Relationship between the general laws of vapor-liquid equilibria and the analytical curve of emission spectrometry

The relationship between the vapor-liquid equilibrium and the analytical curve of emission spectrometry is discussed on the basis of Hirata's equation, i.e., $\text{y}{}_1\text{y}{}_2$ = α($\text{x}{}_1\text{x}{}_2$)^β, where y is the mole fraction in the vapor phase, x in the liquid phase, α and β are constants for binary systems in a certain concentration range, and the indices $\text{1}$ and $\text{2}$ refer to the two components. Evaporation produced by different atomization-excitation systems can be characterized by apparent evaporation constants, α' and β', the values of which fall between the true values, α and β, of the normal distillation, and unity. Two powder techniques were selected representing the limiting cases: injection spark excitation (α' ≈ α, β' ≈ β) and controlled arc excitation (α' ≈ 1, β' ≈ 1). Using these excitation methods, the analytical curves of the impurities in industrial alumina and electrocorundum were studied using cup-electrode techniques with arc excitation. As a result, one of Hirata's rules could be selected for a given pair of elements. An unambiguous correlation between the properties of the analytical curves and Hirata's rules could be established.