Calculation of equilibrium using fugacities

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The discussion centers on the concept of fugacity in chemical equilibrium, specifically the algorithm used to determine equilibrium between liquid and vapor phases. The calculation "(fL/fv)-1" is highlighted, where fL represents the fugacity of the liquid and fv the fugacity of the vapor. The key point is that as different pressures are inputted, this calculation approaches zero, indicating that the fugacities are equal and thus chemical equilibrium is achieved. A question arises regarding the necessity of using fL in the numerator rather than fv, with the assertion that at vapor-liquid equilibrium, the equality of fugacities should make the choice of numerator irrelevant. The discussion seeks clarification on this aspect of the fugacity ratio.
Notwen7
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Its been a while since I took thermo. I was looking through my notes regarding fugacity at chemical equilibrium. There was a clever algorithm used to determine whether the pure compound was at equilibrium based upon the varying pressure with a constant temperature. It had the calculation "(fL/fv)-1" display values, fL being fugacity of the liquid and fv being the fugacity of the vapor. After several inputs of different pressures this calculation will approach 0. Now if "(fL/fv)-1" equals zero then fugacities are equal yielding a chemical equilibrium.

Now if my memory serves there is a reason why we use "(fL/fv)-1" in lieu of "(fv/fL)-1". I am not sure why fL has to be in the numerator. If someone can assist me or show me the right direction I would greatly appreciate it.
 
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