**ideal gas model**is used to predict the behavior of gases and is one of the most useful and commonly used substance models ever developed. It was found that if we confine

**1 mol samples**of

**various gases**in

**identical volumes**and hold the gases at the

**same temperature**, then their measured

**pressures are almost the same**.

Moreover, when we confine gases at lower densities, the differences tend to disappear. It was found, such gases tend to obey the following relation, which is known as the **ideal gas law**:

*pV = nRT*

where:

** p** is the

**absolute pressure**of the gas

** n** is the

**amount**of substance

** T** is the

**absolute temperature**

** V **is the

**volume**

** R **is the ideal, or universal,

**gas constant**, equal to the product of the

**Boltzmann constant**and the

**Avogadro constant.**The power of the

**ideal gas law**is in its simplicity. When any two thermodynamic variables, p, v, and T, are given, the third can easily be found.

The** ideal gas model** is based on the following assumptions:

- The pressure, volume, and temperature of an ideal gas obey the
**ideal gas law**. - The
**specific internal energy**is only a function of the temperature:*u = u(T).* - The molar mass of an ideal gas is identical to the molar mass of the real substance.
- The
**specific heats**—and*c*_{p}— are independent of temperature, which means constants.*c*_{v}

From the microscopic point of view, it is based on these assumptions:

- The molecules of the gas are
**small, hard spheres**. - The only forces between the gas molecules are those that determine the
**point-like collisions**. - All collisions are
**elastic**, and all motion is**frictionless**. - The average distance between molecules is much larger than the size of the molecules.
- The molecules are moving in random directions.
- There is no other attractive or repulsive force between these molecules.

## Validity of Ideal Gas Law

Since **ideal gas** is defined as one in which all collisions between atoms or molecules are perfectly elastic. There are no intermolecular attractive forces, and there is no such thing in nature as a truly ideal gas. On the other hand, all real gases approach the ideal state **at low pressures (densities)**. At low pressures, molecules are far enough apart that they do not interact with one another.

In other words, the **Ideal Gas Law** is accurate only **at relatively low pressures** (relative to the critical pressure p_{cr}) and **high temperatures** (relative to the critical temperature T_{cr}). At these parameters, the **compressibility factor, Z = pv / RT**, is

**approximately 1**. The compressibility factor is used to account for deviation from the ideal situation. This correction factor is dependent on pressure and temperature for each gas considered.