PLENARY ACCOUNT
Influence of Water Structureon Aqueous Sol ubiI ity Forrest W. Getzen' and Thomas M. Ward Department of Chemistry, North Carolina State Uniuersity, Raleigh, N . C. 27607
hl
FORREST W. GETZEN,with the Department of Chemistry, North Caroltna State University since 1961, holds a BSfrom the Virginia Military Institute and a PhD from the Massachusetts Institute o f TechnoloEy. From I956 to 1961 he wairesearch engineer at the Humble Oil Production Research Center in Houston, Tex. From 1964 to 1967, he served as senior science advisor for the United States Engineering Team in the Engineering School, Kabul Uniuersity, Kabul, Afghanistan. His researeh interests are in thermodynamics and colloid and surface chemistry. He is a member of the American Chemical Society, the American Institute of Mining, Metallurgical, and Petroleum Engineers, and the American Society for Quality Control and a Fellow and Professional Chemist-Accredited in the American Institute of Chemists.
THOMAS M. WARD, assistantprofessor of chemistry at North Carolina State University, receiued his PhD from the same school. His interests are in the fields o f surface and solution chemistry with particular attentwn to the relationships between thephysical and chemical properties o f pesticide-related organic compounds and the mechanisms of their sorptive and degradative behauior. He is a member o f the American Chemical Society and North Carolina Academy of Science.
N u m e r o u s studies of water in its various states have heeu made and reported in the literature. Much of the work has been surveyed and reviewed from time to time (Nemethy and Scheraga, 1962; Frank, 1962; Feates and Ives, 1956; Chadwell, 1927). For the most part, the interest has been due to the great abundance of water and to the well-recognized structural features which water possesses as a liquid. The purpose of this plenary account is to focus attention on the influence of water structure on aqueous solubilities through the study of the solubility behavior of a series of nonpolar solutes and to demonstrate a thermodynamic treatment of this solution behavior which depends upon the unique structural characteristics of liquid water as a solvent. The thermodynamic treatment of aqueous solubility behavior is limited to some extent in that it neither favors nor rules out any particular model that has been proposed for water structure. The models which have heen proposed are discussed a t length by Nem6thy and Scheraga (1962). However, this does not detract from the practical results and conclusions which may be drawn from such an approach, nor should it limit the range of applications in which it may he applied to aqueous solubility studies in the future. The interpretation of aqueous solubilities and other phenomena associated with solvation in water has involved both charge and structural characteristics of the solute and the structural nature of the solvent in the neighhorhood of the solute particles. Explanations for aqueous solubilities have emphasized changes in the character of the short range ordered structure of water upon the introduction of the solute particles. Attention has been focused on various phenomena such as the formation of clathrates in aqueous solutions (Claussen, 1951; Jeffrey, 1962; Lindman et al., 1968: Pauling, 1960), iceberg formation (Frank and Evans, 1945), hydrophobic bonding (Kauzmann, 1959), and structure-breaking (Frank and Evans, 1945). While emphasis has been placed upon the changes in water structure associated with a solution process, some attention has been given to the idea that such changes are less significant in the case of low polarity
'Towhom correspondence should he addressed. 122
Ind. Eng. Chem. Prod. Res. Develop.,Vol. 10, No. 2, 1971
Advantage is iaken of the existence of a structural character of liquid water to develop a general thermodynamic treatment for the aqueous solution behavior of nonpolar compounds which can be applied with reasonable confidence. The approach i s used to examine the aqueous solubilities of a series of structurally related alkylamino-striazines and to demonstrate predictable effects of water structure upon their solubilities. The solution data have been combined with heat of fusion measurements and sublimation data to determine standard free energies, enthalpies, and entropies of solution from the gaseous reference state at 1 atm and 25°C for nine of the compounds. The aqueous solution characteristics of all compounds from the gaseous state were found to depend upon water structure in a characteristic manner. Additional influences of solid salute structure were identified for solutions from the solid state. Techniques for obtaining molar heats of fusion from aqueous solubility data, aqueous solubility estimates from molar heats of fusion, and sublimation behavior from aqueous solubilities and molar heats of fusion are illustrated.
solutes than for the more polar compounds and ionic species (Franks and Ives, 1966). Even though some nonelectrolytes will form clathrate-like hydrates in cold aqueous solutions, there appears to be no evidence of any short-range ordering of a clathrate hydrate nature for many solutes of low polarity. I t has been suggested that the solution process for such materials need not depend on the formation of cavities peculiar to the geometry of a few stable gas hydrates or to the use by the solute molecules of pre-existing cavities in pure water, but should depend upon an intrinsic cavity-stabilizing ability of water due to its three-dimensional hydrogen bonding ability so that it can accommodate the stearic requirements of any solute molecule (Franks and Ives, 1966). A thermodynamic treatment based on such arguments has been used to explain the aqueous solubilities of a series of nonpolar gaseous, liquid, and solid compounds (Getzen, 1970). The present work was undertaken to establish and explain the aqueous solubility behavior of a series of structurally related alkylamino-s-triazines on a thermodynamic basis in order to deduce the influence of inherent water solvent structure upon the solution behavior of such materials. The solubilities of such compounds in water has been subject to much less systematic quantitative examination than the strong electrolytes, even though an understanding of their solubility behavior may be useful in distinguishing more clearly the alternative models for water structure. Furthermore, there exists the possibility that the specific chemical behavior and physical nature of these compounds can be understood more clearly from a knowledge of their aqueous solution thermodynamics. The solubilities of the alkylamino-s-triazines have been of recent interest because their derivatives are used as herbicides, fungicides, and dyes. However, little other than room temperature solubilities have been reported for these compounds (Bailey and White, 1965; Freed, 1966; Knuesli et al., 1969; Ward and Weber, 1968). Solubilities of Simazine and Atrazine above and below room temperatures were reported by Bailey and White (1965) and by Freed (1966). Ward and Weber (1968) reported the solubilities of a series of alkylamino-s-triazines as a function of pH at room temperature. These measurements were undertaken to deduce information about the cell entry processes of such compounds. Their explanations for the observed solubility behavior was in terms of the structural differences of the solute molecules and no effort was made to treat their results on a quantitative thermodynamic basis.
The present work determines additional aqueous solubilities above room temperature for the alkylamino-striazines and measures their heats of fusion. When combined with the reported solubilities and sublimation measurements reported by Friedrich and Stammbach (1964) for nine of the compounds, these data can be used to establish the thermodynamic parameters for the solution process. Experimental
Table I lists the molar aqueous solubilities a t various temperatures for 16 structurally related alkylamino-striazines. The commercial trade name of each compound is given for convenience of later discussions. The estimated solubility for Ipatryne a t 2 P C was obtained from procedures outlined in the following sections and is given in parentheses. Other solubilities a t 26°C are those reported by Ward and Weber (1968) for p H 7. The solubility measurements a t 50°C for nine of the compounds were made by using their reported procedure. Solubilities for nine of the compounds at additional temperatures in the range from 0-85"C were obtained from the literature (Bailey and White, 1965; Knuesli et al., 1969). The enthalpies and entropies of sublimation used are those reported by Friedrich and Stammbach (1964). The heats of fusion were determined by differential scanning calorimetry following the procedure described by David (1964). The samples were the same ones as those used for solubility measurements with no additional purification undertaken. They all gave ultraviolet spectra identical to those previously reported (Ward and Weber, 1968). The measurements were made on a Model DSC1B Perkin-Elmer Differential Scanning Calorimeter with independent checks made on a Model DTA-12A Differential Thermal Analysis Apparatus manufactured by the Robert L. Stone Co. (now a Division of Tracor, Inc.), Austin, Tex. Naphthalene with a specific heat of fusion of 35.6 (calig) (Spaght et al., 1932) was used for the calibrations. Triplicate runs were made on each compound. The results of these measurements together with heats of fusion values calculated from the solubility measurements are given in Table 11. Sublimation data for nine of the triazines were obtained from Friedrich and Stammbach (1964). Table I11 gives the values for molar enthalpies and molar entropies of sublimation together with the corresponding free energy changes and sublimation pressures a t 25" C from their work for the nine triazines. The table includes also, in Ind. Eng. Chem. Prod. Res. Develop., Vol. 10, No. 2, 1971
123
~
~~~~
Table I. Molar Aqueous Solubilities of Alkylamino-s-triazines" Temp, Compd
Trode norneb
0
20-22
10
C 27
26
50
85
I. 2-Chloro-s-triazines 4,6-Bis(ethylamino)4-Ethylamino-6-isoprop ylamino4,6-Bis(isopropylamino)4-Ethylamino-6-diethy lamino4-Isopropy lamino-6-diethylamino4,6-Bis(diethylamino)-
Simazine Atrazine Propazine Trietazine Ipazine Chlorazine
0.099'
0.25' 1.53' 0.37' 0.87' 1.64'
1.02'
0.75, 1.6lU 0.20' 1.25' 1.13' 0 .86d
0.25" 3.25
1.31 4.53 0.77
4.17 14.8
11. 2-Methoxy-s-triazines 4,6-Bis(ethylamino)4-Ethylamino-6-isopropylamino4,6-Bis(isopropylamino)4-Ethylamino-6-diethy lamino4-Isopropylamino-6-diethy lamino-
Simatone Atratone Prometone Trietatone Ipatone
162' 85' 33'
120" 76.0d 30.1d 1.8Zd 3.6lU
355 124 46.8
111. 2-Methylmercapto-s-triazines 4,6-Bis(ethylamino)4-Ethylamino-6-isopropylamino4,6-Bis(isopropylamino)4-Ethylamino-6-diethylamino4-Isopropylamino-6-diethylamino-
Simetryne Ametryne Prometryne Trietatryne Ipatryne
20.8" 8.57d 1.67d O.Ogd (0.21)
1.99'
47.0 16.6 4.20
'Concentrations given in (mol/l.) 10'. 'Trade names of J. R. Geigy Co. 'Calculated from ppm value reported by Bailey and White (1965). dReported value from this laboratory (Ward and Weber, 1968). 'Calculated from ppm value reported by Knuesli et al. (1969).
parentheses, the corresponding values for the triazines in our study as estimated from smoothed solubility, sublimation, heat of fusion data following procedures outlined in the following sections.
Table 11. Heats of Fusion of Alkylamino-s-triazines" Form Compd
wt
AH (obsdf
AH
AH
(obsd)'
(colcd)d
I . 2-Chloro-s-triazines Treatment of Data and Calculations
The aqueous solubilities of the triazines studied are well within the Henry's law region for materials of low polarity (Kauzmann, 1959) so that the changes in free energy for the solution processes can be stated as follows. First, for gas-solution equilibrium conditions, the chemical potentials for the solute gas and in solution are equal.
p(1iq) = po(liq)+ RT In y.X = po(gas)+ RT In P = p(gas)
Simazine Atrazine Propazine Trietazine Ipazine Chlorazine
201.7 215.7 229.7 229.8 243.8 257.9
Simatone Atratone Prometone Trietatone Ipatone
197.2 211.3 225.3 225.3 239.3
...
... 7.84
...
5.39 4.82
...
11.53 =t 0.29 8.10 =t 0.14 10.08 =t 0.24 5.37 . . . 4.96 . . . 4.38 . . .
I I , 2-Methoxy-s-triazines
so that
5.90 5.48 4.95
5.59 5.62 5.15
5.62
5.52, 5.83
...
...
5.74 + 0.17 5.55 f 0.05 5.08 . . . 9.71 . . . 5.63 . . .
111. 2-Methylmercapto-s-triazines
RT 1n.y = po(gas) - p"(1iq) + RT In ( P / X ) = f(T) # f ( X ) and, therefore
p(1iq) = p o ( h ) + RT In X with
( P l X )= P(h) p o ( h ) = po(liq) + RT In y; y = P ( h ) / p " Equation 3 is in the form for ideal solution behavior and Equation 4, while being the statement of Henry's law, is in the form of Raoult's law. Equation 5 relates the standard state chemical potential in Equation 3 to that of the pure liquid solute plus a change in chemical potential going from a real pure state to a hypothetical one. Thus, with the hypothetical nature of the solute standard state recognized, the solution behavior can be treated as that for ideal solutions. The solution behavior is ideal for the 124
11.53 8.17 10.07 5.34 5.09
Ind. Eng. Chern. Prod. Res. Develop., Vol. 10, No. 2, 1971
Simetryne Ametryne Prometryne Trietatryne Ipatryne
213.3 227.3 241.4 241.4 255.4
...
...
5.24 5.27 8.91 5.70
5.15 5.27 9.54 6.04
5.43 . . . 5.18 . . . 5.27 =t 0.16 9.23
...
Enthalpy of fusion given in (kcal/mol). * Measured values obtained from Perkin-Elmer Model DSC-1B Differential Scanning Calorimeter. ' Measured values obtained from a Model DTA-12A Differential Thermal Analysis Apparatus, a product of R2bert L. Stone Co. (now a Division of Tracor, Inc.), Austin, Tex. Values calculated from solubility data. The errors are the standard deviations from the mean where three or more solubility values were used for this calculation.
pure liquid solute in a hypothetical state having an equilibrium vapor pressure P ( h ) a t T . The ideal nature of the solution behavior resulting from Equations 3 and 4 has suggested that the hypothetical state behavior reflects that of the second component, water, in its structural characteristics (Getzen, 1970). Also,
the study of the behavior of the solute in the hypothetical liquid state leads to an understanding of the enthalpy changes which result upon mixing a t infinite dilution. In addition, such considerations have led to general expressions which can be used to describe the aqueous solubility behavior of solid, liquid, and gaseous materials of low polarity. Combining Equations 2, 4, and 5 :
po(h)- po(gas) = R T In P ( h ) = &"(gas
-
liquid)(5)
where &.?(gas liquid) is the standard change in chemical potential from gas to liquid. If the structural nature of the standard state is considered, then the corresponding enthalpy and entropy changes may be approximated by:
assumption is valid the excess change in free energy. Alo(ex), is small compared to the total change in free energy and it is a well-behaved function. This has been found true for a number of low-polarity organic solutes (Getzen, 1970), and the behavior of the excess change in free energy has been described by:
Apo(ex) = -(a
AH"(gas --+ liquid) a"(gas
-
-H"(vaporization)
(6)
liquid) zz -a"(sublimation)
(7)
Incorporating these relations into Equation 5 gives:
&"(gas
-+
liquid) = - H o ( v a p ) + TAS"(sub) + Ap"(ex) (8)
Where Abo(ex) is defined as an excess free energy of solution. Corresponding equations for the solution process for solids give for the change in standard state chemical potentials:
&'(solid
-
liquid) = -RT In X = l H o ( f u s )+ +"(ex)
(9)
using
-RT In P = H o ( s u b )- TAS"(sub)
(10)
H " ( f u s ) = AHo(sub) - AHo(vap)
(11)
and Both Equations 8 and 9 incorporate the assumption of marked structural characteristics of the hypothetical standard state of the liquid solute. Presumably when this
cT
+ bTL)- dT(T - e)'
h H " ( e x ) = - ( a - bT')
-+
and
-
(12)
with corresponding excess enthalpy and entropy changes given by:
+ 2 dTL(T- e)
(13)
and
s S o ( e x )= -(c - 2 bT) + d ( 3 T
-
e ) ( T - e ) (14)
Incorporating these relationships into Equation 9 and making use of the observations that for solid solutes the parameter, a , can be taken as zero and for the low-polarity solutes the parameters a! and e remain unchanged, one obtains:
-RT In X
+ dT(T - e)' = AHo(fus) + T(c - bT) = f(X,T,d,e) (15)
Thus, a plot of f ( X , T , d , e )vs. T shows a quadratic behavior which can be used to determine values for AHo(fus), b , and e. Furthermore, if values of AH0(fus) are known, then the values of b and c can be established from the linear plot of g[X,T,AH"(fus),a!,e]as given by:
d ( T - e)' - R In X - a H o ( f u s ) / T= c - bT = g[X,T,aH"(fus),d,e] (16) The determination of the parameters b and c from Equation 15 or 16 establishes the necessary quantities for the description of standard state changes in free energy, enthalpy, and entropy for the solution processes and it permits a comparison of the excess thermodynamic quantities for the solutes. I t should be noted here that the values for AHo(fus),as defined by Equation 11, are taken a t the melting point so that contributions to the standard ~~~~
~
~~
~
~~~
Table 111. Sublimation Parameters of Alkylamino-s-triazines" Compd
AHs, kcol/mol
AS?,eu/mol
AGB, kcal/mol
P x lo'.'
otm at 25" C
I. 2-Chloro-s-triazines Simazine Atrazine Propazine Trietazine Ipazine Chlorazine
31.26 (31.16)a 27.20 (27.65) 29.89 (29.54) (24.83) (24.34j (23.67)
Simatone Atratone Prometone Trietatone Ipatone
23.47 (23.06) 22.57 (22.78) 22.04 (22.23) (26.86) (22.71)
55.93 (55.92) 49.80 (49.84) 54.32 (54.30) (41.21) (41.27) (40.42)
14.58 (14.49) 12.35 (12.79) 13.69 (13.3,5) (12.54) (12.03) (11.62)
0.02 (0.02) 0.88 (0.42) 0.09 (0.16) (0.64) (1.51) (3.01)
11.18 (11.16) 11.08 (11.11) 11.24 (11.23) (12.94) (12.05)
6.41 (6.58) 7.53 (7.16) 5.71 (5.86) (0.33) (1.46)
11.89 (11.96) 11.79 (11.68) 11.67 (11.74) (13.63) (12.27)
1.91 (1.70) 2.26 (2.74) 2.79 (2.49) (0.10) (1.01)
I I . 2 Methoxy-s-triazines ~
41.24 (39.91) 38.53 (39.15) 36.20 (36.91) (46.69) (35.73) 111. 2-Methylmercapto-s-triazines
Simetryne Ametryne Prometryne Trietatryne Ipatryne
24.22 (24.29) 24.11 (23.96) 23.89 (23.97) (27.92) (24.48)
41.33 (41.38) 41.31 (41.20) 40.99 (41.05) (47.94) (40.97)
'Sublimation parameters obtained from the vapor pressure constants reported by Friedrich and Stammbach (1964). Free energy values are for 25" C. ' Sublimation equilibrium pressure calculated from AG". All values in parentheses were obtained from smoothed solubility. sublimation, heat of fusion data as described in this work.
Ind. Eng. Chem. Prod. Res. Develop., Vol. 10, No. 2, 1971
125
IO
L1
I
I
I
I
I
5
02 - c h l o r o - s - t r i a z i n e s 0
0 2-methy Imercopto-s-triozines 2-methoxy-s - triazines ( e ) estimated value
-
z0
O
-5
0 @
E
I u)
n
P \ -10 .-0L
0
0
0
0-15
0Propoz ine I
0
-20
(e)
0 20
0
40 60 80 TEMPERATURE, "C
100
Figure 1. Values of g[X,T,AH"(fus),d,e] vs. centigrade temperature for 2-chloro-s-triazines, 0 ; 2-methoxy-s-triazines, e; and 2-methylmercapto-s-triazines, 0
1
I
200
210
1
1
I
220 230 240 FORMULA W E I G H T
Figure 2. Values of c[X,T,SH"(fus),b,d,e] for alkylamino-s-triazines
- 14
250
I
550
- 12
500
-
- IO 5 -.-
-
-8
Q 5 200
!50
L
0)
E
Y
0 -
0
\
200
E
E
Y
0.
-= :
150 E
E
-4
Simazine
50 -_
IO0
IO0
-2
OC
-.-c $ a
\
TEMPERATURE,
i
IO0
2 - m e t hoxy-s- t r iozines
2.0
I
vs. formula weight
7,5r--
- 16
2-chloro-s-t r iozines
I
Trietotone
"
t
50
Prometone
IO
20
30
40
50
0
60
Figure 3. Solubility vs. temperature for 2-chloro-s-triazines: this laboratory, 0;Bailey and White (1965), e; and Knuesli et al. ( 1 969),
Figure 4. Solubility vs. temperature for 2-methoxy-s-triazines: this laboratory, 0; Bailey and White ( 1 965),e
free energy, enthalpy, and entropy changes due to heat capacity differences and the changes in such differences with temperature are incorporated in the compound specific constants a, b , and e. Values for g[X,T,aH"(fus),d,e]were calculated for all triazines with known solubilities and molar heats of fusion. The solubilities reported in Table I and average observed
heats of fusion from Table I1 along with the values of 0.000408 for d and 291.15 for e (Getzen, 1970) were used for these calculations. Figure 1 shows the behavior of g[X,T,H"(fus),d,e] vs. centigrade temperature for the compounds with known solubilities at two (including 50" C ) or more temperatures. The appearance of the figure suggests that the slope is the same for all the compounds,
e
126
Ind. Eng. Chem. Prod. Res. Develop., Vol. 10, No. 2, 1971
within experimental error. Therefore, a common value of -0.04 for b was determined and used throughout the remaining calculations. Equation 16 can be rearranged to obtain values of the parameter c from the common b , d, and e values and the measured solubilities and heats of fusion. This is given by:
c[X,T,AHo(fus) ,b,d,e] = g [ X , T , ~ H " ( f u s ) , d ,+e ]bT
(17)
Thus, for the compounds with known heats of fusion and solubilities a t one or more temperatures, one can obtain values for the parameter c subject to the restriction that the parameters b, d , and e are common to all compounds of the series. Equation 17 was used to establish the c values for all compounds with measured solubility and heat of fusion values. These c values are shown in Figure 2. Also shown in this figure are estimated c values for those compounds for which heats of fusion were not measured (Chlorazine, Trietatone, and Simetryne) and for which solubilities were not determined (Ipatryne). The estimated c values are identified by the notation, e, in the figure. The estimates for the unknown c values were obtained from linear extrapolations through known c values as indicated in Figure 2. The known c values show a definite increasing trend with molecular weight. There is also an additional recognized displacement of the c values for different compounds having the same molecular weight. Most of the known c values fall in one linear pattern with the c values for two structural isomers falling below. Linear extrapolations in the first group were used for the estimated c values of Chlorazine, Simetryne, and Ipatryne; and a linear extrapolation of the c values of the two structural isomers was used to obtain an estimated
-
c value for Trietatone which is a structural isomer of a compound (Prometone) having a c value in the first group. With individual c values determined for each compound, Equation 16 can be used to establish a heat of fusion from a measured solubility. The calculated heats of fusion values in Table I1 were determined from Equation 16 using the c values shown in Figure 2. The standard deviations shown were obtained from mean l H o ( f u s ) values calculated from solubilities a t three or more temperatures with the parameters b , e , d , and e in Equation 16 held a t their constant values. The calculated LH"(fus) values for Chlorazine and Trietatone were obtained by using the estimated c values. In the absence of a solubility measurement for Ipatryne. no heat of fusion value could be obtained from Equation 16. However, by using the measured heat of fusion (Table 11) for this compound and the estimated c value from Figure 2, one can calculate its solubility as a function of temperature. This solubility value is shown in parentheses in Table I for 26OC. Once the excess free energy parameters b , e, d, and e have been established (for solid solutes), the values of solubility vs. temperature can be determined from values of l H o ( f u s ) . Also, the behavior of the excess thermodynamic parameters (free energy, enthalpy, and entropy of solution) can be described through Equations 12-14. Figures 3-5 show the calculated and measured solubilities as functions of temperature for, respectively, the 2-chloro-s-triazines, the 2-methoxy-s-triazines, and the 2-methylmercapto-s-triazines. With the parameters a , b , d, and e common for all compounds, the behavior of the excess free energy of solution, the excess enthalpy of solution, and the excess entropy of solution falls into a simple pattern. From Equation 13. one sees that the exce 3- enthalpies are the same for all compounds of this
3I- - -
-
2 met h y Imercapto s- t r ia z i nes
I
/ lpatryne
L
0 c
.--
O I 5
E
//
-+
' 0
0.1
i
IT
-
/
--I
a
Q
2
-10-
--2
0
-c
X
--. Y
0)
0
X
Q
0 0
X
0
20
i
-.-
0
V.
E
.-
Atrazine
X Q
: \ 0
Av,'(ex)
3: - 5 -
-
-0
//
0
\
E
-Q
0.2
-15-
--3
-20 -
--4
0 v)
a
IO Prometryne
0
0
Figure 5. Solubility vs. temperature for 2-methylmercaptos-triaziney this laboratory, 0 ; Bailey and White (1965), 0
I 1 0
I
20
I
I
I
60 00 TEMPERATURE,OC
40
I
100
Figure 6. Excess standard molar enthalpy of solution, excess standard molar entropy of solution, and AF"(ex)/T for Atrazine vs. temperature
Ind. Eng. Chem. Prod. Res. Develop., Vol. 10, No. 2, 1971
127
ISo(gas -+ liquid) = -lS'(sub) I
I
I
I
+- IS'(ex)
(19)
and Equations 8 and 11. The Sublimation data for the determination of l H o ( s u b ) and &So(sub) for these nine compounds were from Friedrich and Stammbach (1961). All quantities are shown as a function of formula weight. Similarly. Figures 10-12 show. respectively, the corresponding changes from solid to liquid for all triazines in this study as obtained from:
I
m"(so1id i liquid) = IHo(fus)+ d-I"(ex) (20) Go(solidi liquid) = AS0(ex)
T I
3
I
200
I
I
210 220 230 FORMULA WEIGHT
I
240
0
Figure 7. Standard molar enthalpy of solution from the gas state vs. formula weight for 2-chloro-s-triazines, 0 ; 2-methoxy-s-triazines, 0 ; and 2-methylmercapto-s-triazines, 0
series. (The differences in this quantity are dependent upon differences in the parameter b . ) From Equation 14, one sees that the excess entropies are parallel functions of temperature, differing in the parameter c for the different compounds. Likewise, from Equation 12. one sees that values for l p " ( e x ) / T are parallel functions of temperature, differing also in the parameter c for the different compounds. Figure 6 shows the common behavior of the excess enthalpy of solution vs. temperature and the typical behavior of the excess entropy of solution and $"(ex) / T vs. temperature. Because of the common excess enthalpy of solution and the parallel temperature dependence of the excess entropy of solutions, the relative values for these quantities, as well as those for excess free energy of solution, are temperature independent for the series of compounds. Thus, a comparison of the excess parameters a t one temperature serves to identify their relative magnitudes throughout the entire range of temperatures involved in this work. Furthermore, because of this simplicity of behavior. the relative comparison of total changes in free energy, enthalpy, and entropy at one temperature for a solution process remains valid a t other temperatures. For this reason, the further comparison of the thermodynamic parameters is made a t only one temperature, 25" C. Figures 7-9 show, respectively, the standard state changes of enthalpy, entropy, and free energy per mole from gas to solution for nine of the triazines as obtained from:
IH"(gas 128
-
liquid) = -3Ho(vap) + 3Ho(ex) (18)
Ind. Eng. Chern. Prod. Res. Develop., Vol. 10, No. 2, 1971
(21)
and Equation 9. Figures 7-9 show that the variations are, within a reasonable range of error, linear with formula weight. This observation was used to determine sublimation thermodynamic parameters for the remaining compounds of this study. Linearized values for standard thermodynamic parameters were obtained from the straight lines in Figures 7-9 for each compound of this study. The lines were established by the method of least squares taking the variation of *"(gas + liquid) vs. formula weight as common for the three series of compounds (the chloro-, the methoxy-, and the methylmercapto-s-triazines). The smoothed values were then combined with the heats of fusion and excess thermodynamic parameters through Equations 11, 18, and 19 to give values for the standard enthalpy and entropy of sublimation. These calculated values are shown in Table I11 in parentheses along with the corresponding values obtained from reported work (Friedrich and Stammbach, 1964). Also included in this table are the standard free energies of sublimation and the sublimation pressures calculated for 25" C. For the nine triazines with reported sublimation data, the average deviation (absolute values) for the standard enthalpies of sublimation (obsd - calcd), is 0.87% and the average deviatidn for the standard entropies of sub-
I
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250
Figure 8. Standard molar entropy of solution from the gas state vs. formula weight for 2-chloro-s-triazines, 0;2-methoxy-s-triazines, 0 ;and 2-methylmercapto-s-triazines, 0
limntion is 0.835 with both deviations random-Le., the sums of the deviations are 0. Thus, an error of about 300 cal could be expected for a calculated heat of sublimation of 30 kcal and an error of about 0.5 entropy unit could be expected for a calculated entropy of sublimation of 55 entropy units. These ranges of error are shown in Figures 7-9. The error shown for the standard free energies of sublimation is a l " 0 error obtained from the average of the absolute values of its (obsd - calcd) deviations. I t can be noted that the 300-cal uncertainty in the enthalpy of sublimation is comparable to the maximum standard deviation errors found for the calculated heats of fusion given in Table 11. Discussion of Results
The aqueous solubilities of the structurally related alkylamino-s-triazines of this study are typical for compounds of low polarity in water. The singular structural characteristics of liquid water as a solvent exert the primary influence on the degree of solubility which is observed. However, despite this complex nature of the solution behavior, it has been possible to establish a reasonably clear description of the solution process in terms of thermodynamic parameters. The solution process is best considered as that suggested by Franks and Ives (1966) to be a nonspecific accommodation of the stearic requirements of the solute molecule through an intrinsic cavity-stabilizing ability of water due to its three-dimensional hydrogen bonding ability. This picture of the solution process has led to a quantitative treatment of solution involving a common influence of water structure, a single interaction parameter (the parameter e ) , and thermodynamic parameters of the pure solute. Thus. while the computations are somewhat more detailed than those for ideal solution behavior, the description of the solution process has been accomplished with a minimum of computational parameters. The solution behavior can be analyzed in terms of the influence of the water structure and of the specific contributions of the solute material. The common influence of the water structure is revealed in the behavior of the standard changes in free energy as given by Equations 8 and 9. The assumption is that the solute in its hypothetical state (X = 1) reflects the state of the pure solvent, water, since the two are mixed as an ideal solution. Thus, the water structure manifests itself in the behavior of the hypothetical state of the solute. This behavior is deduced relative to the gaseous or solid solute in a standard state through, respectively, Equation 8 or 9. In the consideration of the influence of the water structure on solubility, the magnitude and behavior of the excess free energy term in Equations 8 and 9 are of particular significance. I n the absence of this term, both equations imply a hypothetical standard state of the solute as liquid in terms of enthalpy and solid in terms of entropy. The same state is inferred for the water under such conditions. The behavior of the excess free energy term, then, reveals the departure of the hypothetical state and the water from this simple model. In this study, the behavior of the excess free energy is established by the use of common parameters which have been attributed to properties of the water ( b , d , and e ) and a single solute specific parameter, e. These results lead to a reasonably simple, straightforward interpretation of the effects of water structure on the
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Figure 9. Standard molar free energy of solution from the gas state vs. formula weight for alkylamino-s-triazines
solution behavior. I t should be emphasized here that more extensive solubility measurements with greater precision than those reported in this work might reveal differences in the parameter, b. However, only small differences in b have been found in this laboratory for a wide range of low-polarity solutes (Wauchope. 1970) and such differences are well within the range of experimental error for this present work. Y o evidence of variations of the parameters d and e among low-polarity solutes has been found. Figure 1 reveals that for a constant b value, a c value can be established from a solubility measured a t a single temperature plus the measured heat of fusion. Thus, one might consider that the conparisons made here are those for a single temperature combined with the influence of the structure of the water. The absence of either a single solubility measurement or the heat of fusion value requires an estimate of the values of c. Figure 2 indicates that a reasonably ordered behavior of c vs. formula weight for a homologous series permits the estimation of a missing c value. Once such c values have been established, the solubilities vs. temperature can be calculated. Figures 3-5 show an excellent agreement between measured and calculated solubility values considering the fact that only one adjustable (solute specific) parameter, e, is involved in the calculations. The general behavior of the excess thermodynamic parameters vs. temperature as illustrated in Figure 6 is typical of the low polarity solutes. Both excess entropy and excess enthalpy values increase with increasing temperature. The combination of these two nonlinear, temperature-dependent parameters yield a nonzero, nonlinear excess free energy parameter. Behavior of the three excess thermodynamic quantities is best explained in terms of the excess entropy. The increasing excess entropy with Ind. Eng. Chem. Prod. Res. Develop., Vol. 10, No. 2, 1971
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Figure 10. Standard molar enthalpy of solution from the solid state vs. formula weight for 2-chloro-s-triazines, 0 ; 2-methoxy-s-triazines, 0 ; and 2-methylmercapto-s-triazines, 8
Figure 1 1 . Standard molar entropy of solution from the solid state vs. formula weight for alkylamino-s-triazines
temperature suggests a breakdown in the structure character of the hypothetical state. The same structure breakdown can be inferred for the water. The increase in the excess enthalpy with temperature results from the breakdown of the water structure and reflects the increase in the energy requirement for cavitation as the water loses its ability to structurally accommodate solute molecules and becomes more like organic solvents (Eley, 1939). The behavior of the excess free energy is, of course, the result of the combined behavior of the other two excess thermodynamic parameters. The simplicity of the behavior of the excess thermodynamic quantities vs. temperature in this work allows a comparison of relative values of the thermodynamic solution parameters a t any convenient temperature. However, it should be emphasized that none of these quantities can be taken as independent of the temperature and care must be taken to make comparisons a t the same temperature. From Figure 6, one should expect a change of more than 15 entropy units for the entropy of solution and a change of more than 5 kcal for the enthalpy of solution as the temperature increases from 0-80’ C. This strong-temperature dependence of the entropy and enthalpy of solution accounts for the observed nonlinear behavior of vs. T for these and other lowpolarity solutes in water (Claussen, 1952) and is again a common reflection of the strong structural changes of the solvent with temperature. Thus, the two major contributions of the water to the solution behavior are the general restriction of solubility by its ordered structure and the marked temperature dependence of solubility due to breakdown of water structure with increasing temperature. A treatment of solution from the gaseous state rather than from the liquid or solid states is desirable in that such treatment eliminates complications of the condensed
phase structure (Butler, 1962; Herrington, 1944, 1951; Thomas, 1968). Figures 7-9 show that a simple pattern of solution behavior results for the gas to solution process. These plots of standard state changes in molar enthalpy, molar entropy, and molar free energy for the solute from gas to liquid a t 25OC are sufficiently well behaved t o be linearized. For the change in enthalpy, the values fall less than 1 kcal apart in each separate series. Differences are observed between the 2-chloro-, the 2-methoxy-, and the 2-methylmercapto-s-triazines,but no significant differences are observed for increasing (-CH,-) groups within a series. The slight negative slope of the lines results from a restriction of the slopes to a common value in the least squaring of the enthalpy, entropy, free energy values of the three figures. For the standard entropy change, Figure 8 shows a definite linear decrease with formula weight for each group of compounds. This behavior suggests that the larger molecules lose somewhat more freedom or flexibility than the smaller ones as they are dissolved or condensed under standard state conditions. It is reasonable to assume then that the changes observed in the standard state entropy of solution result more from increases in the absolute entropy of the gases with formula weight rather than from decreases in absolute entropy of the solute in its hypothetical standard state, the former being attributed to increased degrees of freedom while the latter being attributed to an increased restriction to motion in the condensed phase. The behavior of the molar free energy values of Figure 9 result from the combined behavior of the molar enthalpy and molar entropy values of Figures 7 and 8. The scattering of the molar free energy values for the 2-chloros-triazines is due t o a scatter in the molar enthalpy values since the molar entropies are quite linear. However, the differences in enthalpy values for this family of compounds
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in Figure 7 are quite small when compared with the corresponding values for the same compounds in Figure 10 which shows the standard enthalpy of solution from the solid state. I t is reasonable to speculate that the scatter of the thermodynamic quantities may be due to errors in the heat of fusion measurements for the Z-chloros-triazines and the 2-methylmercapto-s-triazines because of the excellent linearity of the standard state changes in entropy from gas to liquid and to errors in the sublimation data for the 2-methoxy-s-triazines because of the excellent linearity of the standard state changes in free energy. Figures 10-12 show the standard-state changes in molar enthalpy, molar entropy, and molar free energy for the solute from solid to liquid a t 2 F C . There figures show a somewhat more complex behavior for the thermodynamic quantities than the corresponding parameters of Figures 7-9. From a comparison of the thermodynamic parameters for the standard change in state from gas to liquid and from solid to liquid, it is clear that differences in the structure of the pure solid solutes account for much of the complex solubility behavior observed. Of particular note are those compounds for which complete sublimation, solubility, and heat of fusion data are known. For the 2-methoxy-s-triazines and the 2-methylmercapto-s-triazines, the solid to liquid standard enthalpy and standard entropy changes are well behaved, indicating little effects from structural differences in the solids. The 2-chloro-s-triazines, on the other hand, show complications in the behavior of both standard ehthalpy and standard entropy changes from solid to liquid attributable to structural differences in the pure solid solutes since the nonlinear behavior is absent (within experimental error) from the corresponding gas to liquid parameters. The combination of the standard enthalpy changes of Figure 10 and the standard entropy changes of Figure 11 yields the standard free energy values of Figure 12. The pattern of behavior of the standard free energy changes reflects the relative solubility behavior for the entire series of structurally related alkylamino-s-triazines. The analysis of the behavior of the thermodynamic solution parameters for the standard state changes from gas to liquid and from solid to liquid reveals that a primary contribution to the observed relative complex solution behavior is the differences in the structure of the pure solid solutes and not an unusual interaction of the solutes with the solvent. No attempt has been made in this study to ascertain the structural nature of water other than in a thermodynamic sense. The structure referred to for water is implied from the entropy changes which the solute must undergo as it assumes the hypothetical state a t any temperature. When the pure solute is in the hypothetical state, i t can be mixed with water following ideal solution behavior. Therefore, it is assumed that the two pure components of such an ideal binary mixture must be of similar (thermodynamic) structural character. It is important to note that the unique character of water as a solvent is strongly dependent upon temperature. Therefore, it is unwise to consider the thermodynamic state of water without reference to temperature. The physical chemical nature of water is that of a highly ordered or structured system at room temperature as evidenced by its low entropy relative to that which it would have were it a simple liquid (Miller and Hildebrand, 1968).
However, with increasing temperature, the entropy and enthalpy of water increase smoothly, more or less paralleling the changes shown in Figure 6 for S o ( e x ) and l H o ( e x ) for solutes, so that for temperatures in the range of 120°C, the physical chemical nature of water is more that of a liquid which forms regular solutions with nonpolar solutes (Shinoda and Fujihira, 1968). These changes continue so that above 250" C, the solution behavior of water is much like a normal liquid (Marchi and Eyring, 1964). Thus, one can certainly say there is a smooth breakdown of water structure with increasing temperature. I t is reasonable to attribute the singular physical chemical nature of water to the presence and distribution of hydrogen bonds in the system. Certainly, there is current evidence that such bonds exist in abundance a t room temperatures and that they are broken more and more a t the higher temperatures. However, the thermodynamic indications of a singular structural character of water and of the changes in its structural character with temperature given in this work are not sufficient evidence for a unique molecular description of liquid water. Therefore, speculations concerning the actual molecular description of liquid water need not be made here. An accurate, detailed account of the various models proposed for water has been presented elsewhere (Nemethy and Scheraga, 1962). The limitations of the detailed thermodynamic studies of aqueous solubility behavior do not impose serious restrictions upon their practical use. The approach presented here has been used successfully to treat several nonpolar gases, liquids, and solids from measurements reported in the literature (Getzen, 1970), and it has been tested extensively with measured solubilities of solid aromatic hydrocarbons and with literature solubility values for numerous gaseous and liquid hydrocarbons including the alkanes, the olefins, the cycloalkanes, the cycloolefins, and the alkylbenzenes spanning the C, through C16 range (Wauchope, 1970) with equally good results. Thus, in
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a very practical sense, the unique structural character of water as a solvent, especially a t room temperatures, suggests that this thermodynamic treatment is applicable to the nonpolar solutes in general and that it can be applied to the aqueous solution behavior of such materials with confidence. Conclusions
The aqueous solution behavior of a series of structurally related alkylamino-s-triazines has been established. A quantitative thermodynamic treatment of the solution behavior reveals the primary factor controlling their aqueous solubilities is the structural character of the water. This work also reveals that a breakdown of water structure with increasing temperature is evident in the observed solution behavior. Finally, it is revealed that the differences in aqueous solubilities of certain of the structurally related compounds can be attributed to differences in the structure of the pure solid solutes. Techniques for obtaining estimates of heats of fusion from aqueous solubility data and aqueous solubilities from heats of fusion data for low polarity solid solutes have been illustrated. These techniques are based upon the unique structural character of water and they show a considerable promise in the case of the low polarity nonelectrolyte. I t is obvious, however, that extended verification is needed and the limitations and degree of accuracy should be investigated further. I t is to be noted that only one compound specific interaction parameter, c, was required for this work. The other parameters used were those of the pure solute and the common parameters attributable t o the water structure. The simplicity of this treatment suggests that it can be used for understanding and interpreting the wealth of available published solubility data. The treatment lends itself to easy application for comparisons of solubilities of structurally related series of compounds. I t should be noted, however, that this treatment is restricted to the aqueous solubilities of the low-polarity nonelectrolytes and that it should not be applied to the cases of strong solutewater interactions-e.g., strong electrolytes.
David, D. ,J., A n a l . Chem.. 36. 21G2 (19641. Eley, D. D., Trans. Farada) Soc.. 3.5. 1281 (19391. Feates, F. S..Ives, D. J. G.. J . Chem. Soc.. 279d (1956). Frank, H. S.,“Desalination Research Conference.“ Pub. 942, p 141, National Academy of Science-National Research Conference, 1962. Frank, H. S., Evans, M. W., J . Chem. PhJs., 13, 507 (1945). Franks, F., Ives, D. J. G., Quart. Rev. (London), 20, 1 (1966). Freed, V., in “Pesticides and Their Effects on Soil and Water,” S.A. Breth, Ed., ASA Special Publication No. 8, Soil Science Society of America, Inc., Madison, Wis., 1966. Friedrich, K., Stammbach, K., J . Chromatog., 16, 22 (1964). Getzen, F. W., in “Liquid Crystals and Ordered Fluids,” J. F. Johnson and R. S. Porter, Eds., Plenum, New York, N. Y., 1970. Herrington, E. F. C., J . Amer. Chem. Soc., 73, 5883 (1951). Herrington, E . F. G., Trans. Faraday Soc., 40, 481 (1944). Jeffrey, G. A., Dechema-Monographien, 47, 849 (1962). Kauzmann, W., Aduan. Protein Chem., 14, 1 (1959). Knuesli, E., Berrer, D., Dupuis, G., Esser, H., in “Degradation of Herbicides,” P. C. Kearney and D. D. Kaufman, Eds., Marcel Dekker, New York, N. Y., 1969. Lindman, B., Forsen, S., Forslind, E., J . Phys. Chem., 72, 2805 (1968). Marchi, R. P., Eyring, H., ibid., 68, 221 (1964). Miller, K. W., Hildebrand, J. H., J . Amer. Chem. Soc., 90, 3001 (1968). Nemethy, G., Scheraga, H. A., J . Chem. Phys., 36, 3382 (1962). Pauling L., “The Nature of the Chemical Bond,” 3rd ed., Cornel1 University, New York, N. Y., 1960. Shinoda, K., Fujihira, M., Bull. Chem. Soc. Japan, 41, 2612 (1968). Spaght, M. E., Thomas, S. B., Parks, G. S., J . Phys. Chem., 36, 882 (1932). Thomas, L. H., J . Chem. Soc., A:1968, p 2609. Ward, T. M., Weber, J. B., J . Agr. Food Chem., 16, 959 (1968). Wauchope, R . D., PhD dissertation, North Carolina State University, Raleigh, N . C., 1970.
Literature Cited
Bailey, G. W., White, J. L., Residue Reu., 10, 7 (1965). Butler, J. A. V., “Chemical Thermodynamics,” 5th ed., Macmillan, London, 1962. Chadwell, H. M., Chem. Reu., 4, 375 (1927). Claussen, W. F., J . Amer. Chem. Soc., 74, 3937 (1952). Claussen, W. F., J . Chem. Phys., 19, 259, 662, 1425 (1951).
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RECEIVED for review August 28, 1970 ACCEPTED April 1, 1971 Presented a t the Division of Colloid and Surface Chemistry, 158th Meeting, ACS, New York, N. Y., September 1969. This study was supported by Public Health Service research grant FD-0023704 from the Food and Drug Administration.
