# Ideal Gas Law

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Gases | The Ideal Gas Law.

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## Key Questions

• #### Answer:

$p V = n R T$ or $p V = N {k}_{B} T$.

#### Explanation:

Where $p$ is the pressure, $V$ is the volume, $n$ is the number of moles, $N$ is the number of molecules, $T$ is the temperature (in Kelvins) of the ideal gas; $R$ is the ideal gas constant and ${k}_{B}$ is the Boltzmann's constant.

• #### Answer:

Depends on the operating condition

#### Explanation:

Ideal gas law was developed to relate the (microscopic) behavior of atoms to macroscopic properties such as pressure and temperature.The ideal gas law is based on the kinetic theory of molecules.The postulates are as follows:

1. The size of the atoms is small compared to the distance between them.They behave as point particles and their identity (type of element) & distinct properties based on their identity does not matter.
2. Absence of force of attraction or repulsion between molecules.
3. The atoms are in rapid motion and constantly colloid with each other and with the walls of the container .
4. The collisions are perfectly elastic and therefore no energy is lost due to collisions.
5. Kinetic energy of molecules is a function of temperature only.

Gas molecules are found to abide by these postulates at low pressures(below 1 atm) and high temperatures.

The ideal gas equation $P V = n R T$
$\frac{V}{n}$ is the specific molar volume of the gas

The equation can be applied if the following thumb rule is satisfied

$\frac{V}{n}$ > 5L/mole (for diatomic gases)

$\frac{V}{n}$ > 20L /mole (other gases)

• #### Answer:

The ideal gas law makes some assumptions about gases that are not necessarily true. This means that the ideal gas law has some limitations.

#### Explanation:

For example, the ideal gas law makes an assumption that gas particles have no volume and are not attracted to each other.

Here's why the idea gas law has limitations.

1. Imagine that you condense an ideal gas. Since the particles of an ideal gas have no volume, a gas should be able to be condensed to a volume of zero. Reality check: Real gas particles occupy space. A gas will be condensed to form a liquid which has volume. The gas law no longer applies because the substance is no longer a gas!

2. Same scenario. We assume that gas particles are not attracted to each other. Reality check: Real gas particles are attracted to each other. As kinetic energy decreases as a gas is cooled, the particles will eventually move slowly enough that there attractive forces cause them to condense. The gas law no longer applies because the substance is no longer a gas!

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