Selecting internally consistent physicochemical properties of organic compounds

INTRODUCTION

The environmental partitioning behavior of organic chemicals usually is described on the basis of the partitioning between the pure liquid phase, the gas phase, and the dissolved phases in water and n-octanol. This partitioning behavior finds quantitative expressions in the use of the six partitioning coefficients between these phases, such as the vapor pressure, solubility in water, and octanol-water partition coefficient (K_OW). In addition, enthalpies or heats of phase change, such as the heat of solution, are used to express the temperature dependence of these partition coefficients. Cole and Mackay [1] set out the fundamental thermodynamic relationships between these properties, which enable properties to be derived from each other. One common example is Henry's law coefficient (H), which is often estimated as the ratio of saturation vapor pressure (P^s) and water solubility (S_w) [2], thus avoiding the necessity of measuring all three quantities. A check of consistency is possible if all three measurements are available. When measured or estimated data are available for all three properties, they usually are not fully consistent with these constraints. However, when performing model calculations, internally consistent substance data are needed. Those consistent data usually were obtained by calculating data from others, even if measurements of the property are available. For instance, the suggested Henry's law coefficients are always calculated from P^s and S_w by Mackay et al. [2]. Although this approach yields internally consistent chemical properties, it omits available information and it requires judgement, because one could also calculate the water solubility from H and P^s to get consistent data. Here, we address the issue of analyzing such reported values to obtain a consistent set of data, while taking advantage of all measured properties and exploiting the fundamental thermodynamic constraints to which they are subject. The suggested procedure has the additional advantage that it avoids any judgment by the user, and hence the procedure can be incorporated into automated data processing.

When approaching this issue, we need to be aware that the thermodynamic relationships between these properties are not necessarily absolute. For example, when estimating K_AW as the ratio of the saturation vapor pressure and water solubility, we assume that this ratio approximates the air-water partition coefficient at much more dilute conditions. Measurements of K_AW are typically conducted at conditions far from saturation, and environmental conditions usually are also far from saturation in both gas and aqueous phase. Schwarzenbach et al. [3] showed that this rests on the assumption that the aqueous solution activity coefficient does not change as a function of solute concentration, and concluded that this is a reasonable approximation for compounds that are slightly or even moderately soluble in water (<1.5 mol/L).

AN EXAMPLE OF WATER SOLUBILITY, VAPOR PRESSURE, AND HENRY'S LAW CONSTANT

In the following, the suggested approach of obtaining consistent values for P^s, S_w, and H is derived by using 4,4′-dichlorobiphenyl (polychlorinated biphenyl [PCB] 15) as an example. First, the assumption is made that only one measured value exists for each chemical property. If more than one measurement exists for a given property, the most reliable value can be selected or a weighted mean of all values can be calculated. Measured properties at 25°C for PCB 15 are presented in Table 1. The Henry's law coefficient derived from the vapor pressure and water solubility is 17.49 Pa m³/mol, which deviates from the two measured values of 9.66 and 18.94 Pa m³/mol. The actual value probably lies in the range 9 to 20 Pa m³/mol.

As a first step, all properties are transformed into solubilities in units of mol/m³ or dimensionless partition coefficients. The Henry's law coefficient is converted into the dimensionless air-water partition coefficient according to

(1)

Here R is the gas constant 8.314 J/(mol K) and T is absolute temperature (298.15 K in this case).

Table Table 1.. Selected literature values at 25°C for air, water, and octanol solubility, and air-water, octanol-water, and octanol-air partition coefficients. Values with more than one reference are median of cited properties^a

Compound	P (Pa)	References	(mol/m3)	References	SOI (mol/m3)	References	KAW	References	log KOW	References	log KOA	References
PCB 15	7.26 × 10−2	[18]	4.06 × 10−3	[11]	NA		5.77 × 10−3	[26, 27]	5.23	[19]	7.66b	[6]
PCB 28	3.41 × 10−2	[18]	9.28 × 10−4	[11]	NA		1.17 × 10−2	[9]c	5.71	[19]	NA
PCB 29	4.47 × 10−2	[18]	2.18 × 10−3	[11]	NA		1.12 × 10−2	[9]c	5.75d	[19]	7.95b	[6]
PCB 30	9.69 × 10−2	[18]	1.63 × 10−3	[11]	NA		2.71 × 10−2	[26]	5.52d	[19]	NA
PCB 31	3.46 × 10−2	[18]	8.63 × 10−4	[2]	NA		7.77 × 10−3	[28]	5.68	[19]	7.92e	[7]
PCB 33	2.64 × 10−2	[18]	6.90 × 10−4	[2]	NA		NA		5.71	[19]	NA
PCB 44	1.28 × 10−2	[18]	5.65 × 10−4	[2]	NA		1.06 × 10−2	[9]c	5.73	[19]	8.36	[7]
PCB 47	1.53 × 10−2	[18]	1.15 × 10−3	[2]	NA		7.77 × 10−3	[28]	5.94	[19]	NA
PCB 52	1.61 × 10−2	[18]	3.25 × 10−4	[11]	7.43 × 102	[5]	1.30 × 10−2	[9]c	5.79	[19]	8.22	[7]
PCB 61	1.21 × 10−2	[18]	4.42 × 10−4	[11]	9.12 × 102	[5]	1.08 × 10−2	[26]	6.15d	[19]	8.73b	[6]
PCB 77	2.20 × 10−3	[18]	8.39 × 10−5	[11]	NA		4.02 × 10−3	[9]c	6.1 ld	[19]	9.70b	[20]
PCB 95	5.32 × 10−3	[18]	NA		NA		4.91 × 10−3e	[28]	5.92	[19]	8.75	[7, 20]
PCB 101	3.39 × 10−3	[18]	1.40 × 10−4	[11]	NA		1.02 × 10−2	[9]c	6.39d	[19]	8.93e	[7, 20]
PCB 105	8.74 × 10−4	[18]	NA		NA		4.07 × 10−3	[9]c	6.79	[19]	10.01	[20]
PCB 110	1.83 × 10−3	[18]	4.15 × 10−5	[2]	NA		NA		6.20	[19]	9.06	[7]
PCB 116	2.31 × 10−3	[18]	2.33 × 10−4	[2]	NA		1.26 × 10−2	[26]	6.46d	[19]	NA
PCB 118	1.19 × 10−3	[18]	NA		NA		9.86 × 10−3	[9]c	6.57	[19]	9.82	[20]
PCB 126	4.87 × 10−4	[18]	NA		NA		3.34 × 10−3	[9]c	6.67d	[19]	10.35	[20]
PCB 138	5.14 × 10−4	[18]	NA		NA		5.32 × 10−3	[9]c	6.73	[19]	9.66e	[7, 20]
PCB 153	6.83 × 10−4	[18]	1.37 × 10−5	[11]	NA		6.98 × 10−3	[9]c	6.80	[19]	9.55	[7, 20]
PCB 180	1.32 × 10−4	[18]	NA		NA		8.33 × 10−3	[9]c	7.21	[19]	10.20	[7, 20]
p,p′-DDT	3.08 × 10−4	[2]	2.39 × 10−4	[2]	1.61 × 103	[5]	5.28 × 10−4	[29]	6.19	[2]	9.81	[21]
p,p′-DDE	4.82 × 10−3	[2]	5.40 × 10−4	[2]	NA		1.70 × 10−3		5.70	[30]	9.67	[21]
α-HCH	1.42 × 10−1	[2]	1.15 × 10−1	[2]	NA		3.09 × 10−4	[12]	3.81	[2]	7.61	[21]
γ-HCH	3.23 × 10−2	[2]	1.84 × 10−1	[2]	1.57 × 103	[5]	1.43 × 10−4	[12]	3.70	[2]	7.84	[21]
trans-Chlordane	5.78 × 10−3	[2]	8.30 × 10−4	[2]	NA		NA		6.00	[2]	8.86	[21]
cis-Chlordane	4.71 × 10−3	[2]	9.07 × 10−4	[2]	NA		NA		6.00	[2]	8.91	[21]
Chlorobenzene	1.58 × 103	[11]	4.30 × 100	[11]	NA		1.48 × 10−1	[12]	2.80	[2]	NA
1,2,4,5-TetraCBz	1.08 × 101	[11]	4.16 × 10−2	[11]	1.80 × 103	[5]	4.07 × 10−2	[31]	4.50	[2]	5.65c	[6]
1,2,3,5-TetraCBz	1.02 × 101	[11]	3.32 × 10−2	[11]	2.82 × 103	[5]	6.45 × 10−2	[32]	4.50	[2]	NA
Pentachlorobenzene	9.02 × 10−1	[11]	8.19 × 10−3	[11]	1.13 × 103	[5]	2.86 × 10−2	[12]	5.00	[2]	6.28c	[6]
Hexachlorobenzene	9.37 × 10−2	[11]	7.15 × 10−4	[11]	5.63 × 102	[5]	1.79 × 10−2	[12]	5.50	[2]	7.38	[21]
Naphthalene	3.36 × 101	[10]	7.95 × 10−1	[10]	2.29 × 103	[5]	1.72 × 10−2	[12]	3.37	[2]	NA
Biphenyl	3.51 × 100	[10]	1.26 × 10−1	[10]	2.00 × 103	[5]	1.26 × 10−2	[32]	3.90	[2]	NA
Acenaphthene	1.60 × 100	[10]	1.31 × 10−1	[10]	1.37 × 103	[5]	7.46 × 10−3	[8]	3.92	[2]	NA
Fluorene	5.96 × 10−1	[10]	7.57 × 10−2	[10]	1.59 × 103	[5]	3.96 × 10−3	[8]	4.18	[2]	6.79	[33]
Phenanthrene	8.87 × 10−2	[10]	2.74 × 10−2	[10]	1.57 × 103	[5]	1.73 × 10−3	[8]	4.57	[2]	7.60	[33]
Anthracene	1.73 × 10−2	[10]	2.18 × 10−2	[10]	1.06 × 103	[5]	2.28 × 10−3	[8]	4.54	[2]	NA
Fluoranthene	5.23 × 10−3	[10]	6.73 × 10−3	[10]	9.09 × 102	[5]	7.91 × 10−4	[8]	5.22	[2]	8.87	[33]
Pyrene	1.09 × 10−2	[10]	1.18 × 10−2	[10]	2.28 × 103	[5]	6.90 × 10−4	[8]	5.18	[2]	8.81	[33]
Benzo[a]pyrene	7.35 × 10−6	[10]	1.25 × 10−4	[10]	2.64 × 102	[5]	1.86 × 10−5	[12]	6.04	[2]	NA
Benz[a]anthracene	4.42 × 10−4	[10]	7.61 × 10−4	[10]	NA		4.92 × 10−4	[8]	5.91	[2]	NA
Chrysene	1.03 × 10−4	[10]	1.58 × 10−3	[10]	4.53 × 102	[5]	4.28 × 10−5	[34]	5.60	[2]	NA
2,3,7,8-TetraCDF	2.77 × 10−3	[35]	5.32 × 10−4	[11]	NA		6.86 × 10−4	[36]	6.10	[2]	10.01	[35]
1-MonoCDD	3.59 × 10−1	[11]	5.70 × 10−2	[11]	NA		NA		4.75	[2]	7.85	[35]
1,2,3,4-TetraCDD	1.14 × 10−3	[35]	1.51 × 10−4	[11]	NA		8.15 × 10−4	[36]	6.60	[2]	9.70	[35]
2,3,7,8-TetraCDD	2.17 × 10−3	[35]	1.46 × 10−4	[11]	NA		NA		6.80	[2]	10.04	[35]
1,2,3,4,7-PentaCDD	1.53 × 10−3	[35]	1.65 × 10−4	[11]	NA		NA		7.40	[2]	10.66	[35]
1,2,3,4,7,8-HexaCDD	8.78 × 10−4	[35]	7.58 × 10−5	[11]	NA		NA		7.80	[2]	11.11	[35]
1,2,3,4,6,7,8-HeptaCDD	5.99 × 10−4	[35]	9.18 × 10−5	[11]	NA		NA		8.00	[2]	11.42	[35]

• ^a PCB = polychlorinated biphenyl; NA = not available; DDE = dichlorodiphenyldichloroethylene; HCH = hexachlorocyclohexane; CBz = chlorobenzene; CDF = chlorodibenzofuran; CDD = chlorodibenzo-p-dioxin.
• ^b Not measured above 20°C (extrapolated to 25°C).
• ^c Median value of all values cited in Bamford et al. [9].
• ^d Calculated.
• ^e Parameter from Kömp et al. [7] measured with coeluting congener. Value selected for main component of Aroclor mixture.
• ^f Standard with more than 95% PCB-95 used for measurement.

The vapor pressure is converted into solubility in air according to Cole and Mackay [1]

(2)

It is important that all solubilities apply to the same state, that is, either to the liquid or the solid state of the solute. Generally, the liquid state is preferred because it better represents the conditions of chemicals in solution at low environmental concentrations [4] and liquid or supercooled liquid properties are used in quantitative structure-property relationships. Thus, we used the data applicable to the liquid or supercooled liquid state.

Expressed in a logarithmic form, the theoretical relationship between K_AW and solubilities in air and water is

(3)

Inserting measured values for K_AW, S_A, and S_W of PCB 15 into Equation 3 results in a deviation ∈ from the ideal relationship, probably caused by measurement errors

(4)

The goal is to adjust the properties K_AW, S_A, and S_W such that Equation 3 is fully satisfied. Assuming all properties contribute equally to the deviation, they are adjusted by a quantity δ, calculated as ∈/n, where n is the number of adjusted properties

(5)

The adjustment term δ is therefore -0.033. Note that log S_A is increased because it is subtracted from the other properties in Equation 4. Subtracting or adding this δ adjustment term on the log-scale implies dividing or multiplying all parameters by a factor of 10, that is, 0.927. This assumes that all parameters are subject to the same relative or fractional error and all are changed by the same incremental value on a log-scale. The results for PCB 15 are included in Table 2. Adjusting the given K_AW, S_A, and S_W in this way has the advantage that it avoids any judgment on the part of the user and that it takes into account all measured properties. Calculating the K_AW from measured S_A and S_W would also yield consistent properties, but neglects measurements of K_AW.

INCORPORATING RELIABILITY

Some measurements likely are known to be more accurate than others. For example, it may be easier to determine K_AW than solubility in water or vapor pressure for hydrophobic compounds of low volatility. When selecting consistent values of these parameters, assigning greater weight to K_AW may then be desirable. We suggest that a factor μ_i is assigned to each property which ranges from 0 (known with high accuracy) to 5 (highly uncertain). This could be termed an uncertainty factor. The adjustment factor δ is then modified and calculated for each property i as δ_i = ∈.u_i/Σu_i, where the summation is over all n quantities. Clearly, if all u_i values are equal, this reduces to ∈/n. Any scale can be selected for u_i (e.g., 0 to 1 or 1 to 10) as long as it is consistent. The factors can be assigned depending on the nature of the property measured, the method of determination, the use of standards, and the number of determinations. Of course, judgment is involved in the assignment of reliability but in our view this judgment is best applied to the reported determination, not to the final selected parameter value.

APPLICATION TO OCTANOL PARTITIONING

The principle illustrated in the above example can be applied to more complex systems, but it is not immediately obvious how multiple constraints are best applied. Basic constraining equations exist for the system air, water, and octanol, as described by Cole and Mackay [1]. These are

(6)

(7)

(8)

(9)

The subscript A is air, O is octanol, W is water, OW is octanol saturated with water, and WO is water saturated with octanol. The ratio S_O/S_W can be regarded as the partition coefficient between pure octanol and pure water. However, this ratio is not necessarily equal to the K_OW. As has been pointed out [5-7] evidence exists that S_O is not equal to S_OW, nor is S_W equal to S_WO (see the Appendix for details). Further, S_O or S_OW may not be measurable experimentally because of miscibility considerations. Because environmental conditions usually are highly dilute, S_OW is best regarded as an apparent solubility or pseudosolubility defined by K_OW and applicable at high dilution. This octanol-water miscibility issue does not apply to K_OA because in this case the octanol is usually dry. However, calculated values of K_OA that are derived from K_OW and K_AW have been shown to consistently deviate from measured values of K_OA, which also relates to the difference between pure and water-saturated octanol. A semiempirical relationship that estimates the ratio S_O/S_W from measured K_OW values for log K_OW between 1 and 8 is derived in the Appendix. To account for the difference between the two octanol phases, we use the preliminary relationships

(10)

(11)

Table Table 2.. Chemical properties at 25°C calculated or changed to conform to thermodynamic constrains by using the iterative adjustment procedure (see text for details)^a

	P (Pa)	%b	SWl (mol/L)	%	SOl (mol/L)	%	KAW	%	Kow	%	KOA	%
PCB 15	6.47 × 10−2	−7	4.38 × 10−3	8	1.33 × 103		6.21 × 10−3	8	1.61 × 105	−5	4.89 × 107	7
PCB 28	3.15 × 10−2	−8	1.00 × 10−3	8	1.47 × 103		1.27 × 10−2	8	5.13 × 105		1.16 × 108
PCB 29	5.28 × 10−2	18	1.85 × 10−3	−15	2.39 × 103		1.15 × 10−2	3	4.68 × 105	−16	1.12 × 108	26
PCB 30	1.01 × 10−1	4	1.57 × 10−3	−4	1.26 × 103		2.60 × 10−2	−4	3.29 × 105		3.08 × 107
PCB 31	2.71 × 10−2	−22	1.10 × 10−3	28	1.16 × 103		9.90 × 10−3	28	4.01 × 105	−16	1.06 × 108	27
PCB 33	2.64 × 10−2		6.90 × 10−4		1.01 × 103		1.55 × 10−2		5.13 × 105		9.47 × 107
PCB 44	1.31 × 10−2	3	5.51 × 10−4	−2	1.02 × 103		9.57 × 10−3	−9	6.09 × 105	13	1.93 × 108	−16
PCB 47	1.73 × 10−2	13	1.02 × 10−3	−12	3.06 × 103		6.87 × 10−3	−12	8.71 × 105		4.38 × 108
PCB 52	1.37 × 10−2	−15	3.68 × 10−4	13	7.69 × 102	4	1.50 × 10−2	15	6.66 × 105	8	1.39 × 108	−16
PCB 61	9.76 × 10−3	−19	3.62 × 10−4	−18	1.38 × 103	52	1.09 × 10−2	1	1.04 × 106	−26	3.51 × 108	−34
PCB 77	1.31 × 10−3	−40	1.41 × 10−4	68	1.38 × 103		3.76 × 10−3	−6	2.08 × 106	61	2.61 × 109	−48
PCB 95	5.32 × 10−3		4.34 × 10−4		1.22 × 103		4.94 × 10−3	1	8.28 × 105	0	5.69 × 108	1
PCB 101	3.57 × 10−3	5	1.33 × 10−4	−5	1.43 × 103		1.08 × 10−2	5	2.22 × 106	−11	9.94 × 108	16
PCB 105	8.74 × 10−4		8.56 × 10−5		3.65 × 103		4.12 × 10−3	1	6.12 × 106	−1	1.03 × 1010	1
PCB 110	1.39 × 10−3	−24	5.47 × 10−5	32	4.89 × 102		1.03 × 10−2		1.94 × 106	22	8.72 × 108	−24
PCB 116	3.38 × 10−3	47	1.59 × 10−4	−32	2.40 × 103		8.59 × 10−3	−32	2.86 × 106		1.76 × 109
PCB 118	1.19 × 10−3		7.05 × 10−5		2.20 × 103		6.83 × 10−3	−31	4.87 × 106	31	4.58 × 109	−31
PCB 126	4.87 × 10−4		8.00 × 10−5		3.26 × 103		2.45 × 10−3	−27	5.91 × 106	26	1.66 × 1010	−27
PCB 138	5.14 × 10−4		3.42 × 10−5		1.07 × 103		6.06 × 10−3	14	4.88 × 106	−9	5.17 × 109	14
PCB 153	4.62 × 10−4	−32	2.03 × 10−5	48	7.71 × 102		9.18 × 10−3	32	5.62 × 106	−11	4.14 × 109	17
PCB 180	1.32 × 10−4		5.95 × 10−6		8.91 × 102		8.92 × 10−3	7	1.54 × 107	−5	1.68 × 1010	7
p,p′-DDT	3.56 × 10−4	15	2.40 × 10−4	0	1.40 × 103	−14	5.99 × 10−4	13	1.42 × 106	−9	9.72 × 109	51
p,p′-DDE	3.05 × 10−3	−37	8.52 × 10−4	58	2.63 × 103		1.45 × 10−3	−15	8.88 × 105	77	2.13 × 109	−54
α-HCH	1.05 × 10−1	−26	1.55 × 10−1	35	1.01 × 103		2.75 × 10−4	−11	9.55 × 103	48	2.37 × 107	−41
γ-HCH	4.15 × 10−2	−28	2.01 × 10−1	9	1.12 × 103	−29	8.32 × 10−5	−42	8.52 × 103	70	6.69 × 107	−4
trans-Chlordane	6.66 × 10−3	15	7.20 × 10−4	−13	2.27 × 103		3.73 × 10−3		9.00 × 105	−10	8.43 × 108	15
cis-Chlordane	5.70 × 10−3	21	7.49 × 10−4	−17	2.25 × 103		3.07 × 10−3		8.69 × 105	−13	9.77 × 108	21
Chlorobenzene	1.58 × 103	0	4.30 × 100	0	6.94 × 102		1.48 × 10−1	0	6.31 × 102		1.09 × 103
1,2,4,5-TetraCBz	8.78 × 100	−19	5.30 × 10−2	27	1.73 × 103	−4	6.69 × 10−2	64	3.14 × 104	−1	4.89 × 105	9
1,2,3,5-TetraCBz	8.39 × 100	−17	4.33 × 10−2	30	2.01 × 103	−29	7.82 × 10−2	21	4.05 × 104	28	5.94 × 105
Pentachlorobenzene	9.09 × 10−1	1	8.70 × 10−3	6	1.06 × 103	−7	4.22 × 10−2	47	8.21 × 104	−18	2.88 × 106	50
Hexachlorobenzene	6.87 × 10−2	−27	8.95 × 10−4	25	6.14 × 102	9	3.10 × 10−2	73	2.94 × 105	−7	2.22 × 107	−7
Naphthalene	3.70 × 101	10	9.52 × 10−1	20	1.45 × 103	−37	1.57 × 10−2	−9	3.28 × 103	40	9.71 × 104
Biphenyl	4.05 × 100	15	1.50 × 10−1	19	1.23 × 103	−38	1.09 × 10−2	−13	1.14 × 104	43	7.54 × 105
Acenaphthene	2.01 × 100	26	1.37 × 10−1	4	1.00 × 103	−27	5.93 × 10−3	−21	1.04 × 104	26	1.24 × 106
Fluorene	6.32 × 10−1	6	8.08 × 10−2	7	1.40 × 103	−12	3.15 × 10−3	−20	1.97 × 104	30	5.51 × 106	−11
Phenanthrene	9.57 × 10−2	8	2.77 × 10−2	1	1.44 × 103	−8	1.39 × 10−3	−19	4.42 × 104	19	3.74 × 107	−6
Anthracene	4.00 × 10−2	132	1.64 × 10−2	−25	8.09 × 102	−24	9.83 × 10−4	−57	4.24 × 104	22	5.02 × 107
Fluoranthene	5.63 × 10−3	8	4.72 × 10−3	−30	1.20 × 103	32	4.82 × 10−4	−39	1.42 × 105	−15	5.29 × 108	−29
Pyrene	1.18 × 10−2	9	9.69 × 10−3	−18	2.56 × 103	12	4.91 × 10−4	−29	1.45 × 105	−4	5.37 × 108	−16
Benzo[a]pyrene	6.28 × 10−6	−15	1.16 × 10−4	−7	3.55 × 102	35	2.17 × 10−5	17	8.80 × 105	−20	1.40 × 1011
Benz[a]anthracene	5.66 × 10−4	28	5.94 × 10−4	−22	1.63 × 103		3.84 × 10−4	−22	8.13 × 105		7.13 × 109
Chrysene	1.13 × 10−4	10	1.18 × 10−3	−26	7.44 × 102	64	3.88 × 10−5	−9	2.77 × 105	−31	1.63 × 1010
2,3,7,8-TetraCDF	1.69 × 10−3	−39	8.72 × 10−4	64	5.46 × 103		7.81 × 10−4	14	1.49 × 106	19	8.02 × 109	−21
1-MonoCDD	2.85 × 10−1	−20	7.17 × 10−2	26	6.53 × 103		1.61 × 10−3		6.65 × 104	18	5.67 × 107	−20
1,2,3,4-TetraCDD	7.62 × 10−4	−33	2.26 × 10−4	49	2.86 × 103		1.36 × 10−3	67	2.51 × 106	−37	9.32 × 109	87
2,3,7,8-TetraCDD	1.96 × 10−3	−10	1.61 × 10−4	11	7.91 × 103		4.92 × 10−3		6.79 × 106	8	1.00 × 1010	−10
1,2,3,4,7-PentaCDD	1.75 × 10−3	14	1.45 × 10−4	−12	3.70 × 104		4.87 × 10−3		2.28 × 107	−9	5.24 × 1010	14
1,2,3,4,7,8-HexaCDD	1.00 × 10−3	14	6.63 × 10−5	−12	5.91 × 104		6.10 × 10−3		5.72 × 107	−9	1.46 × 1011	14
1,2,3,4,6,7,8-HeptaCDD	7.74 × 10−4	29	7.11 × 10−5	−23	1.05 × 105		4.39 × 10−3		8.29 × 107	−17	3.36 × 1011	29

• ^a PCB = polychlorinated biphenyl; DDE = dichlorodiphenyldichloroethylene; HCH = hexachlorocyclohexane; CBz = chlorobenzene; CDF = chlorodibenzofuran; CDD = chlorodibenzo-p-dioxin.
• ^b Percentages indicate deviation from selected values in Table 1.

Table Table 3.. Properties calculated or changed to conform to thermodynamic constraints with the analytic adjustment procedure (see text for details)^a

	P (Pa)	%b	5Wl (mol/L)	%	5Ol (mol/L)	%	KAW	%	KOW	%	KOA	%
PCB 15	6.74 × 10−2	−7	4.38 × 10−3	8	1.33 × 103		6.21 × 10−3	8	1.61 × 105	−5	4.89 × 107	7
PCB 28	3.15 × 10−2	−8	1.00 × 10−3	8	1.47 × 103		1.27 × 10−2	8	5.13 × 105		1.16 × 108
PCB 29	5.28 × 10−2	18	1.85 × 10−3	−15	2.39 × 103		1.15 × 10−2	3	4.68 × 105	−16	1.12 × 108	26
PCB 30	1.01 × 10−1	4	1.57 × 10−3	−4	1.26 × 103		2.60 × 10−2	−4	3.29 × 105		3.08 × 107
PCB 31	2.71 × 10−2	−22	1.10 × 10−3	28	1.16 × 103		9.90 × 10−3	28	4.01 × 105	−16	1.06 × 108	27
PCB 33	2.64 × 10−2		6.90 × 10−4		1.01 × 103		1.55 × 10−2		5.13 × 105		9.47 × 107
PCB 44	1.31 × 10−2	3	5.51 × 10−4	−2	1.02 × 103		9.57 × 10−3	−9	6.09 × 105	13	1.93 × 108	−16
PCB 47	1.73 × 10−2	13	1.02 × 10−3	−12	3.06 × 103		6.87 × 10−3	−12	8.71 × 105		4.38 × 108
PCB 52	1.59 × 10−2	−1	3.61 × 10−4	11	7.65 × 10-2	3	1.78 × 10−2	37	6.73 × 105	9	1.19 × 108	−28
PCB 61	1.44 × 10−2	19	3.74 × 10−4	−15	1.29 × 103	41	1.55 × 10−2	44	9.63 × 105	−31	2.23 × 108	−58
PCB 77	1.31 × 10−3	−40	1.41 × 10−4	68	1.38 × 103		3.76 × 10−3	−6	2.08 × 106	61	2.61 × 109	−48
PCB 95	5.32 × 10−3		4.34 × 10−4		1.22 × 103		4.94 × 10−3	1	8.28 × 105	0	5.69 × 108	1
PCB 101	3.57 × 10−3	5	1.33 × 10−4	−5	1.43 × 103		1.08 × 10−2	5	2.22 × 106	−11	9.94 × 108	16
PCB 105	8.74 × 10−4		8.56 × 10−5		3.65 × 103		4.12 × 10−3	1	6.12 × 106	−1	1.03 × 1010	1
PCB 110	1.39 × 10−3	−24	5.47 × 10−5	32	4.89 × 102		1.03 × 10−2		1.94 × 106	22	8.72 × 108	−24
PCB 116	3.38 × 10−3	47	1.59 × 10−4	−32	2.40 × 103		8.59 × 10−3	−32	2.86 × 106		1.76 × 109
PCB 118	1.19 × 10−3		7.05 × 10−5		2.20 × 103		6.83 × 10−3	−31	4.87 × 106	31	4.58 × 109	−31
PCB 126	4.87 × 10−4		8.00 × 10−5		3.26 × 103		2.45 × 10−3	−27	5.91 × 106	26	1.66 × 1010	−27
PCB 138	5.14 × 10−4		3.42 × 10−5		1.07 × 103		6.06 × 10−3	14	4.88 × 106	−9	5.17 × 109	14
PCB 153	4.62 × 10−4	−32	2.03 × 10−5	48	7.71 × 102		9.18 × 10−3	32	5.62 × 106	−11	4.14 × 109	17
PCB 180	1.32 × 10−4		5.95 × 10−6		8.91 × 102		8.92 × 10−3	7	1.54 × 107	−5	1.68 × 1010	7
p,p′-DDT	2.75 × 10−4	−11	2.39 × 10−4	0	1.43 × 103	−11	4.63 × 10−4	−12	1.44 × 106	−7	1.29 × 1010	100
p,p′-DDE	3.05 × 10−3	−37	8.52 × 10−4	58	2.63 × 103		1.45 × 10−3	−15	8.88 × 105	77	2.13 × 109	−54
α-HCH	1.05 × 10−1	−26	1.55 × 10−1	35	1.01 × 103		2.75 × 10−4	−11	9.55 × 103	48	2.37 × 107	−41
γ-HCH	3.32 × 10−2	3	1.98 × 10−1	8	1.18 × 103	−25	6.74 × 10−5	−53	8.98 × 103	79	8.86 × 107	27
trans-Chlordane	6.66 × 10−3	15	7.20 × 10−4	−13	2.27 × 103		3.73 × 10−3		9.00 × 105	−10	8.43 × 108	15
cis-Chlordane	5.70 × 10−3	21	7.49 × 10−4	−17	2.25 × 103		3.07 × 10−3		8.69 × 105	−13	9.77 × 108	21
Chlorobenzene	1.58 × 103	0	4.30 × 100	0	6.94 × 102		1.48 × 10−1	0	6.31 × 102		1.09 × 103
1,2,4,5-TetraCBz	9.34 × 100	−13	5.09 × 10−2	22	1.74 × 103	−3	7.40 × 10−2	82	3.24 × 104	3	4.63 × 105	3
1,2,3,5-TetraCBz	8.39 × 100	−17	4.33 × 10−2	30	2.01 × 103	−29	7.82 × 10−2	21	4.05 × 104	28	5.94 × 105
Pentachlorobenzene	7.74 × 10−1	−14	8.62 × 10−3	5	1.07 × 103	−6	3.62 × 10−2	27	8.34 × 104	−17	3.42 × 106	78
Hexachlorobenzene	8.47 × 10−2	−10	8.62 × 10−4	20	6.05 × 102	8	3.97 × 10−2	121	2.99 × 105	−6	1.77 × 107	−26
Naphthalene	3.70 × 101	10	9.52 × 10−1	20	1.45 × 103	−37	1.57 × 10−2	−9	3.28 × 103	40	9.71 × 104
Biphenyl	4.05 × 100	15	1.50 × 10−1	19	1.23 × 103	−38	1.09 × 10−2	−13	1.14 × 104	43	7.54 × 105
Acenaphthene	2.01 × 100	26	1.37 × 10−1	4	1.00 × 103	−27	5.93 × 10−3	−21	1.04 × 104	26	1.24 × 106
Fluorene	6.11 × 10−1	3	7.99 × 10−2	6	1.43 × 103	−10	3.08 × 10−3	−22	2.01 × 104	33	5.82 × 106	−6
Phenanthrene	9.15 × 10−2	3	2.76 × 10−2	1	1.47 × 103	−7	1.34 × 10−3	−23	4.47 × 104	20	3.79 × 107	−1
Anthracene	4.00 × 10−2	132	1.64 × 10−2	−25	8.09 × 102	−24	9.83 × 10−4	−57	4.24 × 104	22	5.02 × 107
Fluoranthene	6.69 × 10−3	28	5.01 × 10−3	−26	1.15 × 103	26	5.39 × 10−4	−32	1.31 × 105	−21	4.25 × 108	−43
Pyrene	1.25 × 10−2	15	1.00 × 10−2	−15	2.51 × 103	10	5.02 × 10−4	−27	1.40 × 105	−8	4.99 × 108	−22
Benzo[a]pyrene	6.28 × 10−6	−15	1.16 × 10−4	−7	3.55 × 102	35	2.17 × 10−5	17	8.80 × 105	−20	1.40 × 1011
Benz[a]anthracene	5.66 × 10−4	28	5.94 × 10−4	−22	1.65 × 103		3.84 × 10−4	−22	8.13 × 105		7.13 × 109
Chrysene	1.13 × 10−4	10	1.18 × 10−3	−26	7.44 × 102	64	3.88 × 10−5	−9	2.77 × 105	−31	1.63 × 1010
2,3,7,8-TetraCDF	1.69 × 10−3	−39	8.72 × 10−4	64	5.46 × 103		7.81 × 10−4	14	1.49 × 106	19	8.02 × 109	−21
1-MonoCDD	2.85 × 10−1	−20	7.17 × 10−2	26	6.53 × 103		1.61 × 10−3		6.65 × 104	18	5.67 × 107	−20
1,2,3,4-TetraCDD	7.62 × 10−4	−33	2.26 × 10−4	49	2.86 × 103		1.36 × 10−3	67	2.51 × 106	−37	9.32 × 109	87
2,3,7,8-TetraCDD	1.96 × 10−3	−10	1.61 × 10−4	11	7.91 × 103		4.92 × 10−3		6.79 × 106	8	1.00 × 1010	−10
1,2,3,4,7-PentaCDD	1.75 × 10−3	14	1.45 × 10−4	−12	3.70 × 104		4.87 × 10−3		2.28 × 107	−9	5.24 × 1010	14
1,2,3,4,7,8-HexaCDD	1.00 × 10−3	14	6.63 × 10−5	−12	5.91 × 104		6.10 × 10−3		5.72 × 107	−9	1.46 × 1011	14
1,2,3,4,6,7,8-HeptaCDD	7.74 × 10−4	29	7.11 × 10−5	−23	1.50 × 105		4.39 × 10−3		8.29 × 107	−17	3.36 × 1011	29

• ^a PCB = polychlorinated biphenyl; DDE = dichlorodiphenyldichloroethylene; HCH = hexachlorocyclohexane; CBz = chlorobenzene; CDF = chlorodibenzofuran; CDD = chlorodibenzo-p-dioxin.
• ^b Percentages indicate deviation from selected values in Table 1.

Table Table 4.. Literature values for internal energy changes (kJ/mol) applying to the supercooled liquid state. Values with more than one reference are the median of cited properties¹

	ΔU	References		References	ΔUAW	References	ΔUOW	References	ΔUOA	References
PCB 15	73.633	[18]	17.066	[17]	NA		−20.9	[37]	−72.597	[6]
PCB 28	75.624	[18]	NA		47.230	[12]	NA		NA
PCB 29	74.322	[18]	14.098	[17]	NA		NA		−72.597	[6]
PCB 30	72.006	[18]	16.815	[38]	NA		−20.4	[37]	NA
PCB 31	75.298	[18]	NA		NA		NA		−83	[7]
PCB 33	75.624	[18]	NA		NA		NA		NA
PCB 44	78.572	[18]	NA		NA		NA		−86	[7]
PCB 47	78.572	[18]	13	[39]	NA	[12]	NA		NA
PCB 52	78.400	[18]	NA		48.437		NA		−86	[7]
PCB 61	81.501	[18]	16.100	[17]	NA		−24.0	[37]	−66.318	[6]
PCB 77	84.756	[18]	25.800	[13, 38]	NA		NA		−73.287	[20]
PCB 95	81.827	[18]	NA		NA		NA		−82.371	[7, 20]
PCB 101	84.029	[18]	13.070	[13, 38]	NA		NA		−79.768	[7, 20]
PCB 105	88.700	[18]	NA		NA		NA		−89.560	[20]
PCB 110	84.182	[18]	NA		NA		NA		−89	[7]
PCB 116	84.182	[18]	NA		NA		NA		NA
PCB 118	86.900	[18]	NA		NA		NA		−89.847	[20]
PCB 126	92.491	[18]	NA		NA		NA		−93.236	[20]
PCB 138	89.504	[18]	NA		NA		NA		−86.880	[7, 20]
PCB 153	89.025	[18]	18.059	[38]	NA		NA		−88.443	[7, 20]
PCB 180	94.137	[18]	NA		NA		NA		−82.411	[7, 20]
p,p′-DDT	90.748	[40]	NA		NA		NA		−88.124	[21]
p,p′-DDE	84.794	[40]	NA		NA		NA		−97.945	[21]
α-HCH	66.052	[40]	NA		51.347	[12]	NA		−61.857	[21]
γ-HCH	68.062	[40]	NA		43.153	[12]	NA		−65.380	[21]
trans-Chlordane	78.323	[40]	NA		NA		NA		−96.414	[21]
cis-Chlordane	79.625	[40]	NA		NA		NA		−98.156	[21]
Chlorobenzene	45.709	[41]	NA		28.851	[12]	−15.0	[37]	NA
1,2,4,5-TetraCBz	55.648	[11]	6.700	[17]	NA		−19.3	[37]	NA
1,2,3,5-TetraCBz	55.024	[11]	7.300	[17]	NA		−19.9	[37]	NA
Pentachlorobenzene	69.486	[11]	12.300	[17]	40.817	[12]	−22.0	[37]	−71.257	[6]
Hexachlorobenzene	75.728	[40, 41]	11.142	[17]	45.507	[12]	−24.3	[37]	−55.788	[21]
Naphthalene	70.340	[42]	NA		44.646	[12]	−15.7	[37]	NA
Biphenyl	81.886	[43]	15.500	[13]	NA		NA		NA
Acenaphthene	80.609	[44]	NA		51.9	[8]	NA		NA
Fluorene	85.983	[44]	NA		48.8	[8]	−19.0	[37]	−82.936	[33]
Phenanthrene	68.751	[40]	NA		51.900	[8, 12]	−19.0	[37]	−75.469	[33]
Anthracene	67.334	[40]	NA		48.800	[8, 12]	−19.7	[37]	NA
Fluoranthene	74.954	[40]	NA		54.907	[12]	−20.8	[37]	−84.563	[33]
Pyrene	76.217	[40]	NA		42.9	[8]	−19.2	[37]	−76.292	[33]
Benzo[a]pyrene	93.122	[40]	NA		36.892	[12]	−25.4	[37]	NA
Benz[a]anthracene	88.394	[40]	NA		66.4	[8]	−23.3	[37]	NA
Chrysene	NA		NA		100.9	[8]	−22.7	[37]	NA
2,3,7,8-TetraCDF	85.813d	[45]	NA		NA		NA		−85.195	[35]
1-MonoCDD	74.759	[22]	19.450	[46]	NA		NA		−61.264	[35]
1,2,3,4-TetraCDD	86.371d	[45]	15.600	[38, 46, 47]	NA		NA		−83.663	[35]
2,3,7,8-TetraCDD	81.710	[22]	NA		NA		NA		−92.661	[35]
1,2,3,4,7-PentaCDD	92.628e	[22]	5.100	[48]	NA		NA		−104.531	[35]
1,2,3,4,7,8-HexaCDD	99.132d	[45]	−2.600	[48]	NA		NA		−98.788	[35]
1,2,3,4,6,7,8-HeptaCDD	103.602d	[45]	−11.500	[48]	NA		NA		−85.195	[35]

• ^a ΔU = heat of phase transition; A = air; W = water; AW = air—water; OW = octanol—water; OA = octanol—air; PCB = polychlorinated biphenyl; NA = not available; DDE = dichlorodiphenyldichloroethylene; HCH = hexachlorocyclohexane; CBz = chlorobenzene; CDF = chlorodibenzofuran; CDD = chlorodibenzo-p-dioxin.
• ^b ΔU_A is obtained by subtracting 2.391 kJ/mol from the enthalpy reported for vapor pressure (ΔH_vp). See text for details.
• ^c Literature values changed to apply to the supercooled liquid state.
• ^d Calculated from relative retention times, with p,p′-DDT as reference compound.
• ^e Calculated.

However, we suggest that additional research be undertaken to measure K_OA, S_O, and S_OW directly by including a broad range of chemicals to improve the understanding of this issue. The chemical properties can now be related to each other by the four Equations 6 to 9. The equations can be combined; for example, Equations 6, 7, plus 9 gives

(12)

in which case the octanol solubility S_O is eliminated. After transforming log S_O/S_W into log K_OW with Equation 10a or 10b, respectively, Equation 11 can be used to determine ∈ and δ_i if data are available for K_OW, K_OA, and K_AW, but not S_A, S_W, and S_O. Similar equations can be derived that relate other combinations.

In this example, all available data can be related to each other in one constraining equation. This is always the case if not more than three or four of the six partitioning properties have been measured. Then ∈ and δ can be calculated as shown. When measured data are available for more than four of the parameters, two constraining equations will be needed to relate all properties. A common example is when data are available for K_AW, K_OW, K_OA, S_A, and S_W but not S_O (which is the case for PCB 15). Equations 6 and 11 may then be used. One option is to apply one equation, deduce the adjustment factor δ, then apply the corrected values to the second. This is problematic because the result will depend on the order in which the equations are applied.

A more rigorous approach is to apply iterations, that is, use both equations to deduce two different values of ∈ and hence δ_i for one property (e.g., K_AW), and adjust the parameters separately by using both equations, then use these adjusted values to deduce new values of ∈. By repeating this iteration, the parameter values will converge to a set consistent with both equations. A third strategy is to calculate the adjustment factors δ_i for both equations separately and to apply mean corrections to the property that occurs in both equations. For example, K_AW, which occurs in Equations 6 and 11, is changed by the mean adjustment according to both equations. Then, K_OW, K_OA, S_A, and S_W are altered to account for the remaining error in Equations 6 and 11. Inserting the values of PCB 15 from Table 1, the correction of log K_AW is -0.0325 (Eqn. 6) and -0.0311 (Eqn. 11), hence log K_AW is corrected by the mean of both (i.e., -0.0318). Both log S_A and log S_W now must be altered to account for the remaining error in Equation 6, which is -0.0975 + 0.0318, that is, -0.0657. If this remaining error is shared among the two properties, both are changed by -0.03285, thus log S_A becomes -4.566 and log S_W becomes -2.359. Adjustment factors for K_OW and K_OA are determined accordingly. This analytic approach yields adjustment factors that can directly be derived from the substance properties without any numerical iteration. The disadvantage of this approach is that it sometimes yields larger δ_i for one property, whereas other properties are changed by a smaller δ_i. Hence, for some properties the absolute deviation from the measurement may be larger as if using the iterative approach.

Strategies two and three have been applied to the data given in Table 1. VisualBasic code used for the two adjustment procedures can be downloaded free of charge from http://www.usf.uos.de/projects/elpos. Tables 2 and 3 report consistent sets of parameters that were obtained by applying the iterative approach (method two) and the analytical approach (method three), respectively. A comparison shows that both approaches generally yield similar results. A deviation between the two methods occurs only if six measured parameters are available. Thus, the adjusted properties of the example chemical PCB 15 are the same when applying both approaches. The deviation between the two selection procedures becomes larger if the measured data lead to larger deviations in Equations 6 through 9. However, large deviations point to inconsistent or erroneous data, suggesting that such data should not be used. Hence, assuming that the input data were measured and selected appropriately, the difference between the two selection strategies is expected to be negligible for applications in the field of environmental research.

TEMPERATURE DEPENDENCE

When attempting to apply chemical fate models to real situations, the temperature dependence of physicochemical properties obviously is of high importance. Recently, several authors have compiled sets of temperature-dependent data [8-12] that must be subjected to the same procedure as the properties at standard temperature. Similar thermodynamic relations constraining the temperature slopes are used for this purpose [1, 13].

In many cases, a simple exponential relationship between physicochemical properties and temperature can be assumed. The expressions often take the form of a modified van't Hoff equation [14]

(13)

where x(T) and x₀ are the given property at temperature T and at reference temperature T₀ (in K), respectively; ΔH is the enthalpy of phase change (in kJ/mol), and R is the universal gas constant (in kJ/mol K). The temperature dependence of solubilities is better expressed in terms of internal energy change, ΔU [15, 16]. The assumption is made that temperature coefficients of water solubilities that were reported in the literature as ΔH are actually heats of solubilization. The enthalpy reported for vapor pressure (ΔH_Vp) must be transformed into a heat of phase transition (ΔU_A) to be applicable to air solubility. Although the difference between ΔH_Vp and ΔU_A is temperature dependent, it can be regarded nearly constant over a limited temperature range. A linear regression of ΔU_A versus 1/T showed a deviation of -2,391 J/mol from ΔH_Vp on a temperature range from 0 to 30°C. Note that this number changes if a different temperature range is considered and that the error of the regression increases for larger temperature ranges. Equation 12 is convenient because of its simplicity, but an important underlying assumption is that ΔU (or ΔH) is constant over the entire temperature range. Therefore, such relations are applicable only within a relatively small temperature range [10, 14]. Sometimes these relations are not applicable within the environmentally relevant temperature range at all; an example is the water solubility and Henry's law constant of benzene. Shiu and Ma [10, 11] discussed limitations of Equation 12 and reported alternative expressions for a range of organic chemicals.

Measured heats of phase transition of organic chemicals exist for evaporation (i.e., pure liquid-vapor transition; ΔU_A or ΔH_Vp); solubilization in water (pure liquid dissolved in water; ΔU_W); as well as air-water, octanol-water, and octanol-air phase transfer (ΔU_AW, ΔU_OW, and ΔU_OA). The temperature dependence of the solubility in octanol rarely has been determined [17]. The measured heat of phase transition for solubilization in water applies to the solid solute and therefore must be converted to apply to the supercooled liquid state according to [13]

(14)

where ΔU_Ws is the measured temperature coefficient, ΔU_fus is the heat of fusion, and ΔU_Wl the heat of phase transition from the pure, supercooled liquid state to aqueous solution. If the reported vapor pressure temperature coefficients already apply to the supercooled liquid state, a change of ΔU_A is not necessary. An example is given by the vapor pressures of PCBs reported in Falconer and Bidleman [18].

Often, not all heats of phase transfer are available for a given chemical, but missing values can be derived. If, for example, ΔU_A and ΔU_W are known, ΔU_AW can be determined from ΔU_A - ΔU_W. To be consistent, all of these internal energies must conform to the condition [1]

(15)

which is equivalent to

(16)

If all three (Eqn. 14) or four (Eqn. 15) measured heats of phase transfer exist, these conditions generally are not fulfilled. In the case of PCB 15, measured heats of phase transition ΔU_A, ΔU_W, ΔU_OW, and ΔU_OA have been reported (Table 4) and, again, the task is to select consistent values. Mathematically, the problem is the same as adjusting the phase solubilities, thus, we can apply the same approach. The basis is Equation 15, which combines all measured heats of phase transfer in one expression. Sometimes five properties, including ΔU_AW, are measured and two equations relate the temperature slopes to each other.

In the case of the temperature slopes ΔU, the adjustment is applied to the absolute quantity rather than to the logarithmic quantity. This is preferable when the error is judged to be normally rather than log-normally distributed. Uncertainty factors can be applied as before. Selected heats of phase transfer are presented in Table 5.

If a set of property values at a temperature significantly below 25°C is required, it may be advisable to apply the temperature adjustment to the properties first and subsequently correct them with the scheme presented above, ensuring that the selected values are close to the measurements. Changing x₀ from Equation 12 and the heats of phase transfer can lead to growing deviations from the originally measured values as the temperature deviates more from 25°C. Taking into account all measured properties and their fundamental thermodynamic relations, we thus derive the following consistent set of physicochemical properties for PCB 15:

where ln refers to the natural logarithm and T₀ corresponds to 298.15 K. All solubilities have units of mol/L. The expression of the K_OW applies to the mixed phases (i.e., water-saturated octanol and octanol-saturated water).

APPLICATION TO 50 CHEMICALS

Vapor pressure, water solubility, octanol solubility, K_AW, K_OW, and K_OA have been compiled from the literature for 50 chemicals, along with data on their temperature dependence (Tables 1 and 3). The set of chemicals contains mainly aromatic compounds of environmental interest covering a broad range of chemical properties. Subcooled liquid-phase vapor pressures range from 10⁻⁵ Pa to 10⁴ Pa and log K_OW values range from 2 to 8. Mainly measured data were taken (Table 1) and corrected to be thermodynamically consistent (Tables 2 and 3). The assumptions for this adjustment procedure are as follows: All properties apply to the same solute state (liquid or solid). All properties apply to the same temperature. Concentrations are dilute. Solubility is independent of solute concentration (or activity coefficients do not change as function of solute concentration). Deviations from ideal thermodynamic relationships are small. Equations 10a and 10b can be used to transform K_OW to S_O/S_OW. Temperature dependence can be approximated by exponential relationship (Eqn. 12). Values of ΔH and ΔU are constant over the considered temperature range. The parameter ΔH_Vp can be transformed to ΔU_A by subtracting 2,391 J/mol. Several recent compilations of physicochemical properties of organic compounds were used to select most of the properties. The selection procedure was as follows. If only one measurement existed for a given property, this datum was taken. If more than one measurement existed and if a value was suggested in one of the recent reviews, the suggested value was taken. If the chemical was considered in an older review, the suggested value was omitted only if newer measurements suggested a different value, that is, more recent publications of new data were taken into account. When no suggestion existed, either a typical value of all values was selected or the mean or median of all measurements was taken, based on judgment.

Two recent publications by Shiu and Ma [10, 11] provided most of the data for the vapor pressures and water solubilities at 25°C. The suggested values for the Henry's law constants in Shiu and Ma [10, 11] were derived from the selected values for vapor pressure and water solubilities. Because this approach neglects measurements of Henry's law constants, these values were not taken. Therefore, a selection of typical, measured K_AW values was made, based on the available data. The selected log K_OWs are mostly taken from Mackay et al. [2] and Makino [19]. For most of the log K_OAs, only one measurement exists. If two values exist from two different studies [7, 20] the mean was selected, because it is not yet possible to decide which of the measurements is more reliable. In case of p,p′-DDT and hexachlorobenzene, two measurements by the same group exist [6, 21] and the newer values were selected.

The approach taken for the temperature slopes was the same. Most temperature slopes were measured between 5 and 30°C. Exceptions existed only for K_OA and are indicated in Table 4. The temperature dependence of vapor pressures was determined indirectly via the gas chromatography retention time method in all cases, except for three polychlorinated dibenzo-p-dioxins (PCDDs) for which heats of vaporization were taken from Rordorf [22].

Data gaps were filled by deriving missing values from others whenever possible. However, in some cases, it was necessary to use values derived from molecular structure information to fill data gaps, which is indicated in Tables 1 and 4. Transformations from solid to supercooled liquid state were performed with substance specific entropies of fusion and melting point temperatures whenever possible. If no entropy of fusion was reported, a default value of 56 J/(mol K) was assumed [2].

The numbers from Tables 1 and 4 were used to either derive missing values or apply the corrections from above if possible. The resulting values along with their relative changes are reported in Tables 2, 3, and 5. The relative changes are mostly less than 50%; however, some exceptions did occur. In most cases the change is well within the range of reported measurements.

The resulting set of data at 25°C is complete (Tables 2 and 3), whereas temperature slopes are not available for all chemicals in Table 4. For the PCBs, Shiu et al. [17] suggested using a mean value of 35 kJ/mol for the solid-phase water solubility. The average ΔU_W for the water solubility of supercooled liquid PCBs in Table 4 is 20 kJ/mol, which agrees well with the value suggested by Shiu et al. [17]. The ΔU_W of PCBs was therefore set to 20 kJ/mol if it could not be derived from measured data. Plotting the measured ΔU_W of PCDDs with four or more chlorine atoms from Table 4 versus the number of chlorines yields a good correlation (R² = 0.996; Fig. 1). Analysis of the available data suggests that ΔU_W is mainly determined by the number of chlorines. Because the measured ΔU_W values also include 2,3,7,8-substituted congeners, the assumption can be made that the ΔU_W of 2,3,7,8-tetrachlorodibenzo-p-dioxin (2,3,7,8-TeCDD) is relatively close to the value of 1,2,3,4-TeCDD. Hence, a ΔU_W of 15.6 kJ/mol is assumed for 2,3,7,8-TeCDD.

If the temperature dependence of K_OW or K_OA is known, one can derive temperature slopes for the octanol solubility. Kömp and McLachlan [7] as well as Harner and Bidleman [20] calculated internal energy changes of the octanol solubility ΔU_O for PCBs from temperature slopes of K_OA and vapor pressure. Although a systematic difference seems to exist between the studies [7], the absolute calculated ΔU_O values were always less than 20 kJ/mol, that is, relatively close to zero. This also holds for the corrected values in Table 5. In fact they are even closer to zero than the values reported by Harner and Bidleman [20] and Kömp and McLachlan [7]. The same is true for most other chemicals; the only exception is benzo[a]pyrene, which has a ΔU_O of 31 kJ/mol. Thus, assuming a ΔU_O equal to zero seems reasonable, if deriving the value from measured data is impossible. Hence, by assuming standard internal energy changes for water solubilities and octanol solubilities, estimating most partitioning data as a function of temperature is possible, although with variable accuracy.

CONCLUSIONS

We suggest that when selecting chemical property data for use in chemical fate models, all available data be taken into account and processed with the methods described here to obtain an internally consistent set of data. Perceived accuracy can be taken into account. We believe that by adopting this approach, not only will more accurate data be obtained, but the determination of key properties that can improve accuracy of selected values may be encouraged. Most problematic is the relationship between K_OW and S_O/S_W, as derived in the Appendix. More data must be gathered to improve this relationship.