An **ideal gas equation** combines volume, pressure, temperature and number of molecules into one equation. The three gas laws such as Gay Lussac’s law, Charles’s law and Boyle’s law give an elementary idea of the change in the physical properties of gases with changes in state functions (volume, pressure and temperature). An ideal gas is the one that follows the above mentioned laws.

An equation has been derived with the help of these three gas laws. This general equation is called as an ideal gas equation. This equation helps us to co-relate values of

- Number of moles
- Pressure
- Volume and
- Temperature

## Difference between ideal gas and real gas:

## Ideal gas |
## Real gas |
---|---|

No definite volume |
Has definite volume |

Ideal gas has no mass |
Has mass |

Collision of gas particles is elastic |
Collision of gas particles is non-elastic |

No energy involved during collision of gas particles |
Attracting energy involved during collision of gas particles |

High pressure |
Low pressure |

Obey all gas laws under all conditions of temperature and pressure |
Obey the gas laws under high temperature and low pressure |

Volume occupied by the molecules is negligible when compared to the total volume occupied by the gas |
Volume occupied by the molecules is not negligible when compared to the total volume occupied by the gas |

The force of attraction among the molecules is negligible |
The force of attraction among the molecules is not negligible at all temperatures and pressures |

A general derivation of the ideal gas equation with the help of gas laws is discussed below:

Boyle’s Law states that, for a fixed number of moles of a gas the volume of a gas varies inversely with its pressure at a constant temperature

\(V ~∝~ \frac{1}{P}\)

Where,

\(V\)

\(P\)

According to the Charles’ Law, at constant pressure, the volume of a fixed mass of a gas is directly proportional to its absolute temperature.

\(V ~∝~ T\)

Where, \(T\)

According to the Avogadro’s Law, at same temperature and pressure, an equal volume of gases contain an equal number of molecules.

\(V~ ∝~ n\)

Where, \(n\)

From equation (1), (2) and (3), we can deduce that,

\(V ~∝ ~\frac{nT}{P}\)

\(\Rightarrow~V\)

Where, \(R\)

Volume at STP = 22.710981 L/mol

Pressure at STP = 1 bar = 105 Pa

Temperature at STP = 273.15

\(R\)

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