# Departure enthelpy for mixture EOS = enthelpy of mixing?

• maistral
In summary, the ideal mixing enthalpy between two components is the sum of their enthalpy of vaporization plus the enthalpy of fusion of the two components.f

#### maistral

Hi. I am well aware that if say, there are two components A and B, the ideal mixing enthalpy between those two components are:
(1) hmix = zA hA + zB hB.

If I want to get the real behavior of a pure component, I am also aware that; say for example, liquid enthalpy:
(2) hL = Href + ∫CpigdT (from Tref → T) + hRL

I am assuming that if I want to calculate the, say, non-ideal liquid enthalpy of a mixute A and B, the following holds true:
(3) hLmix = xA hL,A + xL,B hB + hRLmix
where hRLmix is defined as the liquid departure enthalpy as predicted by any equation of state; and that hL,A and hL,B is basically (2) in this post; ie. the final equation that I am looking for is:

(4) hLmix = xA [Href,A + ∫Cpig,AdT (Tref → T) + hRL,A] + xL,B [(Href,B + ∫Cpig,BdT (Tref → T) + hRL,B] + hRLmix

What I'm after is, if I am going for modelling non-ideal mixtures, I have to calculate the departure enthalpies of each component (to be added to the pure component enthalpies), then the departure enthalpy of the mixture itself (to be added to the final mixture equation ie. (3))? I am theorizing that the enthalpy departure of the mixture is independent of the enthalpy departure of a pure component at a certain T and P. Also, this holds true for vapors, yes?

I'd like a straightforward answer, I am getting really confused from all these quantities.

You're interested in the enthalpies of liquid mixtures, correct?

You're interested in the enthalpies of liquid mixtures, correct?
Actually I am interested in both liquids and vapors. I wanted to predict thermodynamic properties of mixtures by using only standard equations of state (while I know they could bring up inaccuracies, I just wanted to know if this is 'possible' per se).