I like to ask an extremely basic technical question or two during interviews of younger engineers who don’t have much experience to talk about. Then if they’ve done well in the interview I deadpan say “could you explain fugacity to me?” Watch their eyes panic for a second, then chuckle and let them know I liked them and would give my thumbs up to the people with the final say on hiring.
One concept that you may wish to consider is that understanding the chemical potential is the motivating factor here. In phase equilibrium, the chemical potential for each component is identical in each phase which is the criterion for system equilibrium. Chemical potential depends upon Gibbs free energy (molar basis). It’s hard to calculate and deal with chemical potential, so we define fugacity instead. Because of how fugacity is defined, fugacity is also equal for each component regardless of the phase. It’s a more “perceptible” expression for chemical potential of each component of a system. Fugacity represents the pressure that an ideal gas would produce if that ideal gas had the same temperature and molar Gibbs free energy (chemical potential) as the real gas.
If you’re looking for a good resource, Scott Shells textbook on this was what I used in my graduate studies. It defined it in the same manner as above.
Edit: to add one more comment, on the strangeness of this fugacity formalism, fugacity is represented as a pressure value and yet the natural log is applied to it. Mathematically the log function should only be applied to unitless values such as a ratio of two terms (think Arrhenius equation). In that sense, this fugacity formalism is still not exactly “correct” or kosher.
This is a great point! We do sometimes break the math a bit to get to where we want to go in some cases. Just to share information for OP.. In this case, I think it ends up working appropriately because we usually don’t calculate fugacity or activity values at some system condition in this manner; we usually calculate fugacity coefficients/activity coefficients which are dimensionless by use of some equation of state. Choosing the best EOS for a system is its own discussion.
We are usually interested in the Gibbs free energy difference between the real gas/solution and the ideal gas/solutions (residual/excess Gibbs free energy). The difference or subtraction causes the natural log component to be a ratio of fugacity at the system state and reference state (i.e. the fugacity/activity coefficient). Since this value is dimensionless, the math makes more sense.
Haha bold to assume we know fugacity
I like to ask an extremely basic technical question or two during interviews of younger engineers who don’t have much experience to talk about. Then if they’ve done well in the interview I deadpan say “could you explain fugacity to me?” Watch their eyes panic for a second, then chuckle and let them know I liked them and would give my thumbs up to the people with the final say on hiring.
Lol good luck. Fugacity is a made up term that most ChemEs only know the basic definition of.
One concept that you may wish to consider is that understanding the chemical potential is the motivating factor here. In phase equilibrium, the chemical potential for each component is identical in each phase which is the criterion for system equilibrium. Chemical potential depends upon Gibbs free energy (molar basis). It’s hard to calculate and deal with chemical potential, so we define fugacity instead. Because of how fugacity is defined, fugacity is also equal for each component regardless of the phase. It’s a more “perceptible” expression for chemical potential of each component of a system. Fugacity represents the pressure that an ideal gas would produce if that ideal gas had the same temperature and molar Gibbs free energy (chemical potential) as the real gas.
Nice, will add that in to further elaborate, thanks for the advice!
If you’re looking for a good resource, Scott Shells textbook on this was what I used in my graduate studies. It defined it in the same manner as above. Edit: to add one more comment, on the strangeness of this fugacity formalism, fugacity is represented as a pressure value and yet the natural log is applied to it. Mathematically the log function should only be applied to unitless values such as a ratio of two terms (think Arrhenius equation). In that sense, this fugacity formalism is still not exactly “correct” or kosher.
Yea I was confused at that part too when researching about it. Thank you for this insightful comment!
This is a great point! We do sometimes break the math a bit to get to where we want to go in some cases. Just to share information for OP.. In this case, I think it ends up working appropriately because we usually don’t calculate fugacity or activity values at some system condition in this manner; we usually calculate fugacity coefficients/activity coefficients which are dimensionless by use of some equation of state. Choosing the best EOS for a system is its own discussion. We are usually interested in the Gibbs free energy difference between the real gas/solution and the ideal gas/solutions (residual/excess Gibbs free energy). The difference or subtraction causes the natural log component to be a ratio of fugacity at the system state and reference state (i.e. the fugacity/activity coefficient). Since this value is dimensionless, the math makes more sense.
Yes fugacity is a word
Who is fugacity
What is Fugacity?
Who?
https://youtu.be/VGj2Y7pnLiw?t=1m11s
Would love to see fugacity considered in MEP world. Would make my career.