In terms of invariableness of the total concentrations of components in three-component
additive systems [1] (which usually is provided by the conditions of preparation of their initial
composition), the following system of linear equations, in the form of matrix with respect to
temperature coefficients of component activities (or equilibrium concentrations), has been
derived:
(1)
Here symbolizes the enthalpies of formation of the respective species. It has been proved
that the determinant of the matrix of coefficients F, which represent various concentration
functions, is equal to the determinant of the matrix of stability coefficients . Solving the
system of equations (1) in respect to the temperature coefficient for the index of the component
A equilibrium concentration ( ), one can obtain:
(2)
The temperature dependence of the component equilibrium concentration is determined by the
sign and value of the derivative (2). If , then with increasing the temperature the pa
value will also increase. If the derivative (2) takes negative values, then pa decreases when
temperature will grow up. The similar equations have been obtained for the temperature
coefficients of other two components. From the equation (2) it results that the temperature
coefficient of the index of the equilibrium concentration of components at a given initial
composition of the system is directly proportional to the heats of formed species and
inversely proportional to the stability coefficients, which are found in the matching column of
the matrix (1). If the heat of formation and the stability (the stability constants ) of all the
species present in the system are known, then the relations of type (2) may be used for setting of
a given temperature dependence of the equilibrium concentration (or activity) of one of the
existing components in three-component additive systems.