The Richard Stockton College of New Jersey
Chemistry Program, School of Natural Sciences and Mathematics
PO Box 195, Pomoma, NJ
CHEM 3410: Physical Chemistry I — Fall 2008
October 6, 2008
Lecture 15: Chemical potential of an ideal gas
References
1. Levine, Physical Chemistry, Sections 4.6–4.8, 6.1–6.2
Key Concepts
•For a single component system consisting of an ideal gas, we were able to arrive at an expression for
the chemical potential by integrating our expression for dG for a single component system at constant
temperature (dG =V dP ) between some reference pressure P◦and the pressure of interest P:
µ(T, P ) = µ◦(T) + RT ln P
P◦
where µ◦(T) is the chemical potential of the pure gas in the reference state (usually P= 1 bar)
•We can now arrive at expressions for related quantities such as S, since we know that −S=∂G
∂T P,n =∂ µ
∂T P,n
(where the bar above the quantity means per mole, or the molar entropy).
•For an ideal gas in a mixture, we have to account for the actual amount of each gas in the system using
the mole fraction and/or partial pressure. These two quantities are related. For component A, if we
denote the partial pressures as PAand the mole fraction as XA, then we can write the following:
PA=XAPT OT AL
•By doing some more integrating from a starting state of the pure gas at the reference pressure, to
the partial pressure of the gas in the mixture, we arrived at the following expression for the chemical
potential of a gas (i) in a mixture of gases:
µmixture
i(T, P ) = µpure
i(T, P ) + RT ln XA
item The mixing of ideal gases is completely driven by entropy. There is no interaction between gas
atoms/molecules in an ideal gas, therefore ∆Hmix = 0.Going from the unmixed to mixed state results
in an increase in entropy (∆Smix >0) meaning that ∆Gmix <0 (∆G= ∆H−T∆S).
•Based on our expression for the chemical potential of an ideal gas in a mixture, we were able to arrive
at an expression for the free energy of mixing of ideal gases. In general for a system of igases and
then for a two-compoennt system (A & B) we wrote:
∆Gmix =RT XXiln Xi
∆Gmix =RT (XAln XA+XBln XB)
Related Exercises in Levine
Exercises: 4.40, 6.1