Chapter 9: Thermodynamic Behavior of Solutions

The concept of Raoult’s law establishes the model for an ideal solution, stating that the activity of a component is equivalent to its mole fraction. Complementing this, Henry’s law describes the linear behavior of a dilute solute, where its partial pressure is proportional to its mole fraction within a limited concentration range. The Gibbs–Duhem equation acts as a crucial thermodynamic constraint, guaranteeing that if a solute obeys Henry’s law in a dilute solution, the solvent must simultaneously obey Raoult’s law. Deviations from this ideal behavior are mathematically tracked using the activity coefficient, defined as the ratio of activity to mole fraction. When the activity coefficient is greater than unity, the solution exhibits positive deviations; this correlates with endothermic mixing (enthalpy of mixing is positive), signifying that the bonds between unlike atoms are weaker than those between like atoms, promoting clustering or phase separation. Conversely, an activity coefficient lesser than unity indicates negative deviations, resulting from exothermic mixing (enthalpy of mixing is negative), where stronger bonds between unlike atoms encourage atomic ordering. Ideal solutions specifically exhibit zero volume and zero enthalpy changes upon mixing, meaning their molar Gibbs free energy of mixing is solely governed by the positive configurational entropy of mixing. Nonideal behavior is quantitatively described by the regular solution model, which maintains the ideal entropy of mixing but incorporates a parabolic heat of mixing proportional to an interaction parameter (alpha) times the product of the mole fractions. This model predicts conditions for immiscibility and a miscibility gap: if the alpha parameter is positive and exceeds a critical value proportional to the temperature, the Gibbs free energy curve develops negative curvature. The critical temperature (T sub cr) is equal to alpha divided by 2R. The equilibrium phase boundary is the binodal curve, defined by the compositions at the common tangent, and it encloses the spinodal curve, which marks the boundaries of absolute thermodynamic instability for the homogeneous solution. Finally, the chapter adapts this framework for polymer blends using the Flory–Huggins model, which modifies the entropy contribution to account for the long-chain structure of polymers, thereby often limiting their miscibility.