The document discusses equations of state for ideal and real gases. It defines key terms like pressure, volume, temperature and explains gas laws including Boyle's law, Charles' law, and Avogadro's law. The ideal gas law relates these properties. For real gases, the van der Waals equation includes parameters for molecular size and intermolecular forces. In conclusion, the choice of equation of state depends on the substance and conditions being studied.

1. Koya university
Faculty of Chemical Engineering
physical chemistry
Equation of State
2022-2023
supervised by:
Mr. Soran Delawar Jalal
Prepared by:
Dima Jawhar Mustafa

2. physical chemistry: Equation of state
2 | P a g e
Table of Contents
Introduction..............................................................................................................................3
Types of gases: .........................................................................................................................4
Ideal gases: ..........................................................................................................................4
Boyles law:.......................................................................................................................5
Charles law equation of state:..........................................................................................5
Avogadro’s law: ...............................................................................................................6
Real gases:............................................................................................................................6
Van der Waals equation of state.......................................................................................6
Conclusion:..............................................................................................................................7
References:...............................................................................................................................8

3. physical chemistry: Equation of state
3 | P a g e
Introduction
Let us start our discussion by considering the simplest possible macroscopic system:
i.e., an ideal gas. All of the thermodynamic properties of an ideal gas are summed up
in its equation of state, which determines the relationship between its pressure, volume,
and temperature. Unfortunately, classical thermodynamics is unable to tell us what this
equation of state is from first principles. In fact, classical thermodynamics cannot tell
us anything from the first principles. We always have to provide some information, to
begin before classical thermodynamics can generate any new results. In physics,
equations of state attempt to describe the relationship between temperature, pressure,
and volume for a given substance or mixture of substances. The ideal gas law is one of
the simplest equations of state. Although reasonably accurate for gases at low pressures
and high temperatures, it becomes increasingly inaccurate at higher pressures and lower
temperatures.
The equation state is divided into:
1- The ideal gas equation of state
2- The real gas equation of the state

4. physical chemistry: Equation of state
4 | P a g e
Types of gases:
Ideal gases:
ideal gas, also called perfect gas, is a gas that conforms, in physical behavior, to a
particular idealized relation between pressure, volume, and temperature called the ideal,
or general, gas law. (Erik Gregersen,2023)
Equation of state:
It is usually written in the form
PV = n RT
This is known as the equation of state of an ideal gas (or general gas law equation). n
is the number of moles of the gas and R is the gas constant.
P, V, and T are the pressure, volume, and absolute temperature of the gas respectively.
R= called gas constant (8.314 J / (mol·K)
P= Pressure ( Pa = N/m2)
V= Volume ( m3)
T= temperature
N= the number of molecules

5. physical chemistry: Equation of state
5 | P a g e
Boyles law:
For a gas, the relationship between volume and pressure (at constant mass and
temperature) can be expressed mathematically as follows.
P ∝ (1/V)
Where P is the pressure exerted by the gas and V is the volume occupied by it. This
proportionality can be converted into an equation by adding a constant, k.
P = k*(1/V) ⇒ PV = k
As per Boyle’s law, any change in the volume occupied by a gas (at constant quantity
and temperature), the product of the initial pressure and the initial volume of a gas are
equal to the product of its final pressure and final volume (at constant temperature and
a number of moles). This law can be expressed mathematically as follows: (byjus,2023)
P1V1 = P2V2
Charles law equation of state:
Let the volume of gas be V and temperature, T. According to the law at constant
pressure for a fixed amount of gas, (chemistryGod,2019)
Volume is directly proportional to temperature, V ∝ T.
The above expression is the mathematical expression of Charles's law. Removing the
proportionality,
Charles's law equation, V=kT Here, k is a proportional constant. Finally, rearranging
the above equation,

6. physical chemistry: Equation of state
6 | P a g e
Avogadro’s law:
There are a few ways to write this gas law, which is a mathematical relation. It may be
stated: (Anne Marie Helmenstine, 2019)
k = V/n
where k is a proportionality constant V is the volume of a gas, and n is the number of
moles of a gas
Avogadro's law also means the ideal gas constant is the same value for all gases, so:
constant = p1V1/T1n1 = P2V2/T2n2
V1/n1 = V2/n2
V1n2 = V2n1
Real gases:
A real gas is defined as a gas that at all standard pressure and temperature conditions
does not obey gas laws. It deviates from its ideal behavior as the gas becomes huge and
voluminous. True gases have velocity, mass, and volume. They liquefy when cooled to
their boiling point.(vedantu,2023)
Van der Waals equation of state: The Van der Waals equation of state may be
written:
Notice: The van der waals equation of state differs from the ideal gas by the addition
of two adjustable parameters ( a and b ). These parameters are intended to correct for
the omission of molecular size and intermolecular attractive forces in the ideal gas
equation of state. Parameter (b) corrects for the finite size of molecules and parameter
(a) corrects for the attractive force between the molecules.(libritexts,2018)

7. physical chemistry: Equation of state
7 | P a g e
Conclusion:
Based on the analysis and data presented in the equation of state report, the following
conclusions can be drawn:
An equation of state is a mathematical relationship that describes the behavior of a
substance under different conditions, such as pressure, temperature, and volume.
There are various equations of state that have been developed for different types of
substances, such as ideal gas equation, van der Waals equation, Boyles law, Charles’s
law, Avogadro’s law, among others.
The choice of equation of state depends on the nature of the substance being studied
and the conditions under which it is being studied. No single equation of state is
applicable to all substances and conditions.
Overall, the equation of state is an essential tool in the study of thermodynamics and
physical chemistry the behavior of substances under different conditions, and it plays a
crucial role in the development of new technologies and materials.

8. physical chemistry: Equation of state
8 | P a g e
References:
1. byjus,(2023), equation of state of Boyles law.[online] Available:
https://byjus.com/chemistry/boyles-law/ [Accessed: Mar./19/2023]
2. Anne Marie Helmenstine,(2019), Avogadro's Law Equation.[online]
Available: https://www.thoughtco.com/definition-of-avogadros-law-605825
[Accessed: Mar./19/2023]
3. chemistryGod,(2019), The Equation of Charles's Law.[online] Available:
https://chemistrygod.com/charles-law-equation [Accessed: Mar./19/2023]
4. Erik Gregersen,(2023),ideal gas definition.[online]. Available:
https://www.britannica.com/science/ideal-gas [Accessed: Mar./19/2023]
5. Libretexts,(2018), real gas equation of state.[online] Available:
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry
_Textbook_Maps/Book%3A_Thermodynamics_and_Chemical_Equilibrium_(
Ellgen)/02%3A_Gas_Laws/2.12%3A_Van_der_Waals'_Equation [Accessed:
Mar./19/2023]
6. vedantu,(2023),real gas definition.[online] Available:
https://www.britannica.com/science/ideal-gas [Accessed: Mar./19/2023]