This document discusses the concept of fugacity, which was introduced by Gilbert Newton Lewis to represent the behavior of real gases. Fugacity is derived from the Latin word for "escaping tendency" and is used extensively in studying phase and chemical reaction equilibria involving gases at high pressures. The document explains that fugacity is defined such that the relation dG = RTd loge f always holds, whether the gas is ideal or real. For an ideal gas, fugacity is proportional to pressure, but for real gases, fugacity and pressure are not directly proportional and the ratio f/P is not constant. Reference states are used to evaluate actual fugacities at various pressures.

1. Chemical Thermodynamics
Fugacity & concept Fugacity

2. Contents
1. Introduction
2. Concepts of Fugacity
3. Reference

3. INTRODUCTION
◦ The concept of Fugacity was introduce by Gilbert Newton
Lewis.
◦ Fugacity is widely used in solution thermodynamic to
represent the behaviour of real gases.

4. • Fugacity is derived from Latin word ‘fleetness’ or the ‘Escaping
Tendency’
• Fugacity has been used extensively in the study of phase and
chemical reaction equilibria involving gases at high pressures.

5. Concepts of Fugacity
◦ G.N lewis (1901) by untilising the free energy function gave the concept of fugacity
to represent the actual behaviour of real gases. The fugacity is mostly employed in
connection with gas mixture as well as gases.
For an infinitesimal reversible stage of an isothermal change, we have from 𝒅𝑮 =
𝑽 𝒅𝑷 − 𝑺 𝒅𝑻,
𝒅𝒈 = 𝑽 𝒅𝒑 ….(1)
For 1 mole of an ideal gas, 𝑽 =
𝑹𝑻
𝑷
. So from equation (1), we have
𝒅𝑮 = 𝑹𝑻.
𝒅𝑷
𝑷
= 𝑹𝑻 𝒅 log𝒆 𝑷 …(2)

6. For a real gas, a function ‘𝑓’ Known as fugacity is introduced and is defined in such a
manner that the relation,
𝒅𝑮 = 𝑹𝑻𝒅 log𝒆 𝒇, ….(3)
◦ always hold good, whether the gas is ideal or real.
On integration of equation (3), we get,
𝑮 = 𝑹𝑻𝒅 log𝒆 𝒇 + 𝒍 …(4)
◦ where, 𝐼 =integration constant which is dependent on the temperature and nature of the
gas. On integrating equation (3) between proper limits, we get,
𝑮𝟏
𝑮𝟐
𝒅𝑮 =
𝒇𝟏
𝒇𝟐
𝑹𝑻 𝒅 log 𝒇
𝑮𝟐 − 𝑮𝟏 = 𝚫𝐆 = 𝐑𝐓 log𝒆
𝒇𝟐
𝒇𝟏
…(5)

7. or
where, the subscripts 1 and 2 represent the initial and final states,
respectively.
◦ For an ideal gas, equation (5) becomes,
𝜟𝑮 = 𝑹𝑻 log𝒆
𝑷𝟐
𝑷𝟏
…(6)
◦ Comparing equation (5) and (6), we see that,
Fugacity ∝ Pressure
◦ If we take proportionality constant as unity, then
Fugacity = Pressure

8. For a real gas, the values of 𝑓and 𝑃 are not proportional to one another and 𝑓/𝑃
is not constant. As the pressure is lowered, the behaviour approaches that of ideal
behaviour. So, the gas at very low pressure is taken to be the reference state and it
is postulated that :
lim
𝑝→0
𝑓
𝑃
= 1
o This postulate makes the evaluation of actual fugacities at various pressures possible. Since
pressure is expressed in atmosphere; fugacities are also expressed in atmosphere.

9. Reference
Authors :- Dr. J.N. Gurtu, A. Gurtu
Book :- Pragati’s ADVANCED PHYSICAL CHEMISTRY

10. Thank You
Upload By -
Gayatri sahu
M.Sc. 1st
Semester
2022