nonideality

Nonideality is the deviation of a real system from an ideal model, caused by interactions between particles, finite molecular size, and other non-ideal effects. It is relevant in gases, liquids, solutions, electrolytes, and polymers, and it is essential for accurate predictions of thermodynamic properties and phase behavior.

In gases, the ideal gas law assumes no interactions and point particles. Real gases diverge from PV = nRT, especially at high pressure, and are described by the compressibility factor Z = PV/(nRT). Nonideality is often represented by virial equations of state or by more general models such as van der Waals or Peng-Robinson equations, which account for intermolecular forces and molecular size.

In solutions and mixtures, ideal behavior is described by Raoult's law and simple mixing rules. Real mixtures exhibit nonideality described by activity coefficients gamma_i, with the true activity a_i = gamma_i x_i and the chemical potential mu_i = mu_i^0 + RT ln a_i. Nonidealities arise from solute–solvent interactions, polarity, hydrogen bonding, or size and shape differences. For electrolytes, ionic interactions require models like Debye-Hückel theory or extended frameworks. For liquid mixtures, semi-empirical models such as NRTL or UNIQUAC are commonly used to estimate activity coefficients.

Nonideality also affects phase equilibria, fugacity, and transport properties, influencing partial molar properties and diffusion. It is a central consideration in chemical engineering, physical chemistry, and materials science, underpinning the design of separation processes, crystallization, polymer solutions, and cryogenic systems.