Editing Ideal solution (section)

== Formal definition ==
Different related definitions of an ideal solution have been proposed. The simplest definition is that an ideal solution is a solution for which each component obeys [[Raoult's law]] <math>p_i=x_ip_i^*</math> for all compositions. Here <math>p_i</math> is the [[vapor pressure]] of component <math>i</math> above the solution, <math>x_i</math> is its [[mole fraction]] and <math>p_i^*</math> is the vapor pressure of the pure substance <math>i</math> at the same temperature.<ref name=Atkins>P. Atkins and J. de Paula, ''Atkins’ Physical Chemistry'' (8th edn, W.H.Freeman 2006), p.144</ref><ref>T. Engel and P. Reid ''Physical Chemistry'' (Pearson 2006), p.194</ref><ref>K.J. Laidler and J.H. Meiser ''Physical Chemistry'' (Benjamin-Cummings 1982), p. 180</ref>

This definition depends on vapor pressure, which is a directly measurable property, at least for volatile components. The thermodynamic properties may then be obtained from the [[chemical potential]] μ (which is the [[partial molar property|partial molar]] [[Gibbs energy]] ''g'') of each component. If the vapor is an ideal gas,

:<math>\mu(T,p_i) = g(T,p_i)=g^\mathrm{u}(T,p^u)+RT\ln {\frac{p_i}{p^u}}.</math>

The reference pressure <math>p^u</math> may be taken as <math>P^o</math> = 1 bar, or as the pressure of the mix, whichever is simpler.

On substituting the value of <math>p_i</math> from Raoult's law, 
:<math>\mu(T,p_i) =g^\mathrm{u}(T,p^u)+RT\ln {\frac{p_i^*}{p^u}} + RT\ln x_i =\mu _i^*+ RT\ln x_i.</math>

This equation for the chemical potential can be used as an alternate definition for an ideal solution.

However, the vapor above the solution may not actually behave as a mixture of ideal gases. Some authors therefore define an ideal solution as one for which each component obeys the fugacity analogue of Raoult's law  <math>f_i = x_i f_i^*</math>. Here <math>f_i</math> is the [[fugacity]] of component <math>i</math> in solution and <math>f_i^*</math> is the fugacity of <math>i</math> as a pure substance.<ref>R.S. Berry, S.A. Rice and J. Ross, ''Physical Chemistry'' (Wiley 1980) p.750</ref><ref>I.M. Klotz, ''Chemical Thermodynamics'' (Benjamin 1964) p.322</ref> Since the fugacity is defined by the equation 
:<math>\mu(T,P) = g(T,P)=g^\mathrm{u}(T,p^u)+RT\ln {\frac{f_i}{p^u}}</math>

this definition leads to ideal values of the chemical potential and other thermodynamic properties even when the component vapors above the solution are not ideal gases. An equivalent statement uses thermodynamic [[activity (chemistry)|activity]] instead of fugacity.<ref>P.A. Rock, ''Chemical Thermodynamics: Principles and Applications'' (Macmillan 1969), p.261</ref>