A continuous thermodynamics approach to chemical equilibrium within an isomer group

As the number of carbon atoms increases in an homologous series the number of isomers becomes so large that it becomes advantageous to use standard thermodynamic properties for the isomer group and to use probability density functions to represent the distribution of properties within the isomer group. The Pearson type III probability density function is used to represent the distribution of the standard Gibbs energy of formation within an isomer group. The standard Gibbs energy of formation of the isomer group is expressed in terms of the minimum, mean, and standard deviation of this probability density function. The probability density function for the equilibrium mole fraction within the isomer group is expressed in terms of these same properties for the isomer group and the temperature. Two types of equations are derived for the calculation of the other standard thermodynamic properties of an isomer group from the probability density function for the standard Gibbs energy of formation. The use of these equations is illustrated by the calculation of isomer group properties for the decanes at 1000 K in the ideal gas state.