Partial Molal Volumes and Compressibilities of Phosphoric Acid and Sodium Phosphates in 0.725 Molal NaCl at 25 °C † PDF

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Partial Molal Volumes and Compressibilities of the Homologous Series of Sodium Alkylcarboxylates, R6COONa-RlzCOONa, in Aqueous Solution EINAR VIKINGSTAD, ARNE SKAUGE, AND HARALD HOILAND Department of Chemistry, University of Bergen, N-5014 Bergen, Norway Received December 22, 1977; accepted March 2,...

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Partial Molal Volumes and Compressibilities of the Homologous Series of Sodium Alkylcarboxylates, R6COONa-RlzCOONa, in Aqueous Solution EINAR VIKINGSTAD, ARNE SKAUGE, AND HARALD HOILAND Department of Chemistry, University of Bergen, N-5014 Bergen, Norway Received December 22, 1977; accepted March 2, 1978 The changes in partial molal volume (AV m) and compressibility (AKm) in the formation of micelles have been determined at 25°C for the homologous series of sodium-alkylcarboxylates, RfCOONa-RlzCOONa. AV m has been determined by density measurements and by conductance measurements at different pressures. AKm has been evaluated from the conductance measurements and from ultrasound measurements. For each quantity the two independent methods of measurements gave consistent values. AV m and AKm both increase with increasing chain length of the surfactant, but not in a linear manner. An analysis of the quantity AV m shows that the difference between successive values of AV m in the homologous series does not represent the group partial molal volume of the CH2 group added to the micelle. The fraction of counterions associated with the micelles has been determined by EMF measurements, using a membrane electrode. This quantity was found to increase with increasing chain length. INTRODUCTION

series of sodium alkylcarboxylates from R6COONa to R~aCOONa. Our main interest is to extend the information gained from the studies of AV m and AKm for sodium dodecanoate (1, 2). Also the effect of chain length on the fraction of counterions associated with micelles,/3, has been investigated by a membrane electrode method. AV m and AKm have been determined by two independent methods of measurement, and the results are compared for consistency.

Thermodynamic studies of surfactant solutions are very important to the understanding of micelle formation. In earlier works ( 1 - 3 ) the change in partial molal volume, AV m, in the formation of micelles from the singly dispersed state and the corresponding change in partial molal compressibility, AKm, have been investigated for sodium, potassium, and tetramethylammonium dodecanoates and for sodium dodecanoate in solutions containing NaC1. It was found that AVm and AKm decreased slightly with increasing ionic size of the counterions and with increasing concentrations of added NaCI. Some authors (4-8) have investigated AV m for homologous series of surfactants, especially for sodium alkylsulfates and for alkyl-trimethylammonium bromides. They have found that AVmincreases with increasing chain length of the surfactant. In this work AVm and AKm have been determined at 25°C for the homologous

MATERIALS AND METHODS

The sodium alkylcarboxylates, RfCOONaR10COONa and RlzCOONa, have been made by mixing equivalent portions of the corresponding acids and NaOH in a water/ ethanol mixture. The synthesis has been described in detail elsewhere (1, 9). The acids were all Sigma grade, 99-100%, and the NaOH was from EKA, Sweden. Ten solutions were made of each surfactant in the concentration range 0.01 mole 240

0021-9797/78/0662-0240502.00/0 Copyright © 1978 by Academic Press, Inc. All rights of reproduction in any form reserved.

Journal of Colloid and Interface Science, Vol. 66, No. 2, September 1978

SODIUM ALKYLCARBOXYLATES TABLE I Critical Micelle Concentration and Fraction of Counterions Associated with the Micelles for Sodium Alkylcarboxylates at 25°C CMC -+ 1% (molal)

RrCOONa RrCOONa R8COONa RgCOONa R10COONa RllCOONa RI3COONa

fl --- 0.02

0.79 0.405 (0.39% 0.38b) 0.210 0.109 0.056 0.0278e 0.0080

0.57 0.60 (0.59% 0.60a) 0.64 0.68 0.72 0.74e

a Refs. (15) and (19). b Ref. (14). c Ref. (16). a Refs. (18) and (19). e Ref. (1).

Further details o f the m e t h o d s of measu r e m e n t s are given elsewhere (10-12). The fraction of counterions associated to the micelles, r , was determined b y E M F m e a s u r e m e n t s using a m e m b r a n e electrode. Details of these m e a s u r e m e n t s were given in an earlier w o r k (3). RESULTS AND DISCUSSION

The Effect o f Chain Length on CMC It has been d e m o n s t r a t e d that a change in the chain length of a surfactant causes a change in the CMC. Shinoda et al. (13) have shown that for a h o m o l o g o u s series this relation can be e x p r e s s e d b y a linear function: log CMC = A - B ' N ,

kg -a to four times the critical micelle concentration (CMC). The concentrations were determined b y weight. The specific conductivities o f these solutions w e r e determined at 1,200, 400, 800, 1200, and 1600 bars at 25°C. Densities were m e a s u r e d at 25°C with a P a a r density m e t e r ( D M A 02C), and isentropic coefficients of compressibility were d e t e r m i n e d b y ultrasound m e a s u r e m e n t s .

o

241

[1]

where A and B are empirical constants, and N is the n u m b e r of carbon a t o m s in the chain o f the surfactant. The C M C values obtained for the sodium alkylcarboxylates f r o m conductivity measurements at 25°C are s h o w n in Table I and are in good a g r e e m e n t with previously obtained values (13-19). Figure 1 shows a plot of log C M C as a function of the n u m b e r of carbon a t o m s in the chain of the surfactant. F r o m Fig. 1 it is clear that the present C M C values fit v e r y well the linear function p r o p o s e d by Shinoda et al. Using a linear regression p r o g r a m the empirical constants A and B were d e t e r m i n e d to be 1.90 and 0.286, respectively.

-0.5

The Effect o f Chain Length on the Fraction o f Associated Counterions

~: -I.0

-1.5

-2.0

6

8

I0

12

14

N, number of carbon atoms

FIG. I. Log CMC for the sodium alkylcarboxylates as a function of the chain length of the surfactant.

The fraction of counterions associated with the micelles, r , has been determined by E M F m e a s u r e m e n t s using a m e m b r a n e electrode described in an earlier w o r k (3). The activity o f N a + ions was determined at concentrations a b o v e and below the CMC. The results for the sodium alkylc a r b o x y l a t e s are s h o w n in Table I. fl increases s m o o t h l y with increasing chain Journal of Colloid and Interface Science, Vol. 66, No. 2, September 1978

242

VIKINGSTAD, SKAUGE, AND HOILAND T A B L E II A p p a r e n t Molal V o l u m e s a n d t h e C h a n g e in Partial Molal V o l u m e in Micelle F o r m a t i o n for Sodium Alkylcarboxylates at 25°C AVm + 0.4 cm3 mole-1

R6COONa RTCOONa RsCOONa RgCOONa R~0COONa RllCOONa RlaCOONa

Conductance

Density

8.6 8.8 9.5 10.2 10.8

8.8 _+ 0.8 8.9 9.2 9.6 (10.6 b) 10.2 11.2 c (11.0 ~) 14.3 _+ 1.0

V, - 0.2 cma mole-t A 0.1 0.3 0.4 0.6 1.0

Vg

V~,

Vg

116.8 132.4 (132.14 °) 148.3 164.2 (164.0 b) 179.9 195.5 c (195.90) 226.4

118.1 133.5 149.5 165.4 180.7 196.1 c 226.5

126.9 142.4 158.7 175.0 190.9 207.3 c 240.8

a Ref. (14). b Ref. (28). c Ref. (1).

length. This effect has previously been demonstrated by Shedlovsky et al. (20) and by Evans (21). The value of fl obtained for sodium octanoate is in excellent agreement with literature values (16, 18, 19). It is known (13, 21) that the aggregation number and the micelle radius increase with increasing chain length. Then the increase in /3 can be ascribed to the increased surface area of the miceUe and the reduced electrostatic repulsion.

Effect of Chain Length on AV m In earlier works (1, 2) it was demonstrated that the change in partial molal volume of the surfactant in the formation of micelles, AV m, can be determined by two independent methods of measurement, each based on the pseudophase model for micelle formation. The CMC can be determined from conductivity measurements as the break in the slope when the specific conductivity is plotted versus molality. Determination of CMC at different pressures allows calculation of AV m from the following equation (6): AVm=(I+fl)RT(.

OlnCMC) OP r" [2]

For the shortest chain length, R6COONa, Journal of Colloid andlnterface Science, Vol. 66, No. 2, September 1978

the CMC is 0.79 mole kg-1, and the specific conductivity must be determined well above this concentration to find the CMC. At these high concentrations the specific conductivity is not linearly dependent on the molality, and hence the CMC could not be determined as a function of pressure for R6COONa. For all the other surfactants the CMC showed a dependence on pressure similar to that found in an earlier work for RllCOONa (1). The results for AV m at 25°C are shown in Table II. The AV m can also be determined from density measurements (1, 4-5): AV

TM

= V~

-

V~,

[3]

where V. m and V. s are the partial molal volume of the surfactant in the micellar state and in the singly dispersed state, respectively. A typical plot of V. as a function of molality of the suffactant is shown in Fig. 2. The value of V~, at the CMC is taken as V~, and V~ was found by using a saturation function to the plot above CMC [see Ref. (1)]. The results for AVTM are shown in Table II, as are those for V~, V~, and V~. The estimated uncertainty in AVm is +-0.4 cm 3 mole-L From Table II it is clear that AV m from the two independent methods of measurement are in excellent agreement. The values

243

SODIUM A L K Y L C A R B O X Y L A T E S

v~ em3mol -I 139

138

137 I

136

135

134

133 0.i

0.2

0.3

0.4

0.5

0.6 molallty

0.7

0.8

0.9

I.0

i.i

1.2

FIG. 2. V , as a function of concentration for sodium octanoate at 25°C.

of AV m for RTCOONa, RgCOONa, and R11COONa are in good agreement with previously obtained results (14, 28). Values of AV m for the shortest chain lengths (RnCOONa,RTCOONa) are likely to be more uncertain than the others. The concentrations involved in these measurements are high and far from the ideal state. One of the assumptions of the pseudophase model is that the interactions between the micelles

are small. This assumption is not valid for the high concentrations of R6COONa and RrCOONa, and this might cause an error in AV m for these surfactants. Some authors (4, 5) have found a linear relationship between AV m and the chain lengths of a homologous series of surfactants, giving a constant increment AVcn~ to AV m for each CH2 group added. However, Musbally et al. (7, 22) have not found

T A B L E III

Apparent Molal Compressibilities and the Change in Partial Molal Compressibility in Micelle Formation of Sodium Alkylcarboxylates at 25°C ( A r m ± 5)" 10 4 c m a b a r -1 mole -I

R6COONa RrCOONa RsCOONa R9COONa R~oCOONa R~COONa R~3COONa

Conductance

Ultrasound

104 ± 10 112 115 127 135

84 92 102 114 124 139 155 ± 10

(r,~s) -+ 2)- 104 c m 3 b a r -~ m o l e -~ A

8 10 12 10 15

,x~s ~

r~s~

~>

-71 -74 -75 -78 -77 -81 -82

-45 -53 -57 -63 -65 -69 -68

39 39 45 51 59 70~ 89

Ref. (1). Journal of Colloid and Interface Science, V o l . 6 6 , N o . 2, S e p t e m b e r 1978

244

VIKINGSTAD, SKAUGE, AND HOLLAND

such linearity for alkylsulfates from their precise measurements. Table II shows that AV m for the alkylcarboxylates is not linearly dependent o f the chain length. AVcn2 seems to increase with increasing chain length. This might be explained by the uncertainty in the determination o f AV m for R6COONa and RTCOONa. H o w e v e r , if we identify the interior of the micelle with a liquid hydrocarbon, then AV TM as a function o f chain length should be comparable with the variation of V . for liquid alkanes. It turns out that AVcH~ for liquid alkanes increases with increasing chain length of the alkanes (manuscript in preparation), thus verifying the results obtained for AV m.

We will now analyze the quantity AV m in further detail. The formation o f micelles can be represented by the equilibrium (surfactant NaX): n N a + + n X - ~ (XnNam) n-m + (n - m ) N a ÷.

[4]

The X - ions can be divided into two groups, H C + CH~COO-, where HC is the hydrocarbon part of the surfactant molecule. Below the CMC, the measured quantity V¢ c a n be expressed by: V¢ = V¢(Na+,aq) + V¢(CH2COO-,aq) + V¢(HC,aq).

[5]

Above the CMC, V . can be expressed by:

V¢ -

CMC

CMC CMC V¢(HC,aq) V¢(CH2COO-,aq) + - V¢(Na+,aq) + - -

C

+

C

C

c - CMC

+

(1 - /3)V¢(Na+,aq) + c - CMC

c - CMC

/3V¢(CH2COO-Na +,ass)

(1 - fl)V.(CH~COO-,ass) +

The notations aq and ass c o r r e s p o n d to singly dispersed state and micellar state, respectively. At the surface of the micelle there are strong interactions between the C O 0 - ions and the N a + ions, hence we cannot separate the group partial molal volumes of the CH2COO- ions and the N a ÷ ions in the micellar state. Further, Eq. [6] is based on the assumption that V.(CH2COO-,ass) is independent of/3. It is p r o b a b l e t h a t t h e q u a n t i t y V¢(CH~COO-,ass) is dependent on the chain length o f the surfactant, due to differences in micelle surface charge and the extent of hydration for different surfactants. Thus the values o f the different group partial molal volumes in micellar state in Eq. [6] are different for different surfactants and cannot be transferred from one chain length to another. Journal of Colloid and Interface Science, Vol. 66, No. 2, September 1978

c - CMC

V.(HC,ass).

[6]

The quantity V~ is defined as the 4 last parts of Eq. [6] when c >> CMC, and V~ is simply V¢ in Eq. [5]. Putting AV(HC) = V.(HC,ass) - V¢(HC,aq) and AV(CH~COO-) = V.(CH2COO-,ass) V¢(CH2COO-,aq), we obtain: -

AV m = AV(HC) + AV(CH2COO-) + fl[V.(CH2COO-Na+,ass) - V.(CH2COO-,ass) - V.(Na+,aq)]. [7] This can be expressed as: AV m = AV(surfactant) +/3AV(Na+).

[8]

This equation is in excellent agreement with our earlier results (2) where AV m was found to be linearly dependent on/3: AV m = AV(HC) + AV(ion)

[9]

SODIUM ALKYLCARBOXYLATES

245

K¢ 20 ¸ f J

-20

-/40

-60

-80

0.05

O.1

0.15

0.2

0.25

o.3

molality

F I G . 3. K~ts > a s a f u n c t i o n o f c o n c e n t r a t i o n

AV(ion) in this equation was defined as the change in partial molal volume of the ionic head groups o f the surfactant and the N a + ions in micelle formation. H o w e v e r , from our p r e s e n t analysis and assumptions AV(ion) = AV(Na+). In the earlier work (2) AV(Na ÷) was determined to be - 6 . 4 cm 3 mole -1. This result is in good agreement with the analysis by Kaneshina et al. (6). This means that the partial molal volume o f the N a ÷ ions at the micelle surface is about - 1 3 . 0 cm ~ mole -1, which is a very low value. H o w e v e r , there is experimental evidence (23-25) that the associated N a ÷ ions are hydrated to the same extent as in the solution, and the high surface charge o f the micelle can explain this low value. It is clear from our analysis o f AV TM that the change in AV TM when one CH~ group is added to the surfactant chain is not the group partial molal volume o f a CH2 group in the micelles. The increment in AV TM with increasing chain length is an effect o f both the added CH2 group and the increased fraction o f counterions associated to the mice|les. H e n c e the A in Table II is not the

for sodium decanoate

a t 25°C.

group partial molal volume o f CH2 in the micelles. This is a point previously overlooked in literature (4, 6).

Effect of Chain Length on AKm The quantity AKTM is defined by the equation (26): AKIn ---

i~'~---'/T

[10]

H e n c e AKm was determined from the conductivity measurements where A V m was determined as a function of pressure (1, 2). The results for AKn' at 25°C are shown in Table III. The change in the isentropic partial molal compressibility of micelle formation, Arm, can be determined from ultrasound measurements (1, 12): AK~ =

~ns

ss

K~> and Kom...