The difference between the definition of the chemical potential in mathematical terms and its evaluation from experimental data is emphasized. A detailed analysis of the treatments used for mixtures of non electrolytes is used as a guide for the understanding of the treatment required for electrolyte systems. In both cases, the activity coefficients are calculated from data obtained in isothermal closed systems. The perfect analogy between these two cases is demonstrated. Also in both cases, the conditions required for the interpretation of the chemical potential as partial molar property cannot be satisfied experimentally in the measurements. The solution to this apparent impasse is based on a clear distinction between the mathematical and the physical worlds of thermodynamics. Answers are given to the main arguments against the measurement of individual ionic activities. (C) 2011 Elsevier B.V. All rights reserved.