Editing Ideal solution (section)

== Consequences ==
Solvent–solute interactions are the same as solute–solute and solvent–solvent interactions, on average. Consequently, the enthalpy of mixing (solution) is zero and the change in [[Gibbs free energy]] on mixing is determined solely by the [[entropy of mixing]]. Hence the molar Gibbs free energy of mixing is
:<math>\Delta G_{\mathrm{m,mix}} = RT \sum_i x_i \ln x_i </math>
or for a two-component ideal solution 
:<math>\Delta G_{\mathrm{m,mix}} = RT (x_A \ln x_A + x_B \ln x_B)</math>
where m denotes molar, i.e., change in Gibbs free energy per mole of solution, and <math>x_i</math> is the mole fraction of component <math>i</math>. Note that this free energy of mixing is always negative (since each <math>x_i \in [0,1]</math>, each <math>\ln x_i</math> or its limit for <math>x_i \to 0</math> must be negative (infinite)), i.e., ''ideal solutions are miscible at any composition'' and no phase separation will occur.

The equation above can be expressed in terms of [[chemical potential]]s of the individual components
:<math>\Delta G_{\mathrm{m,mix}} = \sum_i x_i \Delta\mu_{i,\mathrm{mix}}</math>
where <math>\Delta\mu_{i,\mathrm{mix}}=RT\ln x_i</math> is the change in chemical potential of <math>i</math> on mixing. If the chemical potential of pure liquid <math>i</math> is denoted <math>\mu_i^*</math>, then the chemical potential of <math>i</math> in an ideal solution is

:<math>\mu_i = \mu_i^* + RT \ln x_i.</math>

Any component <math>i</math> of an ideal solution obeys [[Raoult's Law]] over the entire composition range:
:<math>\ p_{i}=(p_{i})_\text{pure} x_i </math>
where <math>(p_i)_\text{pure}</math> is the equilibrium vapor pressure of pure component <math>i</math> and <math> x_i\,</math>is the mole fraction of component <math>i</math> in solution.