This chapter extends thermodynamics to systems whose composition can change by introducing the concepts of mixing, partial molar quantities, and chemical potential. Students will learn how composition influences the Gibbs function, why mixing is generally spontaneous, and how chemical potential serves as the driving force behind changes in composition. The chapter concludes by developing the Gibbs-Duhem equation and fugacity, providing tools for describing both ideal mixtures and real gases.
Mixing changes the entropy, enthalpy, and Gibbs function of a system. In this objective, students will learn why ideal mixtures exhibit \(\Delta H_{\mathrm{mix}}=0\), \(\Delta S_{\mathrm{mix}}>0\), and \(\Delta G_{\mathrm{mix}}<0\), making mixing a spontaneous process.
The properties of a mixture depend on the contributions of its individual components. Students will learn how partial molar quantities describe these contributions and how they can be used to calculate the total properties of a mixture.
The chemical potential describes how the Gibbs function changes as the composition of a system changes. Students will learn why chemical potential serves as the driving force behind mixing, phase changes, and chemical reactions.
Chemical potentials depend on both pressure and composition. Students will derive and apply expressions describing these dependencies for pure substances and ideal mixtures.
The Gibbs-Duhem equation places important constraints on the chemical potentials of the components of a mixture. Students will learn how this relationship is derived and how it can be used to relate changes in the chemical potentials of different components.
Real gases often deviate from ideal behavior. Students will learn how fugacity and the fugacity coefficient provide corrections that allow the simple ideal-gas expressions for chemical potential to be extended to real systems.