$1.$The relation between fugacity and the chemical $\_\_\_\_\_\_\_\_\_$ provides a deeper understanding of phase equilibria.

In binary systems, the $\_\_\_\_\_\_\_\_\_$ model simplifies the calculation of activity coefficients by assuming ideal mixing rules.

The $\_\_\_\_\_\_\_\_\_$ test is used to assess the thermodynamic consistency of vapor$-$liquid equilibrium data for binary mixtures.

$\_\_\_\_\_\_\_\_\_$ thermodynamics is a field that applies statistical mechanics to calculate properties of mixtures, including activity coefficients.