Визначення ідентифікованості параметрів математичної моделі електропровідності у кондуктометричних моделях

Using an aqueous solution of acetic acid an example, this study has investigated a mathematical model of the electrical conductivity of weak electrolyte dilute solutions. To resolve the issue of identification and reliability in determining the parameters for the mathematical model of the electrical conductivity of dilute solutions of weak electrolytes, the determinant of the Fisher information matrix was calculated. The issues related to determining the association constants and the limiting molar electrical conductivity of weak electrolytes under different conditions of experimental experiments were identified and explained. This paper reports results of mathematical processing of conductometric data for aqueous solutions of acetic acid. It was established that for weak, associated electrolytes, when determining the association constants and the limiting molar coefficients, it is necessary to take into account the existence of a correlation between them. It is proven that at large values of the association constant (5.58 * 104 mol/L) the determinant of the Fisher information matrix is close to zero and there is a structural non-identification of parameters for the mathematical model of electrical conductivity of dilute solutions of weak electrolytes. It is shown that the results of mathematical processing of conductometric data for aqueous solutions of acetic acid indicate the presence of structural non-identification. This is confirmed by the values of the determinant of the Fisher information matrix, which is equal to 5.5 * 10-8, and the normalized index of 0.988. Analysis of the shape of the surface of the objective functions of the studied mathematical models and the form of the average error ellipse reveals the existence of a canyon with an almost flat bottom, which complicates the interpretation and reliability of parameters for the mathematical model of electrical conductivity. The results confirm the possibility of structural non-identification of parameters for the mathematical model of the electrical conductivity of dilute solutions of weak electrolytes