Thermodynamic properties are calculated for mixtures of ideal gases in equilibrium for temperatures up to 15,000° K. Results for air and a model Mars atmosphere are given. The equilibrium composition of a gas mixture at a given temperature and pressure is determined by minimizing the Gibbs free energy. Species of the following types are included in the mixture: atoms and atomic ions, diatomic and linear triatomic molecules and ions, and electrons. Quantum statistical mechanics is used to determine thermodynamic properties of each species. For the diatomic species, accurate evaluations of vibrational anharmonicity, vibration-rotation interaction, and rotational stretching corrections are carried out. Comparisons are made between results with and without the above corrections.