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Chemical Potential of Ideal Fermi and Bose Gases
Published in Kavati Venkateswarlu, Engineering Thermodynamics, 2020
Chemical potential is quantified by fugacity. If a chemical with two different fugacities is kept in two different compartments that are in contact, the flow of chemical potential takes place from the compartment of higher fugacity to the compartment of lower fugacity. This will be continued until there is an equilibrium—i.e., the fugacities are equal—at which net transfer is zero. Fugacity can be effectively used for the calculation of chemical equilibrium of real gases based on the condition that the chemical potential of the reactants is equal to the chemical potential of the products. Fugacity has pressure dimensions and is a kind of effective pressure. Fugacity is the pressure that an imaginary gas will have so that it is the chemical potential at a specified temperature to be the same as the chemical potential of the real gas. Fugacity is equal to its pressure when the gas is an ideal gas. In chemical thermodynamics, fugacity can be used to compute the chemical equilibrium constant of a real gas, which is an effective partial pressure of a real gas that replaces mechanical partial pressure. Fugacity has the dimensions of pressure. This effective partial pressure is equal to the pressure of an ideal gas that has the same temperature and molar Gibbs free energy as the real gas.
Equilibrium Partitioning
Published in J. Mark Parnis, Donald Mackay, Multimedia Environmental Models, 2020
The advantage of the use of fugacity as an equilibrium criterion is that the properties of each phase are treated separately using a phase-specific equation. By contrast, partition ratios treat phases in pairs, which can obscure the nature of the underlying phenomena. We may detect a variability in K12 and not know from which phase the variability is arising. Further complications arise if we have a large number of phases to consider. For example, with ten phases, there are then 90 possible partition ratios, of which only nine are independent. By comparison, there are only ten Z-values needed to define this system at equilibrium.
Modeling the Fate of 2,4,6-Trichlorophenol in Pulp and Paper Mill Effluent in Lake Saimaa, Finland
Published in Mark R. Servos, Kelly R. Munkittrick, John H. Carey, Glen J. Van Der Kraak, and PAPER MILL EFFLUENTS, 2020
Donald Mackay, Jeanette M. Southwood, Jussi Kukkonen, Wan Ying Shiu, Debbie D. Tam, Dana Varhaníčkova, Rebecca Lun
Fugacity is a thermodynamic property which is related to chemical equilibrium. It is logarithmically related to chemical potential and may be equated to the partial pressure for an ideal gas. Fugacity thus has units of pressure and has been described as an “escaping pressure or tendency”.
A Gibbs energy minimization study on the biomass gasification process for methanol synthesis
Published in Biofuels, 2020
Majid Emami-Meibodi, MohammadReza Elahifard
Form as the total number of chemical elements and c as the number of final components, the material balance obeys:where aij is the number of atoms of element j in molecule i, and bj is the total amount of element j in the mixture. It has been proved that with the real gas assumption, the following set of m nonlinear equations should be solved numerically for the m unknown Lagrange Multipliers, ,where , , , and for . The Newton–Raphson method will be applied to find the . Here the fugacity coefficients are calculated using the Peng–Robinson equation of state. The values of pure Gibbs free energy of the final products at a specified temperature are estimated using NASA Glenn coefficients [26] correlations.
Molecular simulation of shale gas adsorption in type III kerogen organic matter
Published in Petroleum Science and Technology, 2022
Jizhen Zhang, Denglin Han, Chenchen Wang, Wei Lin, Huiwen Zhang, Shuo Li
The fugacity coefficient is calculated by Peng-Robinson (PR) equation (Peng and Robinson 1976). The multi-component gas composition of shale gas reservoir is simplified as a mixture of 80% CH4 and 20% C2H6 (Curtis 2002; Furmann et al. 2014). Figure 1 shows the relationship between pressure and fugacity coefficient. The radial distribution function of each atom in the adsorption structure was calculated by canonical ensemble (NVT). The molecular dynamics calculation of 1 ns was carried out by Andersen thermal bath. The step length was 1 fs. The first 5 × 105 steps made the system reach equilibrium, and the last 5 × 105 steps were used to calculate the thermodynamic properties.