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15: Chemical Potential, Fugacity, Activity, and Equilibrium

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  • In Chapters 11-14, we define chemical potential, fugacity, and activity. We find numerous relationships among these quantities. In Sections 15.1 and 15.2, we summarize the principal relationships between chemical potential and fugacity and between chemical potential and activity. Thereafter, we introduce some basic ideas about the chemical potentials, fugacities, and activities of liquids, solids, solvents, and solutes. We use these ideas to relate standard Gibbs free energy changes to fugacities and activities in systems at equilibrium.

    • 15.1: The Chemical Potential and Fugacity of a Gas
      The fugacity of a gas in any system is a measure of the difference between its chemical potential in that system and its chemical potential in its hypothetical ideal-gas standard state at the same temperature. The chemical potential of A in a particular system, μA , is the change in the Gibbs free energy when the amounts of the elements that form one mole of A pass from their standard states as elements into the (very large) system as one mole of substance A .
    • 15.2: The Chemical Potential and Activity of a Gas
      To make predictions about processes involving substance A, we need information about the chemical potential of A. Introducing the fugacity does not introduce new information; the fugacity is merely a convenient way to relate the chemical potential to the composition of the system. The fugacity relationship is valid whether we can actually measure the chemical potential or not. To use the relationship for practical calculations, we must know both, of course.
    • 15.3: The Pressure-dependence of the Fugacity and Activity of a Condensed Phase
      So far, we have investigated fugacity and activity only for gases. Let us now consider a system that consists entirely of substance A present as either a pure liquid or a pure solid. We assume that the temperature is fixed and that the pressure on this condensed phase can be varied. For our present discussion, it does not matter whether the condensed phase is a liquid or a solid.
    • 15.4: Standard States for the Fugacity and Activity of a Pure Solid
      If substance is a liquid at one bar and the temperature of interest, pure liquid is the standard state for the calculation of the enthalpy and Gibbs energy of formation. From thermal measurements, we can find the standard Gibbs energy of formation of this liquid. If we can measure the vapor pressure of the substance and find an equation of state that describes the behavior of the real vapor, we can also find its fugacity and the standard Gibbs energy of formation of its hypothetical ideal gas
    • 15.5: The Chemical Potential, Fugacity, and Activity of a Pure Solid
      The relationship between the standard Gibbs free energy of formation of a substance whose standard state is a solid and the Gibbs free energy of the substance in its hypothetical ideal-gas standard state is essentially the same as described in the previous section for a liquid. In each case, to find the fugacity of the condensed phase in its standard state, it is necessary to find a reversible path that takes the condensed-phase substance to its hypothetical ideal-gas standard state.
    • 15.6: Chemical Potential, Fugacity, and Equilibrium
      In practice, a great many substances are non-volatile. The Gibbs free energy of formation of their hypothetical ideal-gas standard states and their fugacities cannot be measured. For such substances, we have recourse to other standard states and use activities to express the equilibrium constant.
    • 15.7: Chemical Potential, Activity, and Equilibrium
      The relationship between the equilibrium constant and the standard Gibbs free energy change for a reaction is extremely useful. If we can calculate the standard Gibbs free energy change from tabulated values, we can find the equilibrium constant and predict the position of equilibrium for a particular system. Conversely, if we can measure the equilibrium constant, we can find the standard Gibbs free energy change.
    • 15.8: The Rate of Gibbs Free Energy Change with Extent of Reaction
      If a reacting system is not at equilibrium, the extent of reaction is time-dependent.
    • 15.9: Problems

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