Difference between revisions of "Comparing activity coefficients between different thermodynamic frameworks"

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(Created page with "'''Question:''' I am comparing the activity coefficient of the nitrate ion (NO<sub>3</sub><sup>1-</sup>). I looked up the value in OLI Studio for the AQ thermodynamic framew...")
 
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Below, I am hoping to provide further reasoning on the basis of thermodynamic fundamentals.
 
Below, I am hoping to provide further reasoning on the basis of thermodynamic fundamentals.
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Part 1.
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In an equilibrium solution at a given temperature and pressure, Gibbs-Duhem equation must hold, i.e.,
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[[File:Eqn1.png]]
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where a<sub>i</sub> is activity of species i: a<sub>i</sub>=m<sub>i</sub>∙γ<sub>i</sub> and a<sub>0</sub>=a<sub>w</sub> (water activity), and n is the number of species in the solution.
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Equation (1) can be integrated as (where n<sub>0</sub> is set to be 55.508 for 1 kg H<sub>2</sub>O):

Revision as of 21:13, 28 September 2020

Question:

I am comparing the activity coefficient of the nitrate ion (NO31-). I looked up the value in OLI Studio for the AQ thermodynamic framework and also in the MSE thermodynamic framework. They differ by over 50% with the MSE derived values being much larger. Why?

Response: From Peiming Wang, PhD. OLI Systems


I agree with the concept that obtaining different activity coefficient values from the two different models (i.e. AQ vs. MSE) under the same total salt concentration, temperature, and pressure conditions if speciation is different (e.g. with or without the ion-pair such as NaNO3(aq) in the NaNO3 solution). This is because activity coefficients are a function of each and all individual species (ions or neutral), and the speciation in the two models are different, resulting in different equilibrium concentrations for individual species, and thus, different activity coefficients.

Below, I am hoping to provide further reasoning on the basis of thermodynamic fundamentals.

Part 1.

In an equilibrium solution at a given temperature and pressure, Gibbs-Duhem equation must hold, i.e.,

Eqn1.png

where ai is activity of species i: ai=mi∙γi and a0=aw (water activity), and n is the number of species in the solution. Equation (1) can be integrated as (where n0 is set to be 55.508 for 1 kg H2O):