On the solubility of non-ionic organic solutes in seawater

Introduction

The solubility of an non-ionic organic solute (subscript _N) in water, s_N0/mol L^–1, can be estimated by means of several well-known linear solvation energy relationships (LSERs). An examples of such an LSER is that of Kamlet et al. [1, 2] for 25 °C:

where V_NI is the computer-generated intrinsic molar volume of the solute [3], π^* is its solvatochromic polarity/polarizability index, β is its solvatochromic electron pair donicity index, and t_F is the fusion/melting temperature of the solute (if it is solid at the relevant temperature for the solubility). Another example is the general solubility equation of Yalkowski et al. [4, 5]:

where P^o_W is the logarithm of the 1-octanol/water partition coefficient of the solute [6]. A further example is the LSER of Abraham and Le [7]:

where V_X is the McGowan molar volume of the solute [8], α is its solvatochromic hydrogen bond donicity [with β and π^* as in eq. (1)], and R_S is the excess molar refraction [7].

Given the solubility of a solute in pure water, the question now arises: what would be its solubility in an electrolyte solution (subscript _E) of molar concentration c_E/mol L^–1, and specifically, what would be its solubility in seawater? The latter question is of environmental importance and it should be useful if this solubility could be estimated within reasonable limits.

The general description of the effect of an electrolyte on the solubility of a solute is in terms of the Setchenow expression, relating the solubility in the presence of the electrolyte, s_NE/mol L^–1, to that in its absence:

This proportionality with the concentration of the electrolyte is generally valid up to 1 mol L^–1, and the proportionality coefficient k_NE is called the Setchenow constant. It is depends on the natures of both the solute and the electrolyte. The latter may also be a mixture as is seawater, and because of the proportionality that holds down to infinite dilution of the electrolyte, k_NE should be additive in the values of the constituent ions of the electrolyte.

This paper presents correlation expressions that permit the estimation of the solubility of non-ionic organic solutes in seawater, given their solubilities in pure water [either experimental values or estimated by expressions such as (1)–(4)] following the principles in a previous paper by the author discussed below.

The database

The composition of seawater in terms of its ionic or salt constituents depends to some extent on the location, salinity, temperature and other conditions of sampling, but Table 1 lists a representative recent set of values for salinity 3.5 % at 25 °C. The ionic composition (subscrtipt _I), c_I/mol L^–1, is from Gros et al. [9] and the salt composition, c_E/mol L^–1, is from Mistry et al. [10]. Note that the ionic composition lacks an entry for the hydrogencarbonate anion present in the salt composition, but its presence is very minor and it has practically no effect on the salting out ability by the constituents of seawater regarding non-ionic organic solutes.

The solubility of hydrocarbons with ≥5 carbon atoms in water and seawater was critically examined by Shaw et al. [11] in 1989 and their solubility in water was re-examined by Maczynski and Shaw et al. [12] in 2005. A review of the effects of salts on the solubility of non-ionic organic compounds in seawater was published by Xie et al. [13] in 1997, including also several compounds other than hydrocarbons. A few more recent references have also solubility data for seawater [14–17].

The combined list of for 25 °C is shown in Table 2 as log(s_N0/s_NE) values, whether originally each solubility datum is presented as mol L^–1, mg L^–1, Henry’s law constant for volatile solutes, etc. Solubility values expressed as g (100 g solution)^–1 [11] cannot be compared directly between pure and seawater and the data should be multiplied by the densities of the solutions to convert them eventually to the common mol L^–1 scale. Since those solubilities expressed as g (100 g solution)^–1 are very small, the densities of pure water, 997.045 kg m^–3 and of mean seawater, 1023.3 kg m^–3 (salinity 3.5 %) [30] at 25 °C may be employed for this purpose.

The accuracy of the listed log(s_N0/s_NE) values depends on those of the individual solubilities in the two media. The reported uncertainties of the ‘recommended’ or ‘tentative’ solubility values [10, 11] in pure water range from ±2.3 % for benzene and o-xylene to ±12.5 % for m-xylene and cumene, and those for seawater should be at least as large, because fewer determinations have been made of them. Solubilities <0.2 g (kg solution)^–1 are too uncertain to be included in the present evaluation and are not shown in Table 2.

Correlations of the relative solubilities

The author has shown [31] that two descriptors of the salts and two of the solutes are sufficient for the correlation and eventual prediction of the relative solubilities in salt solutions and pure water, log(s_N0/s_NE). The descriptors for the salts are the conventional standard molar volumes of the constituent ions V_I^{∞ conv} [32] (and their fractional concentrations of the total ions ν_I [9]) and their intrinsic molar volumes V_I,intr = (4πN_A/3)(kr_I)³, where k = 1.213 [31, 33], taking care of voids around the ions (except for sulfate, where k = 1 was used), and r_I are the ionic radii [31]. The values at 25 °C for seawater are shown in Table 1. Also shown there are the values for the constituent salts, the fractional concentrations ν_E [10], their standard molar volumes V_E^∞, and the corresponding intrinsic volumes V_Eintr. The V_E^∞ are the sums of the stoichiometrically weighted V_I^{∞ conv} and the V_Eintr = Σν_IV_I,intr. The small differences between the ionic and salt concentrations in the two references employed [9, 10] cause the quantities Σν_IΔV_I^{∞ conv} = Σν_I(V_Iintr – V_I^{∞ conv}) and Σν_EΔV_E^∞ = Σν_E(V_Eintr – V_E^∞) to differ somewhat, and their average, 9.0 ± 0.4 cm³ mol^–1 is used henceforth.

The descriptors of the solutes are their molar volumes (the Le Bas values, V_LB/cm³ mol^–1 [13], are used) and either the Hildebrand solubility parameter δ_H/MPa^0.5 or the Kamlet–Taft polarity/polarizability index π*, with values shown in Table 2. Both these quantities were taken from [18] for liquid solutes where available. Solubility parameters δ_H had to be calculated for solid solutes from the molar enthalpies of formation of their crystals and those of their gaseous forms [27, 29] and the molar volumes [28] of the solutes. Other values of δ_H were obtained from data in [19, 21, 23, 26]. Polarity/polarizability index, π*, values for the nitroaromatic and some other solutes were taken from [20, 22, 24, 25]. Values in parenthesis were estimated.

Most of the relative solubility data, log(s_N0/s_NE), where subscript _E pertains to seawater, are for aromatic solutes. The solubilities of aliphatic hydrocarbons in pure water and seawater were too small to yield reliable log(s_N0/s_NE) data. The few available values of this variable pertain to carbonyl compounds: aldehydes and ketones, but the variability of the δ_H and π* descriptors cover a too narrow range (7.4 % and 11.0 %) to make them necessary for the correlations of the relative solubilities, for which the solute molar volume descriptor, V_LB, suffices. The correlation expressions according to [31] then become for both aliphatic and aromatic solutes:

where the term 2.0 δ_H does not apply to aliphatic solutes, Fig. 1, and:

Fig. 1

Calculated, eq. (6) with the δ_H descriptor, vs. experimental solubilities of solutes in seawater and pure water at 25 °C, log(s₀/s), for aromatic solutes (•) and aliphatic ones (○).

where the term 68π* does not apply to aliphatic solutes, Fig. 2.

Fig. 2

Calculated, eq. (7) with the π* descriptor, vs. experimental solubilities of solutes in seawater and pure water at 25 °C, log(s₀/s), for aromatic solutes (•) and aliphatic ones (○).

Discussion

The overall span of the available log(s_N0/s_NE) data of the aromatic solutes is not large (about 0.2 units) and the average deviations with the δ_H descriptor (0.025 units, Fig. 1) is somewhat larger than with the π* descriptor (0.020 units, Fig. 2), but the overall agreement of the calculated and the experimental values is satisfactory. The low log(s_N0/s_NE) value for acetone, 0.053, and that for toluene, 0.083, are obviously outliers and were not included in the correlation expression. The agreement in Figs. 1 and 2 of the present paper is better than that achieved for the salting out constant of sodium chloride shown in Fig. 2 of [31], for the data from Xie et al. [13] and of Ni and Yalkowski [34], involving both aromatic and aliphatic solutes.

Although seawater consists mainly of aqueous sodium chloride, the presence of the other salts does have an effect on the solubility of non-ionic organic solutes as is seen, e.g., in the review [13]. Therefore, the correlation expression (6) differs somewhat from the general expression, eq. (12) in terms of the π* descriptor in [31]. The variety of aliphatic solutes that could be considered here is too small to warrant a reliable prediction for other aliphatic solutes, but in the case of aromatic solutes this should be possible by means of eqs. (6) or (7), depending on whether δ_H or π* values for solutes not included in the present set are available or can be estimated.