Fugacity
and Activity in Thermodynamics
Fugacity
and Chemical Potential
How to
determine fugacity of a gas?
Fugacity
and Activity:
G.N. Lewis in 1901 introduced the concept of fugacity to
explain the actual behavior of real gases in chemical equilibrium at high
pressures. It is mainly employed in connection with gases mixture but the
introductory treatment is restricted to pure gases.
Fugacity indicates the escaping tendency of a component or
a substance. High gas pressure indicates the tendency of gas molecules to
escape outside the container. Similarly high fugacity indicates a greater
tendency of a component or a substance to escape, dissolve or intermix.
Fugacity may be explained as a substitute for pressure to
explain the behavior of real gases and the activity may be defined as the
substitute for the concentration to explain the behavior of a non- ideal or
real solution. Mathematically, fugacity (f) is defined as
LimP→0 f/P = 1
i.e. as the pressure approaches zero fugacity approaches
pressure. This means that fugacity is the measure of the pressure of the real
gases.
We know that Gibb’s free energy is equal to
dG = VdP - SdT
Now, at constant temperature dT= 0,
Hence above equation becomes dG = VdP eq…… (1)
For one mole of an ideal gas equation of state becomes PV =
RT
Therefore, V
= [RT/P] eq……(2)
Hence Gibb’s free energy eq becomes, dG = [RT/P]dP = RT d
(lnP)
Above equation is for ideal gas, if the gas is not ideal
then pressure is replaced by fugacity
Hence,
dG = RT d(lnf) eq……(3)
Chemical Potential and Fugacity :
In a mixture of real gases, the chemical potential of
constituent i is given by
μ = μi0 + RTlnfi
Where fi is the fugacity of the constituent i in the mixture. Similarly in non-
ideal solutions the chemical potential of any component i is given by
μ = μi0 + RTlnai
where ai is the activity of the component i in the solution.
Activity:
It has been observed that
thermodynamic variables (H, S, G etc.) of a substance in pure state are
different from those in a state of solution .i.e., when a substance goes into
solution the state of aggregation or dispersion changes and H, S and G also
change. This means apart from pressure and temperature these variables also change
with change of composition. The concept of activity gives an index to measure
these changes when a pure substance goes into state of solution.
Fugacity
and activity coefficient:
To get fugacity the pressure has to be corrected by
multiplying with suitable factor.
f = γ × P eq……(4)
γ is called activity coefficient of the gas, γ = f/P
Hence activity coefficient of a gas can be defined as,” the
ratio of fugacity of a gas to the pressure of the gas in the same state.”
For ideal gases γ is always equal to 1. For real gases γ is
always less than 1.
Similarly in non-ideal solutions the concentration has to
be corrected to give activity as follows
a=
γ × C
eq…….(5)
γ represents the
activity coefficient of that component of a solution whose concentration is C.
γ = a/C
For ideal solutions γ = 1 so a=C
Determination of fugacity of a gas:
To determine the fugacity of a gas at any pressure where it
deviates from ideal behavior the following procedure is used.
We know dG = VdP from eq….(1), and dG = RT d(lnf) from eq….(3)
So,
VdP = RT dln f eq……(6)
[
Δlnf/δP]T = V/RT
For an ideal gas the volume of 1 mole RT/P. For a real gas
this volume is represented by a and
is given by
a = RT/P- V
V = RT/P- a
By putting the value of V in eq ….(6) we get
RT (dP/P) – adP =RT dlnf
Dividing both side sby RT we get
dlnf = dP/P – a(dP/RT) or dlnf
= dlnP - a(dP/RT)
dlnf – dlnP = -a(dP/RT)
dln(f/P) = -a (1/RT )dP
If this result is integrated between low virtually zero,
pressure and given pressure P at constant temperature then
dlnf = -1/RT 0P∫ adP
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| Graphical method for determination of fugacity |
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