# 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.
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?

Chestermiller said:
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).

## 1. What is departure enthalpy for mixture?

Departure enthalpy for mixture is a thermodynamic property that describes the deviation of the enthalpy of a mixture from an ideal mixture. It takes into account the interactions between the different components in a mixture and is used to understand the behavior of non-ideal mixtures.

## 2. How is departure enthalpy for mixture calculated?

Departure enthalpy for mixture can be calculated using various equations of state (EOS) such as the Peng-Robinson or Redlich-Kwong equations. These equations use parameters such as temperature, pressure, and mole fractions to determine the departure enthalpy.

## 3. What is the significance of departure enthalpy for mixture?

Departure enthalpy for mixture is important in understanding the thermodynamic properties of real mixtures, which are often non-ideal. It allows for the prediction of phase behavior, heat and mass transfer, and other properties of mixtures that are used in various industrial processes.

## 4. How does departure enthalpy for mixture differ from enthalpy of mixing?

Enthalpy of mixing is the enthalpy change when two or more substances are mixed together. It assumes ideal behavior and does not take into account the interactions between the components. Departure enthalpy for mixture, on the other hand, accounts for these interactions and gives a more accurate representation of the enthalpy of a non-ideal mixture.

## 5. Can departure enthalpy for mixture be negative?

Yes, departure enthalpy for mixture can be negative. A negative value indicates that the actual enthalpy of the mixture is lower than the ideal enthalpy, which can occur when there are attractive interactions between the components. A positive value, on the other hand, indicates repulsive interactions between the components.

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