The thermodynamic treatment of fluids at elevated pressures and temperatures has been laid out in numerous publications (e.g. Gillespie, 1925, 1936; Beattie 1930, 1949, 1955; Beattie and Stockmayer, 1951). For the derivation of the general accepted forms of the fugacity the so called "general limit method" is used, which avoids basically indefinite integrals* if real fluids are handled using ideal gases as a reference model. In most textbooks of physical chemistry the "general limit method" is also used to introduce the term fugacity. While the reasoning and the derived equations are correct, it seems that many students and some teachers misunderstand the logic behind "general limit method" which leads to errors in textbooks, publications, and lecture notes, at least in geosciences. This problem is especially true for the necessary reference and standard conditions of fluids, which requires a sufficient low pressure P* such that a fluid behaves as an ideal gas. This again makes it sometimes difficult for students to get a grip on the term fugacity.
IIn my opinion much of the confusion caused by the "general limit method" can be avoided using very similar logic, but rearranging the necessary equations. In addition no assumptions have to be made, but the principal and simple properties of an ideal gas are used directly avoiding the limit considerations. These properties are that the particles have zero volume with no acting intermolecular forces. As the resulting equations defining the fugacity are identical to the "general limit method", some intermediate results may or may not enhance the understanding of the practically used reference and standard conditions. To improve the understanding of the derivation intermediate steps are also included.
*Integrals of the form 
are indefinite, the volume of a fluid is indefinite at a pressure of 0.
