Study Material

# Ideal gas: laws, model, behavior and examples

We explain Ideal gas with law, model, behavior and examples. An  ideal gas or perfect gas is one in which the molecular attraction or repulsion force between the particles that compose it is considered insignificant, therefore, all its internal energy is kinetic, that is, energy associated with movement. ideal gas law

In such a gas, the particles are usually quite far apart from each other, although from time to time they collide with each other and with the walls of the container. ideal gas law

On the other hand, in the ideal gas, neither the size nor the mass of the particles matter, since it is assumed that the volume occupied by them is very small compared to the volume of the gas itself.

This, of course, is only an approximation, because in reality there is always some degree of interaction between atoms and molecules. We also know that particles do occupy space and have mass. ideal gas law

However these assumptions work quite well in many cases, for example in low molecular weight gases , in a good range of pressures and temperatures.

However, gases with high molecular weight, especially at high pressures or low temperatures, do not behave at all as ideal gases and other models created in order to describe them with greater precision are needed.

## First experiments

The laws that govern gases are empirical, that is, they arose from experimentation. The most notable experiments were carried out throughout the seventeenth, eighteenth, and early nineteenth centuries. ideal gas law

In the first place are those of Robert Boyle (1627-1691) and Edme Mariotte (1620-1684), who independently modified the pressure  in a gas and recorded its volume change , finding that they were inversely proportional: the higher the pressure, the lower the volume.

For his part, Jacques Charles (1746-1823) established that the volume and the absolute temperature were directly proportional, as long as the pressure was kept constant.

Amadeo Avogadro (1776-1856) discovered that two identical volumes of different gases contained the same number of particles, as long as the pressure and temperature were the same. And finally Joseph de Gay Lussac (1778-1850), stated that by keeping the volume fixed, the pressure in a gas is directly proportional to the temperature. ideal gas law

### The ideal gas laws

These discoveries are expressed by simple formulas, calling  p  the pressure, V  the volume, n the number of particles and T the temperature of the ideal gas:

#### Boyle-Mariotte law

As long as the temperature is fixed, the following occurs:

p⋅V = constant

#### Charles Law

When the gas is under constant pressure:

V / T = constant

#### Gay Lussac Law

Keeping the gas at a fixed volume it is satisfied that:

p / T = constant

Identical volumes of gas, under the same pressure and temperature conditions, have the same number of particles. Therefore we can write:

V ∝ n

Where n is the number of particles and ∝ is the symbol of proportionality.

## Ideal gas model

The ideal gas model describes a gas such that:

-When the particles interact, they do so for a very short time, through elastic shocks, in which momentum and kinetic energy are conserved.

-Its constituent particles are punctual, in other words, their diameter is much smaller than the average distance they travel between one collision and another. ideal gas law

-The intermolecular forces are non-existent.

-Kinetic energy is proportional to temperature.

Monatomic gases -whose atoms are not bound together- and low molecular weight, under standard conditions of pressure and temperature (atmospheric pressure and 0ºC temperature), have such behavior that the ideal gas model is a very good description for them.

### Ideal gas equation of state

The gas laws listed above combine to form the general equation that governs the behavior of the ideal gas:

V ∝ n

V ∝ T

Therefore:

V ∝ n⋅T

Also, from Boyle’s law:

V = constant / p

So we can state that:

V = (constant xn⋅T) / p

The constant is called the gas constant and is denoted by the letter R. With this choice, the ideal gas equation of state relates four variables that describe the gas state, namely n, R, p and T, leaving: ideal gas law

p⋅V = n⋅R⋅T

This relatively simple equation is consistent with the ideal gas laws. For example, if the temperature is constant, the equation reduces to the Boyle-Mariotte law.

### The gas constant

As we have said before, under standard conditions of temperature and pressure, that is, at 0ºC (273.15 K) and 1 atmosphere of pressure, the behavior of many gases is close to that of the ideal gas. Under these conditions, the volume of 1 mole of the gas is 22,414 L.

In that case:

R = (p⋅V) / (n⋅T) = (1 atm x 22.414 L) / (1 mol x 273.15 K) = 0.0821 atm ⋅ L / mol ⋅ K

The gas constant can also be expressed in other units, for example in the SI International System it is worth:

R = 8.314 J⋅ mol -1 ⋅ K -1

When solving a problem using the ideal gas law, it is convenient to pay attention to the units in which the constant is expressed, since as we can see, there are many possibilities.

## Behavior of an ideal gas

As we have said, any gas under standard conditions of pressure and temperature and that is of low molecular weight, behaves very close to the ideal gas. Therefore, the equation p⋅V = n⋅R⋅T is applicable to find the relationship between the four variables that describe it: n, p, V and T. ideal gas law

In this way we can imagine a portion of ideal gas enclosed in a container and made up of tiny particles, which from time to time collide with each other and with the container’s walls, always elastically.

This is what we see in the following animation of a portion of helium, a monatomic noble gas: Helium is a noble gas, the image shows a portion of helium atoms in a container. The red ones serve to better distinguish the movement.

## Examples of ideal gases

An ideal gas is a hypothetical gas, that is, it is an idealization, however, in practice many gases behave in a very close way, making it possible for the model p⋅V = n⋅R arroT to give very good results. precise.

### Noble gases ideal gas law

Examples of gases that behave as ideal under standard conditions are noble gases, as well as light gases: hydrogen, oxygen and nitrogen.