2 replies to this topic

[Jorge Kley]

Hello everybody.

I'm working on the calculations of solution properties. But I'm struggling on the following:

How do I calculate the property of liquid a mixture when the temperature is above the boiling point of one of its pure compounds?

I'm using the following approach for a given property M:

M=M(ideal solution)+M(excess)

Ideal solution is calculated from the pure compounds properties, and excess term is calculated from an activity coefficient model (since Gibbs free energy is a generating function it is possible to find the excess specific volume, enthalpy, etc. from activity coefficient model).

The issue is to evaluate the pure compound property for the ideal solution term, since it will be a vapour, not a liquid...

Take as example the binary solution water+ethanol at 1 atm. Water boiling point is around 100 °C, ethanol boiling point is around 77 °C.

If this mixture has 20 % (mol) of ethanol at 1 atm, it will start to bubble around 84 °C. If I want to calculate the specific volume of this mixture at 80 °C, how should I evaluate the specific volume of ethanol to include it on the ideal solution term?

Thanks.

[MrShorty]

I think it starts with knowing enough about your property and your estimation method to know what your method expects. For example, most activity coefficient based models that I see use "property of pure component at T and saturation pressure" for its reference pressure. If that is the reference condition, then you will use that. So, for your ethanol + water at 80 C example, you will calculate the saturated liquid density of ethanol (and water) at 80 C (whatever pressure that happens to correspond to) for the pure component property, and the 1 atm isn't even a part of calculating the pure component properties.

 

In the event that the model is insistent that the pure component properties be calculated at T and P, then I would expect some discussion in the model describing how to calculate some of these "hypothetical" liquid states. For a property like density of a liquid much colder than its critical temperature and at low pressures, I would expect to see the discussion suggest that substituting saturated liquid density introduces minimal error.

 

In the end, it comes down to knowing enough about your activity coefficient model and exactly what it is using for its reference condition, and how much pressure really impacts your calculation. If the activity coefficient model is using "pure component property at saturation" as its reference condition, then use that for your pure component property. If it is using "(hypothetical) pure component at T and P" then use that. Some properties (like volume/density of a liquid well below its critical temperature) will usually be insensitive to pressure, so you can adjust pressure as needed to get a suitable value for the pure component property.

[Jorge Kley]

Thank you MrShorty.

 

That was exactly my point. Most thermodynamics books do not mention this "problem" of the ideal solution reference state. Some of them talk briefly about it, and recommend either using an hypothetical property (extrapolating some equation or using the meta stable root from an EOS) or doing some approximation to the saturated state.

 

I was just curious to see if someone else had a different idea or maybe discuss other approach.

 

Additionaly, I've found an article which shows that we can use other reference states to avoid the hypothetical ones: https://pubs.acs.org....1021/ie8006566