Analytic expressions for the equilibrium distributions of isomer groups in homologous series

The equilibrium distribution of isomer groups in a homologous series is a function of the ratio of the number of hydrogen atoms to the number of carbon atoms at a given temperature and is independent of the pressure, except for homologous series with the molecular formulas CnH2n. Alternatively, the distribution can be taken to be a function of the equilibrium partial pressure of ethylene for all homologous series. An advantage of using the partial pressure of ethylene as the independent variable is that the equilibrium distribution can be expressed as an analytic function of the carbon number at higher carbon numbers. The distribution functions have been derived for the alkanes and alkenes for the case that the standard Gibbs energies of formation of the isomer groups are a linear function of carbon number. Experimentally it is found that a linear relation is approached as the carbon number is increased. Expressions are derived for the mean carbon number and the carbon number contributing the largest weight fraction for given conditions, without calculating the whole distribution using a general equilibrium program.