) 3660 assigned to monomers. ( • ) 3640 assigned to linear dimers. (&) 3628 assigned to linear trimers. (e) 3550 assigned to cyclic dimers. (D) 3450 assigned to cyclic trimers. (A) 3350 assigned to cyclic tetramers. ( x ) 3280 assigned to

cyclic pentamers. (G) 3205 assigned to cyclic hexamers.

531

532 SON~A MARTINEZ

coefficient is r = 0.999) which permits an assignment o f characteristic frequencies for different i-reefs as pre- viously described in the l i terature [1, 3, 4]: the results are shown in Fig. 1. With these assignments, the el values can be calculated f rom the systems of equat ion 0):

c= +2 o,,+o2cI+ ,[o,, . . . " - - - - . (1) e, Le2~ e2~J Leu e ~ j

The system of Eqn. (1) was evaluated at alcohol concentration intervals of 0.001 M, permitting the calculation of the molar extinction coefficients for each concentra t ion [1]. The values ofe~, ~z~, ea~ and e2~ were calculated by 4 x 4 matrices set f rom absorbance measurements in the concentra t ion range 0.001-0.014 M (upper part of Fig. 2).

El

2701 ~o ¢2o L 2t,0 f ¢, ,o~

F ~o , ;~,~' 'o.o;,"~.o,,o.o 210" , at o.oo ~ 0.0

180[- m. ~ . . ' - "

"""~" ¢ s ~ o.o o.oo~ o.oo9 - o'.o,4

1 2 0 ~ ..

6O

30

i 0.0375 0.0405 0.0&45 0.0475

C, Alcoholic tool / 1

Fig. 2. e~ (mol/l) of assigned conglomerates vs molar concen- tration. ( I ) e I = 2.6, (+) ezt = 23.7, (A) e3t = 25.5, (©) e~ = 10.6, ( I ) ea~ = 70.0, ( x ) e,~ = 111, (D) es, = 127 and (A)

e~ = 172.

In the same way, values of ~3c, e,u, esc and e6c were evaluated by 4 x 4 matrices set f rom absorbance measurements in the concentra t ion range 0.0375-0.0475 M (lower par t o f Fig. 2). F r o m these data, and the values o f concent ra t ion extrapolated for optical density = 0 in Fig. 1 for each polymer, we can evaluate the values o fe t , e2~, e2¢, £31,83c , 84.c, ~5c and e6c as shown in Fig. 2. All e~ values were fitted by the least squares method. The extrapolated e~ values, the stan- dard error of est imate between e~ and the molar concentrat ion, the l inear correlat ion coefficient be- tween e~ and concentra t ion (r,,.c) and the linear corre- lation coefficient between ~ and D~ are shown in Table 1 [6].

With the e~,.o and D~ values o f different polymeric species (Figs 1 and 2) association constants can be calculated, for each concentrat ion,

Ci Ci Kl~ = --=" K 0 =

0 ~ ' C~.C._.' Ci

K~- 1. ~ = - - (2) C1" C~_ 1

The association equil ibrium constants were calcu- lated by the least squares method. In Table 2, we

Table 1. Extrapolated molar extinction coefficients values for different conglomerates (e~), standard error of estimate between e~ and molar concentration C(S,,.c) linear corre- lation coefficient between ej and C (re.c) and linear corre-

lation coefficient between e~ and optical density (r,,.o,)

Conglomerate i ej e~ S~,c r~,.c r~.o,

Monomer et 2.6 5:0.33 -0.85 + 0.84 Linear dimer e2~ 23.7 5:2.36 -0.84 + 0.81 Cyclic dimer e~ 10.6 -t-0.18 -0.80 +0.81 Linear trimer ca, 25.5 + 1.21 -0.90 +0.88 Cyclic trimer e~ 70.0 5:6.75 - 0.89 + 0.89 Cyclic tetramer e4, 111 5:0.38 -0.99 +0.99 Cyclic pentamer es, 127 5:2.30 -0.98 +0.98 Cyclic hexamer e6, 172 +4.05 -0.90 +0.92

Table 2. Example of K 12, calculated by our method and fitted by least squares method ( y = 3.485x+2.18). Coefficient of linear correlation is r = 0.772, standard deviations are cry = 0.317 and err = 0.07. In addition this table shows the mean value and standard

error of estimate between K12 , and concentration (Syx)

Concentration Mean (mole/l) D3660 D355o K12 , value Syx

0.01 0.01802 0.00130 2.553 2.565 5:0.20 0.02 0.03857 0.00560 2.400 0.04 0.07172 0.01770 2.194 0.06 0.10679 0.03655 2.043 0.07 0.I 1350 0.04455 2.205 0.08 0.12784 0.05499 2.145 O.lO 0.13750 0.07750 2.614 0.12 0.14569 0.09326 2.802 0.14 0.15676 0.10708 2.778 0.16 0.16115 0.11633 2.856 0.18 0.16900 0.1300 2.902 0.20 0.I 7710 0.1450 2.948 0.25 0.1769 0.1426 2.906

Methanol/n-hexane i.r. studies 533

present an example of K 12, calculated by our method and fitted by the least squares method.

The association constant values are given in Table 3. The linear correlation between the experimental and the calculated values of concentration by the substi- tution of K 0 in the expression for the analytical concentration of the mixture

C = C1 + 2 K t 2 c 2 + 3 K t 3 C a t + . . . . . 6K~6 c 6 (3)

was found to be r = 0.99 and the standard error of estimate S = 0.005 [6].

The K12, value was evaluated by the LIDDEL and BECKER method [31, giving in this case 2.50 which was fairly well coincident with 2.57 obtained by our method. Furthermore, our value for K t2 = K12~ + K12, = 3.67 is coincident with 3.526 (108 K) given

by WOLFF and HOPPEL [7]. F rom these K~-1. ~ values it can be assumed that

polymers are formed from monomers, in agreement with HOFFMANN'S method [8]

(K 12c" K23c" K34c" K45c" K56c )t/5 = 43.68

and

KUS = 44.5 16(7

for cyclic conglomerates and

(Kl21" K2ai) 1/2 = 26.7 and K]/a 2 = 26.7

for linear conglomerates. We can determine oligomers not only qualitatively

but also quantitatively in a given concentration range. These results are given in Table 4.

Averaoe association enthalpy per hydrooen bond

The enthalpy engaged in hydrogen bonds for every conglomerate is proportional to the frequency dif- ference (~ - V , ) between the absorption bands of the polymers and monomers [1].

F rom the application of a modified van't Hoff equation [1]

A R ~ ~ AS1 • ASt - k + - - ~ - (4) I n K t i = + R =

A H 0 AS1 In Ki~ = R ~ ¢ R ~

k F(V=-V,) (~m-Vj) 7 ASx

- grL i + J _l+R

Table 3. The K', (l/m)and K~ (mole fraction unit) for the methanol/n- hexanb system at 30°C (I = linear and c = cyclic)

Reaction K o K~j K~

At +AI = A2! Kt21 1.11 +0.08 8.30+0.64 At + At = A2, Kt2c 2.57 +0.20 19.2 + 1.48 3At = A31 K t 3 z 12.8+0.99 716.0+55 3At = Aac Kta , 7.99+0.62 447.0-1-94 A21+ AI = Aal KzlaJ 11.505-0.89 86.3+6.6 A2c+At = Aa, K2,3, 3.12+0.24 23.3+ 1.8 Az~+At = Aa, Azla, 7.77+0.60 58.0+4.5 4Al = A~ Kt4~ 214.0+ 16 89561 +6896 A,~ + At = As, K~sc 7.68+0.59 57.4+4.4 5At =A5¢ Kt~ 1716-t-132 537 x 10'*+41 x 104 6At = A ~ Ktt,, 7465+575 175x 106+13x 106 Azl = A2, K212c 2.31 +0.18 2.31 +0.18 A31 = A 3~ K313c 1.0 + 0.08 1.0 + 0.08 A3c + At = A~ K3c ~ 23.8 + 1.83 178.0+ 13.7 As~+At = A~ Ks,6¢ 4.65+0.36 34.85-2.68

Table 4. Monomeric and polymeric fractions for the methanol/n-hexane system at 30°C

Analytical Monomeric l-Dimeric c-Dimeric I-Trimeric c-Trimeric c-Tetramic c-Pentameric c-Hexameric fraction fraction fraction fraction fraction fraction fraction fraction fraction

0.0035 0.74 0.11 - - 0 . 0 6 9 . . . . 0.0075 0.74 0.11 - - 0 . 0 6 9 . . . . 0.01 0.74 0.11 0.025 0 . 0 6 9 . . . . 0.02 0.74 0.10 0.054 0 . 0 6 1 . . . . 0.04 0.73 0.095 0.083 0.059 0.0092 0.013 0.0021 0.0003 0.08 0.61 0.074 0.137 0.053 0.033 0.059 0.029 0.005 0.1 0.52 0.066 0.146 0.053 0.041 0.075 0.042 0.012 0.15 0.41 0.050 0.143 0.047 0.047 0.080 0.052 0.014 0.2 0.34 0.045 0.140 0.042 0.048 0.080 0.056 0.016

5 3 4 S O N I A M A R T i N E Z

for cyclic conglomerates or

AH o ASI ln Kii = R T ~- R

k [ (V . -~ i ) (V,--V~)-I+ASl

- RTL ( i - l ) +-~-L-~j R for linear conglomerates; and by plotting In Kl i (in molar fraction unities) vs A~ti (in J /mol) and or other similar equations (Fig. 3), we obtain for cyclic con- glomerates (3)

Y~ = - 0.00476x - 7.10 (r = 0.999; Sy~ = _+ 0.18)

and for linear conglomerates

Y~ = -0 .0312x - 7 . 1 0 (r = 0.999; Sy~ = -I-0.051).

By replacement, we calculate k = 78.5 for linear con- glomerates and 12.6 for cyclic conglomerates and for both conglomerates AS~/s = -7 .1 . With these values we can calculate A H , and AHij for different con- glomerates [1]. These results (Table 5) show a satisfac-

24 20f 16

12I / K~sc t / K14c

/ 'K K / ~ K~3c /#~" 213[ O 12C /

' - , 0 ' 0 0 " '

- A g i m J / m o l

Fig. 3. Ln K o as a function of ATif: (O) for cyclic con- glomerates, (A) for linear conglomerates.

Table 5. The AH~j and AS~ values for the methanol/n- hexane system at 30°C

K~ AH u + 10% (J/mol) ASu+ 10% (J/mol)

Kl21 18 781 49.5 K12 16580 30.1 K131 2(15 025) 2(22) K ~ 3, 3(11 786) 3(22) K14~ 4(11 681) 4(28) K~ ~c 5(11 455) 5(12) KI6 ¢ 6(i1 439) 6(11) K2~31 2(16 903) 2(47.7) Ku2 ~ 16 580 48 K3tac 11 756 39 K2,ac 2(11 476) 2(25) Kac,~ 2(11 780) 2(17) K,,,sc 2(11 570) 2(21) K s ~ 2(11 440) 2(23)

tory agreement with the literature data[8 ,9] . We replace the different calculated AHi and K i in the equation

- R T I n K i = AHi - TAS i (5)

and calculate ASi. The calculated mean values of ASi for linear and cyclic conglomerates are shown in Fig. 4.

According to the equation [1]:

S(O = - ½[AS(i+ l) - ASi] i 2

+ [(ASi+ ~ - A S i ) + A S ~ ] i + A S I (6)

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

For linear conglomerates

S(i h = --8.5i 2 q- 77i + 60 (7)

90

t 70

60

-6 50 E

40

<~ 30

20

10

0t

I I I "l t J l

2 3 /, 5 6 7 i, Polymers grade

Fig. 4. The calculated values of AS o vs i (polymer grade). (A) Linear polymers (fl), (©) cyclic polymer (a).

S(i 360 )

300 o~

240

180

1204 '~

60

0 4 7 10 13

i, Polymer grode 16

Fig. 5. The entropy S (i) as a function of i (polymer grade). (A) Linear polymer (fl), (©) cyclic polymer (~,).

Methanoi/n-hexane i.r. studies 535

and for cyclic conglomerates

s(0 ' = - 6 t z + 72i + 60 (8)

(see Fig. 5). For i= 1, this entropy value shows a satisfactory agreement with the literature data [9, 10]. This figure also shows that the possible cyclic polymers formed are from i = 2 to i - - - - 12. Nevertheless, the most probable are hexamers. The possible linear polymers formed are from i = 2 to i = 9, and as tetramers are the most likely of the polymers to exist.

Activity coefficients

The fA and fn values are calculated from SAROLEA- MATHOT'S equation [1, 11]

In the range 0.75-1 mole fraction we use

z - 2 ~/2 _ _ X o

X~ 2

fA = X---~ X f z - 2 X ) ~\--F-- ~+x~

A = :12

-- x AI F 1/~J, i XO ]z/2 (9a)

f'4--X°'LxA(~z2XA+Xa)(I+2/zZ-.XA,'(I--2/zZ, XA,)-' f ' = z - 2

~ X x + X ( I+2/zF.XA.(1--2 /zF.XA,) -1 (9b)

(9c)

where A = alcohol, B = solvent, with Y4X °, = 1.5, Y.X °, --0.099 and z = 2.5. These values are calcu- lated [10] with X °, = X A, = 0.016, Kt2 = 19.2 y K i - L i = 58.83 (arithmetic mean value be- tween different K i - L l) for the system (see Table 3). The same value for KH,~ is obtained using an alternative method to find the suitable Ki-i, i [-11, 12].

We obtained agreement between values calculated with this method and those calculated from pressure measurement ['7] at 308 K in the range 0.1-0.3 mole fraction, as shown in Fig. 6.

10

z~

~ a

o o 6 o

12

immicibies l i q u i d s

b

fe

/ 0'2' d4' 0 ' 6 ' d . ' 10

A l c o h o l i c m o l o r f r a c t i o n

Fig. 6. The activity coefficient vs alcoholic mole fraction. (A) Experimental values, ((3) calculated values in this work.

5A(A)42:4-5

These equations are obtained in the same form as previously but consider the only presence of cyclic polymers.

The coefficients of linear correlation between calcu- lated values [Eqns (9)] and experimental values [7] of the activity coefficients and the standard error of estimate are r = 0.990, S = + 0.49 forfA and r = 0.998, S = +0.17 for fB.

It is also possible that polymers are formed by other mechanisms, since we were also able to calculate the association constants K2t2¢, K4~ and K2~3c. Finally, we want to emphasize the usefulness of this method for the calculation of cyclic and linear molecular aggre- gates that it is not possible to determine using classical methods, as happens in all systems involving hydrogen bondings (alcohols, amines, acids).

Work is in progress on the determination of the thermodynamic functions of methanol/n-hexane sys- tems in other temperature ranges using NMR spectra.

Acknowledgemem--I wish to express my thanks to Professor Dr. Josl~ EDWARDS who suggested this work. I would also like to acknowledge the Departamento de Investigaci6n y Biblioteca de la Universidad de Chile for support of this research (Q 2003 8522).

REFERENCES

[1] S. MARTINEZ and J. EDWARDS, Mortars. Chem. 112, 563 0981).

[2] S. MART][NEZ and J. EDWARDS, Spectrochim. Acta 38A, 383 (1982).

[3] U. LIDDEL and E. D. BECKER, Spectrochira. Acta 10, 70 (1957).

[4] C. BOORD~ROn, J. J. P~RON and C. SANDORFV, J. phys. Chem. 76, 804.

[5] M. VAN THIEL, E. D. BECKER and G. C. PIMENTEL, J. chem. Phys. 27, 95 (1957).

536 SONX ̂MARTINEZ

[6] M. R. SPIEGEL, Theory and Problems of Statistics. Schaum, New York (1961).

[7] H. WOLFF and H. E. HOPPEL, Ber. Bunsenges. phys. Chem. 72, 715 (1968).

[8] E. G. HOFFMANN, Z. phys. Chem. 55B, 179 (1943). [9] G. C. PIMENTEL and A. L. MAC CLELLAN, The

Hydrooen Bond. Freeman, San Francisco (1960). [10] Tables Landolt-Bornstein. Zahenwerte and

Funktionenen II, Vol. 4, Part 4. Springer, Berlin (1961). [11] L. SAROLEA-MATHOT, Trans. Faraday Soc. 49, 8 (1953). [12] S. MARTINEZ and J. EDWARDS, Mortars. Chem. 112, 683

(1981).