An ambiguity in the definition of the activity coefficient at infinite dilution
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where Y~ is the nominal activity coefficient at Xo = 0 and eo is the interaction parameter, defined by eo - d In y o / d x o
J. P. NEUMANN and M. VENKATRAMAN As a part of a recent review of the binary copper-oxygen system by Neumann et al.,J an analysis was made of the thermodynamic behavior of the dilute solutions of oxygen in liquid copper. Although most of the Gibbs energy data by the various investigators were in reasonable agreement in the temperature range from 1400 to 1500 K, a statistical analysis revealed a "bimodal" distribution of the data. That is, the data, for example in terms of the activity coefficient of oxygen in liquid copper at infinite dilution, T~, clustered into two separate groups. In a subsequent study by Venkatraman et al.,Z it was shown that this bimodal distribution is primarily due to the use of different reference electrodes in the studies that employed solid-state emf techniques. However, another factor that may also contribute to the systematic difference in the activity coefficient data is an ambiguity in the definition of the activity coefficient at infinite dilution. It is the purpose of the present communication to discuss this ambiguity. Similar to the properties of many other solid or liquid solutions, the thermodynamic behavior of dilute solutions of oxygen in liquid copper is characterized by two distinct regions (Figure 1). In the concentration range from Xo (atomic fraction oxygen) = 0 to - 0.01, Henry's law is obeyed, that is, the activity coefficient Yo is constant at constant temperature. In the concentration range from Xo = 0.01 to - 0.10, the logarithm of the activity coefficient is a linear function of the oxygen concentration, obeying an expression proposed by Wagner 3 and Chipman, 4 again at constant temperature, In To = In Y~ + eoxo
[1]
-1.3 -1.4 -1.5
T = 1473 K
~0-- 0
-1,6
Equation [1] is very useful in describing the variation of the activity coefficient To as a function of the oxygen concentration in the appropriate composition range, but it must be kept in mind that the constant term Y~ is only a nominal value, obtained by extrapolation to Xo = 0. It is to be distinguished clearly from the true y~ in Henry's law region. In order to illustrate the difference between Y~ (true) and Y~ (nominal), the activity measurements of oxygen in liquid copper by Stichel 5 and Osterwald et al. ~ are presented as examples, The data in both publications are based on solidstate emf measurements using the cell: air(Po2 = 0.21 atm)/ZrO2/O in liquid Cu The measurements by Stichel 5 show (Figure 2) that in the concentration range up to Xo -~ 0.01 the slope of the emf vs log Xo curve is constant, indicating Henrian behavior. The activity coefficient obtained from the data in this region has a constant value In T~ (true) = - 1 . 6 0 --- 0.02 (standard state pressure is 1 atm). In the composition range above Xo -~ 0.01, the data by Osterwald et al. 6 indicate (Figure 1) that, in accord with Eq. [1], In To is a linear function of the oxygen concentration. The curve can be describe
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