J . Phys. Chem. 1990, 94, 6034-6041
6034
A Calorimetric Study on the Self-Association of an Amphiphik Phenothiazine Drug in Aqueous Electrolyte Solutions D. Attwood,* P. Fletcher, Department of Pharmacy, University of Manchester, M13 9PL. UK
E. Boitard, J-P. D u b , and H. Tachoire Laboratoire de Thermochimie, Universite de Prouence. F- 13331 Marseille Cedex 03, France (Received: August 25, 1989; In Final Form: December 21, 1989)
The association characteristicsof an amphiphilicphenothiazinedrug, promethazine hydrochloride, in aqueous solutions containing high concentrations of electrolyte have been examined by heat conduction calorimetry. The application of deconvolution techniques has permitted the continuous determination of the concentrationdependence of the apparent molar enthalpy extending to regions of high dilution. Theoretical treatments have been derived to describe thermogenesis in solutions of amphiphilic compounds exhibiting a range of association patterns. The calorimetric data for promethazine hydrochloride in the presence of 0.2-0.6 mol dm-’ sodium chloride could be satisfactorily described by an association scheme in which a primary unit of 3-4 monomers is formed below the critical micelle concentration by a continuous self-association process and grows with increasing concentration by the stepwise addition of monomers. Values of the stepwise equilibrium constants and the molar enthalpy changes for the formation of the primary units and for the stepwise addition of monomers have been derived.
Introduction The association of phenothiazine drugs has been widely studied by using a variety of experimental techniques.l In aqueous solution and in solutions of low electrolyte concentration, association commences at a critical concentration and is thought to be micellar in nature. However, a recent study2 has shown that, although the concentration dependence of the osmotic coefficients of several phenothiazine drugs in aqueous solution may be simulated by using equations based on the mass-action model of micellization, the ion-ion interaction parameters required to produce a good fit of data were strongly negative, suggesting premicellar association. Time-average light-scattering meaof phenothiazines containing high cons u r e m e n t ~on ~ ,solutions ~ centrations of added electrolyte have shown anomalous scattering behavior which has been discussed in terms of an association model which assumes the formation of a primary micelle at the critical micelle concentration (cmc) and its subsequent growth with increasing concentration according to a cooperative stepwise association model. We have previously demonstrated the value of heat conduction calorimetry for the study of self-associating drug ~ y s t e m s . ~ Application of deconvolution techniques permits the continuous determination of the variation of apparent molar enthalpy with concentration. The sensitivity of the equipment is such as to allow measurement in solutions of high dilution and to investigate the possibility of any premicellar association in these systems. Theoretical treatments have been proposed to describe enthalpy changes in solutions of amphiphiles in which the micelles increase in size by stepwise monomer addition with concentration increase above the cmc. In such models, the primary micelles have been assumed to be formed either by a single-step process6 or by continuous association.’ These models have previously been ( I ) Attwood. D.; Florence, A. T. Surfacranr Systems; Chapman & Hall: London, 1983; Chapter 4. (2) Attwood, D.; Dickinson, N . A,; Masquera, V.; PErez-Villar, V. J . Pfiys. Cfiem. 1987, 91, 4203. (3) Attwood, D.; Natarajan, R. J . Pfiarm. Pfiarmacol. 1983, 35, 317. (4) Attwood, D. J . Cfiem.Soc., Faraday Trans. I 1982, 78, 2011. (5) A t t w d , D.; Fletcher, P.; Boitard, E.; DUES.J-P.; Tachoire, H . J . Pfiys. Cfiem. 1987,91, 2970. (6) Attwood, D.; Fletcher, P.; Boitard, E.; D u k , J-P.; Tachoire, H. In Sutfacranrs in Solution. Mittal, K. L., Ed.;Plenum: New York, 1988; Vol. 7, p 265. (7) Attwood, D.; Boitard, E.; Dubes,J-P.; Tachoire, H. Colloids SurJ, in press.
0022-3654/90/2094-6034$02.50/0
applied in an analysis of the calorimetric data for the phenothiazine drug, promethazine hydrochloride, in aqueous solutions containing 0.6 mol sodium chloride. We now report an extension of this study in which the association of promethazine hydrochloride is examined in the presence of a range of concentrations of added sodium chloride of between 0.1 and 0.6 mol dm-3. Theoretical treatments of the variation of instantaneous thermal power (Le., thermogenesis) with concentration in solutions which exhibit a variety of association patterns have been applied to the data. Molar enthalpy changes and equilibrium constants for the formation and growth of the primary micelles have been derived. Experimental Section
Calorimetric Equipment. Calorimetric measurements were performed at 30 OC on a modified Arion-Electronique conduction calorimeter, the design, operation, and calibration of which have been described previously.5 The transfer function of such equipment may lead to signal deformation and, in order to measure the instantaneous power, P, absorbed by the environment of the reaction during the course of an experiment, it is essential to deconvolve the response by compensation of the principal time constant^.*^^ As in the previous study,5 deconvolution of the calorimetric output was achieved by analog filteringi*12 of the calorimetric output. Maferials. Promethazine hydrochloride [ I0-(2-(dimethylamino)propyl)phenothiazine] (Sigma Chemical Co. Ltd.) conformed to the purity requirements of the British Pharmacoepia and as such contained not less than 98.5% of the specified compound. Sodium chloride was of AnalaR grade. Theoretical Section Two main association schemes have been considered, one in which a primary micelle is formed at the cmc by a single-step association, and the other in which this micelle is formed by a (8) Navarro, J.; Torra, V.; Maqueron, J. L.; D u b , J-P.; Tachoire, H. Tfiermochim.Acta 1980,39, 73. (9) Cesari, E.; Torra, V.; Maqueron, J. L.; Prost, R.; Dub&, J-P.; Tachoire, H.Tfiermochim.Acra 1982, 53, l , 17. (IO) D u b , J-P.; Barr&, M.; Boitard, E.; Tachoire, H. Tfiermochim.Acta 1980. 39, 63. ( I I ) D u k , J-P.; Kechavarz, R.; Tachoire, H. Tfiermocfiim.Acta 1984, 79, 15.
(12) Cesari, E.; Torra, V.; Maqueron, J. L.; Dubes, J-P.; Kgchavarz, R.; Tachoire, H . Tfiermocfiim.Acta 1984, 79, 27.
0 I990 American Chemical Societv
The Journal of Physical Chemistry, Vol. 94, No. 15, I990 6035
Self-Association of a Phenothiazine Drug continuous association process. In both schemes, the primary micelle is considered to grow with increasing concentration by a stepwise association process. For the first of these schemes, two association models are considered for micellar growth in the post-cmc region. In the second scheme, two association models are considered for the formation of the primary micelle with a common model of micellar growth in the post-cmc region. Single-Step Formation of Primary Micelle. The association scheme may be represented as follows. Assuming that the micellar aggregates have a negligible concentration below the cmc, formation of the primary micelle may be assumed to be the single-step process nA,
* A,,
(1)
The equilibrium constant for the formation of the primary micelle, A,,, from n monomeric units A I is K , and the molar enthalpy of formation of this micelle is AH,,. The growth of this micelle by increase of concentration above the cmc may be represented by An + A I
An+(q-l)+
+
&+I
A I * An+q
(2)
with corresponding equilibrium constants, K,,+l, K H 2 ,..., K H q and molar enthalpies of formation, AH,,+l, AH,,+2, ..., Addition of successive equilibria gives the global equilibrium from the primary for the formation of the secondary micelle A, micelle thus An + 9AI
(13) where AH is the molar enthalpy change for monomer addition, which is the same for each step of the process, Le. AH,,+I AHn+2 = AH,,, = AH The relative apparent molar enthalpy $L(m) at molality m may be shown to be
QT(t) is the heat content absorbed by the formation of all the associated species present in the solution at time t . The experimental data may be fitted to the preceding equations by assuming a fixed relationship between the stepwise equilibrium constants. Two association models were considered.
Model 1 The equality of all stepwise association models is assumed, Le.
Kn+l = Kn+2
KK,,+~
Kn+q = K
(15)
Introducing this relationship into eqs 1 1 and 12 gives
Y =
(3)
An+q
The global equilibrium constant K*,+q and molar enthalpy of formation for this process AH*,+q are given by
K*n+q =
Similarly it can be shown that the total power PT(t), related to the formation of all the associated species present in a solution of molality m(r) is
Kn[ml(t)ln = - a p 1 - Kml(t) 1 - X
where a = K , / K n and X = K m , ( t ) and
(4)
i= I
From eq 9 the molality of the solution may be written Q
AH*n+q = CAHn+i
x n a p ap+I m(t) = - + -+ K 1-X ( 1 - 3 2
(5)
i= I
Addition of the equilibria of eqs 1 and 3 gives the global equilibrium for the formation of the secondary micelle An+qfrom monomers thus The global equilibrium constant for the above equilibrium is K*,,,,+, and the corresponding molar enthalpy of formation, where
Substituting dY/dt and dZ/dt into eq 13 yields
[ =1 ]- ]x+ A H [
+ X + 11 dx -dt+ -a3
MT(t)aP[n(l- X) (1
4
AH*,,Hq = AH,
+ AH*,,+q = AH, + i=CAH,,+, (8) I
It can be shown6 that the total molality of all species in solution at time t is given by m ( t ) = m l ( f ) nY z = N T ( t ) / h f T ( f ) (9)
+
+
where NT(t) is the total number of moles at time t , hfT(t) is the total mass of solvent at time t in the calorimeter as given by
hfT(f)= Mo
+ d1t
(10)
where M ois the initial mass of solvent in the cell and dl the rate of addition of solvent
Model 2 Stepwise association constants are related to the aggregation number by the expression K,,,, = K ( n + g - l ) / ( n q) with q 2 1 (21)
+
Introducing this relationship into eqs 1 1 and 12 gives a
4
vn+i
ip+i
Z = anz-
+i
6036 The Journal of Physical Chemistry, Vol. 94, No. 15, 1990
Attwood et al.
p/mp
0
0.02
0.04
m/mol kd'
0.08
Figure 2. Variation of the function q5L with concentration, m,at 30 OC for promethazine hydrochloride in (A) 0.1; (B) 0.2; (C) 0.4; and (D) 0.6 mol dm-' NaCI.
equilibria gives the global equilibrium for the formation of the primary micelle; thus nA,
10
30
(28)
The global equilibrium constant K*, for the formation of the aggregate A, and the corresponding molar enthalpy AH*, are given by
70
50
* A,
t/min
K*, = I"IKj
Figure 1 . Thermograms at 30 "C for the dilution of aqueous solutions of promethazine hydrochloride (0.25 mol kg-l) in (A) 0.1; (B) 0.2; (C) 0.4; and (D) 0.6 mol dm-' NaCI. Curves a represent uncorrected instrumental response; curves b are reconstituted thermograms after de-
j=2 n
AH*, = CAHj
convolution.
(30)
j=2
TABLE I: A Comparison of Critical Micelle Concentrations from Calorimetric and Light-ScatteringTechniques' for Promethazine Hvdrochloride in Aaueous Electrolvte at 30 OC cmc, mmol dm-' NaCl concn, mol dm-' calorimetry light scattering 0.10 31.0 31.0 0.20 19.5 0.40 13.5 13.8 0.60 9.0 9.0
The molality of the solution at time t is given by X(l - X ) KanX" m(t) = K(1 - X )
+
Subsequent growth of the primary micelle A,, is assumed to occur according to eq 2 with global equilibrium constants and molar enthalpy of formation given by eqs 4 and 5 , respectively. Addition of the equilibria represented by eqs 3 and 28 gives the equilibrium for the formation of the aggregates An+qfrom monomeric species; thus ( n + q)A1
An+9
(31)
The global equilibrium constant K*n,n+qand the molar enthalpy of formation are given by
K*n,n+9 = K*nK*n+9
AH*,,,+, = AH*,
(24)
(32)
+
(33)
The total molality m ( t ) of all the species present in the solution at time t can be shown to be7
Substituting dY/dt and dZ/dr into eq 13 yields
m(t) = m,(t)
N(t) + nY + Z + R , = W t )
(34)
with Y =
with
-dx-dt
( 4- d , m ( t ) ) K X ( l- X )
[ K N ( t )- M T ( r ) ] [ n- ( n - 1)a+ hfT(t)x(l- X )
Z =
(26) n
Limited Premicellar Association. In the following treatment the primary micelle is assumed to be formed by limited stepwise association according to A1 + AI * A2 A2 A,,
R, = C ~ ' K * ~ [ m , ( t ) ] j j=2
Similarly it can be shown that the total power, PT(t), associated with the formation of all the associated species present in a solution of molality m ( t ) is
+ A1 * A, + A,
A,
(27)
with corresponding equilibrium constants, K2, K3, ...,K,, and molar enthalpies of formation, AH2, AH3. ..., AH,,. Addition of successive
(37)
") +
(n - 1 ) dt
AH[,,,
+ M T ( t ) dt
The Journal of Physical Chemistry, Vol. 94, No. IS, 1990 6037
Self-Association of a Phenothiazine Drug
IC
0
4
0.05
lo-
:I_, ... ..
,
.,,
. ... ... , . . ,,,
,
_.....
Figure 3. Simulation of the concentration dependence of P / d 2 for promethazine hydrochloride in (A) 0.1; (B) 0.2; (C) 0.4; and (D) 0.6 mol dm-' NaCl using model 1.
0.05
0.05
0
10
10
0
0.05
0.05
m/moi kg-' Figure 4. Simulation of the concentration dependence of P / d 2 for promethazine hydrochloride in A, 0.1; B, 0.2; C, 0.4; and D, 0.6 mol dm-' NaCl using model 2.
where R2 is defined as
R2 =
n
- I)K*,[m,(t)]j
(39)
association process and may be solved by assuming a relationship between aggregation number and equilibrium constant. In this study we have assumed two such relationships.
j-2
and AHA and AH are respectively the molar enthalpy changes for monomer addition during the formation of the primary micelle and during its subseauent growth. Similarly the relative apparent molar enthalpy dL(m)at molality m may be shown to be AHA[R2 + ( n - 1)Yl ZAH &(r) (40) dL(M) = -NT(Q m(0 Equations 34, 38, and 40 are general expressions for this type of
-
-
+
Model 3 This model assumes the equality of all stepwise association constants in the Dremicellar region. Above the cmc, the aggregate A, is assumed to grow such that the equilibrium constants increase with aggregation number according to K,+i = K ( n + i - l ) / ( n + i ) (42)
Attwood et al.
6038 The Journal of Physical Chemistry, Vol. 94, No. 15, 1990
TABLE 11: Limiting Aggregation Numbers, Stepwise Association Constants, and Molar Enthalpies for the Formation and Growth of Micelles of Promethazine Hydrochloride in Aqueous Electrolyte at 30 'C As Calculated from Models 1, 2, 3, and 4 NaCl concn, a," kJ mol dm-' n K A , kg mol-' AHA, kJ mo1-l K , kg mol-' AH,kJ mol-l moP
9
(2.0 f 0.1) x (2.2 f 0.1) x (9.0 f 0.1) X (3.0 f 0.1) x
0.1 0.2 0.4 0.6
26 29
0. I 0.2 0.4 0.6
8 12 16 28
0.1 0.2 0.4 0.6
4 4 4 4
12f l5f 22 f 38f
0. I 0.2 0.4 0.6
3 3 3 3
3 4 4 4
15
I 1 1 1
f 0.5 f 0.5
f 0.5 f 0.5
IO" 1022
IOu 1052
Model I -20.2 f 0.3 -90.0 f 0.9 -56.9 f 0.5 -342 f 3
30.8 f 43.9 f 87.4 f 88.6 f
Model 2 -4.6 f 0.1 -21.0 f 0.3 -54.3 f 0.5 -96.9 f 0.9
26.1 f 41.7 f 63.0 f 89.2 f
Model 3 -12.5 f 0.2 -13.7 f 0.2 -10.2 f 0.2 -5.7 f 2
47 f 68 f 109 f 173 f
Model 4 -37.4 f 0.4 -40.8 f 0.4 -40.7 f 0.4 -44.3 f 0.4
41 f 63 f 90 f 118 f
1 1
2 2
I 1
2 2
1 1
2 2 1 1
2 2
-35.6 -34.5 -15.1 -16.5
f 0.4
f 0.4 f 0.2 f 0.2
1 1 1 1
-9.1 -3.9 -1.8 -1.6
f 0.2 f 0.1 f 0.1 f 0.1
4 7 3
-1 3.9 i 0.2 -14.4 f 0.2 -14.0 f 0.2 -14.4 f 0.2
4 4 6 3
-12.9 -14.0 -13.7 -14.0
4 4 6 4
f 0.2 f 0.2 f 0.2 f 0.2
5
OStandard deviation of AH values.
From these two hypotheses we may write
K*j = f i K j = KAJ-l and K*, = KA*l j=l
(52) (43) with
with j = 2, 3, ..., n and
K*,+i = fIKn+i= n K i / ( n + i) i= 1
(53) (44)
with i = 1, 2, ..., i, ..., m. An expression for total molality m(t) may be derived as follows. Substitution of eqs 41-44 into eqs 35-37 and 39 gives
where
Model 4
In this model it is assumed that in the premicellar region the aggregates form according to a continuous association mode of n steps, in which the equilibrium constants are such that K = K d ' / ( j - 1) (54) As in model 3, the primary aggregate is assumed to grow in a cooperative manner according to eq 42. The global constants arising from these two hypotheses are Substitution of eqs 45-48 into eq 34 and rearrangement yields
m ( t ) =.
with j = 2, 3, ..., n and K*n+ias defined by eq 44. The total molality m ( t ) may be derived from eq 34 by using the following expressions (49)
Solution of eq 49 for given values of the parameters n l , KA, and K permits the evaluation of m , ( t ) . The total power absorbed PT(t) at a molality m(t) may then be determined from eq 38 by using the expressions for Y and Z given by eqs 47 and 48 and the following derivatives of the functions R2, Y, and 2.
(57)
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990 6039
Self-Association of a Phenothiazine Drug
I
M mol" p'd2
IC
A
0
0
0.05
ID
I" 0
0.05
0.05
0
0.05
m/mol kg-' Figure 5. Simulation of the concentration dependence of P/d2 for promethazine hydrochloride in (A) 0.1; (B) 0.2; (C) 0.4; and (D) 0.6 mol dm-3 NaCl using model 3.
P/dz
C
A
kJ mor'
0
0.05
0
ID
IB 0
0.05
0
0.05
0.05
m/moi kg-'
Figure 6. Simulation of the concentration dependence of P/d2 for promethazine hydrochloride in (A) 0.1; (B) 0.2; (C) 0.4; and (D) 0.6 mol dm-I NaCl using model 4.
The expression for m(t) derived in this manner is with dml/dt as given in eq 53 and
(60) Equation 60 allows the determination of m l ( t )for given set of the parameters n, KA, and K. The total power absorbed, PT(t), a t a molality m(t) may be determined from eq 38 by using the expressions for Y and Z given in eqs 5 8 and 59 and the following derivatives.
+ c()+ l)[KAml(t)]' + IF1
A =1
j= I
Results and Discussion Figure 1 presents calorimetric data for promethazine hydrochloride in a range of concentrations of added electrolyte, both as raw thermograms (curve a) and after deconvolution of the signal by inverse filtering (curve b). A comparison of curves a and b
6040 The Journal of Physical Chemistry, Vol. 94, No. 15, 1990
10
0
kJ m o i '
m/mol kg-'
I
2kd'JP m o l '
n- 3
r\
Attwood et al.
n- 2
0
0.05
m/rnol kg4
sf:;'
I
kJ
0.0 5
n= 4
10
0
m/mol kg"
0
0.05
Figure 7. Influence of the value of n on the best fit of model 3 to graphs of P/d2 as a function of concentration for promethazine hydrochloride in 0.4 mol dm-' NaCI.
m / m o l kf'
0.0 5
Figure 8. Influence of the value of n on the best fit of model 4 to graphs of P/d2 as a function of concentration for promethazine hydrochloride in 0 6 mol dm-' NaCI.
reinforces the point made previouslyS of the importance of deconvolution of data for these systems. Inflection points noted in the deconvolved thermograms are in good agreement with the apparent cmcs as determined previously by light-scattering techniques4 (see Table I). In the association schemes outlined above, expressions have been derived for the total power, PT. This parameter is related to the experimentally determined instantaneous power P by the relationship Pr = P - P"
and hence where P" is the power at infinite dilution and d2 is the rate of addition of the drug. Simulation of the concentration dependence of P/dz has been used in this study as a means of determination of the thermodynamic parameters of association. For each association model, values of P / d 2 were computed as a function of molality by using the relevant equations for m ( t ) and PT(t). Iteration of the parameters n, K , K,,, AH,and AH,, (models 1 and 2 ) and n, K , KA, AH, and AHA (models 3 and 4) using a leastsquares procedure gave best fit curves for each association model. It should be noted that these parameters could also be determined by simulation of plots of the relative apparent molar en, a function of m . Such plots may be derived thalpy, $ ~ ( m )as from the experimental data as explained previously5 by using where P is the average power at a point in the titration when the concentration is m,i.e.
Plots of 4 L ( m ) against m are shown in Figure 2 and may be simulated by an iterative procedure similar to that described above, using eq 40 (models 3 and 4).
0
0.02
0.014
0.06
m/mol kg-
0
a02
0.04 W m o i ke"
0.0 6
Figure 9. Variation of the percentage of species, mi, present in solutions of promethazine hydrochloride in (a) 0.1 mol dm-' and (b) 0.6 mol dm-) sodium chloride as a function of molality, m,as calculated by using model 4 with the values of i indicated'and with the equilibrium constants of Table I I .
J . Phys. Chem. 1990, 94, 6041-6048 Figures 3 and 4 illustrate the best fit to the experimental P / d 2 against m plots achieved by the two models (models 1 and 2) which assumed a single-step formation of the primary micelle. The values of the equilibrium constants and molar enthalpies of formation of aggregates are given in Table 11. Whilst neither of these models gave a satisfactory fit to all systems it is clear that a model of micellar growth which assumed a cooperative mode of association (model 2) provided a better representation of the data than an association model in which K was independent of concentration. Figure 4 shows an improvement of fit with model 2 as the salt content of the system was increased; indeed in 0.6 mol dm-’ NaCl the fit might be considered satisfactory, as was reported previously.6 However, the higher cmc of systems of lower salt content permitted a more thorough evaluation of the fit in the pre-cmc region and it is clear from Figure 4 that this model is not able to predict the correct curvature of the plots in the premicellar region. The discrepancy between experimental and predicted values of P / d 2 in this low-concentration region was in excess of the experimental uncertainty ( X i 1 kJ mol-’) and consequently this model was rejected. Figures 5 and 6 show an excellent representation of the experimental data over the whole concentration range for both models (models 3 and 4) which assumed the formation of the primary micelle by a continuous association process and its subsequent growth by cooperative association. This fit was maintained over the whole range of electrolyte concentration studied with no dependence of the value of n on the concentration of added electrolyte for either model (see Table 11). The values of the equilibrium constants and molar enthalpies of formation of aggregates which relate to these models are given in Table 11. Both models gave good fits to the data over the range of electrolyte concentration studied, and both generated the expected increase of equilibrium constants with increase of added electrolyte. The values of K calculated for the promethazine/0.6 mol dm-’ NaCl system compare with a K value of 242 mol kg-’ as derived from a previous light-scattering study4 using a similar post-cmc association scheme. The relatively large decrease of AHA for model 3 suggests that the formation of the primary aggregate is becoming less favorable with increase in the salt concentration. whereas the
604 1
opposite is indicated by the predicted increase of KA. Model 4, which indicated an increasingly exothermic formation of the primary micelle with increasing electrolyte concentration, is more consistent with the effects which would be expected and is probably a more realistic model. Our computations have indicated that the fit in the pre-cmc region for both of these models was highly sensitive to the assumed aggregation number, n, of the primary micelle. Figures 7 and 8 show the poor fits which resulted when the value of n was varied by only 1 unit from the best fit values of Figures 5 and 6. Similar effects were noted at all electrolyte concentrations. The concentration-dependent changes in the percentage of the various species present in solution, as calculated from model 4, are shown in Figure 9 for sodium chloride molarities of 0.1 and 0.6 mol dm-’. It is apparent that our studies have provided clear evidence of limited premicellar association in these systems. The deviation of the osmotic coefficient in water of several phenothiazine drugs, including promethazine hydrochloride, from ideal values at concentration below the cmc has led to similar conclusions.2 Evidence for a stacking arrangement of monomers in the micelles of the phenothiazine drugs has been presented from N M R datal3 and it has recently been suggested that the micelles formed in aqueous solution may be formed from several short stacks hydrophobically bonded together to form roughly symmetrical units.I4 The results of the present study lend support to this idea and suggest that the short stacks envisaged by these workers may be composed of some three or four monomers. Registry No. Promethazine hydrochloride, 58-33-3.
Supplementary Material Available: Tables of values of P / d 2 as a function of molality for promethazine hydrochloride in 0.1, 0.2,0.4, and 0.6 mol dm-’ NaCl (1 1 pages). Ordering information is given on any current masthead page. (13) Florence, A. T.; Parfitt, R. T. J . Phys. Chem. 1971, 75, 3554. (14) Atherton, A. D.; Barry, B. W.J . Colloid Znferface Sci. 1985, 102, 479.
Uptake of SO,(g) by Aqueous Surfaces as a Function of pH: The Effect of Chemical Reaction at the Interface J. T. Jayne, P. Davidovits,* Department of Chemistry, Boston College, Chestnut Hill, Massachusetts 02167
D. R. Worsnop, M. S. Zahniser, and C. E. Kolb Aerodyne Research, Inc., Billerica, Massachusetts 01821 (Received: December 6, 1989) The uptake of SO2@)by fast-moving water droplets was measured as a function of pH and surface-gas contact time in the range 0.5-10 ms. In the high pH range (>5) a parameter governing the uptake of S02(g)by water is the rate for the reaction of SO2with H 2 0 to form HSO,-. The experimentally observed uptake is significantly greater than predicted by the rate measured for this reaction in bulk liquid water. Likewise at low pH, where uptake is limited by Henry’s law solubility, the uptake is significantly greater than predicted. These observations together with the observation of uptake as a function of time suggest that at the gas-liquid interface the S02-H20reaction is facile, forming a HS03--H+ surface complex which is in equilibrium with the gas-phase SO,. The species enters the bulk water as HS03- via this complex. The equilibrium ratio of densities of the surface complex (cm-2) and gas-phase SO,(cm-’) is 0.13 cm-I at 10 O C . Kinetic and thermodynamic parameters governing surface interactions are derived and discussed.
Introduction Heterogeneous gas-liquid reactions involving water droplets in clouds and fogs are important mechanisms for the chemical 0022-3654/90/2094-6041$02.50/0
transformation of atmospheric trace gases. In such heterogeneous reactions, the rate for trace gas uptake is pivotal to understanding of the transformation process. (See, for example, refs 1-5.) An atmospherically important heterogeneous process is the trans@ 1990 American Chemical Society
