The solubility and isotopic fractionation of gases in dilute aqueous solution. I. Oxygen

Abstract

A very precise and accurate new method is described for determination of the Henry coefficient k and the isotopic fractionation of gases dissolved in liquids. It yields fully corrected values for k at essentially infinite dilution. For oxygen the random error for k is less than 0.02%, which is an order of magnitude better than the best previous measurements on that or any other gas. Extensive tests and comparison with other work indicate that systematic errors probably are negligible and that the accuracy is determined by the precision of the measurements. In the virial correction factor (1+λP_t), where P_t is the total pressure of the vapor phase, the coefficient λ for oxygen empirically is a linear decreasing function of the temperature over the range 0–60°C. The simple three-term power series in 1/T proposed by Benson and Krause,

$$\ln k = a_0 + a_1 /T + a_2 /T^2 $$

provides a much better form for the variation of k with temperature than any previous expression. With a₀=3.71814, a₁=5596.17, and a₂=−1049668, the precision of fit to it of 37 data points for oxygen from 0–60°C is 0.018% (one standard deviation). The three-term series in 1/T also yields the best fit for the most accurate data on equilibrium constants for other types of systems, which suggests that the function may have broader applications. The oxygen results support the idea that when the function is rewritten as

$$\ln k = - (A_1 + A_2 ) + A_1 \left( {\frac{{T_1 }}{T}} \right) + A_2 \left( {\frac{{T_1 }}{T}} \right)^2 $$

it becomes a universal solubility equation in the sense that A₂ is common to all gases, with T₁ and A₁ characteristic of the specific gas. Accurate values are presented for the partial molal thermodynamic function changes for the solution of oxygen in water between the usual standard states for the liquid and vapor phases. These include the change in heat capacity, which varies inversely with the square of the absolute temperature and for which the random error is 0.15%. Analysis of the high-temperature data of Stephan et al., in combination with our values from 0–60°C, shows that for oxygen the fourterm series in 1/T,

$$\ln k = - 4.1741 + 1.3104 \times 10^4 /T - 3.4170 \times 10^6 /T^2 + 2.4749 \times 10^8 /T^3 $$

where p=kx and p is the partial pressure in atmospheres of the gas, probably provides the best and easiest way presently available to calculate values for k in the range 100–288°C, but more precise measurements at elevated temperatures are needed. The new method permits direct mass spectrometric comparison of the isotopic ratio³⁴O₂/³²O₂ in the dissolved gas to that in the gas above the solution. The fractionation factor α=³²k/³⁴k varies from approximately 1.00085 (±0.00002) at 0°C to 1.00055 (±0.00002) at 60°C. Although the results provide the first quantitative determination of α vs. temperature for oxygen, it is not possible from these data to choose among several functions for the variation ofInα with temperature. If the isotopic fractionation is assumed to be due to a difference in the zero-point energy of the two species of oxygen molecules, the size of the solvent cage is calculated to be approximately 2.5 Å. The isotopic measurements indicate that substitution of a³⁴O₂ molecule for a³²O₂ molecule in solution involves a change in enthalpy with a relatively small change in entropy.