### Ideal gas law

As we studied in:

Boyle’s Law: V∝ \frac{1}{P}

Charle’s Law: V∝ T

Avogadro’s Law: V ∝ n

by combining the three laws: V ∝ \frac{nT}{P}

The ideal gas law: It is law which is applied to all gases that exhibit ideal behaviour and obey the gas laws perfectly. It states that: **the volume of a given amount of gas is directly proportional to the number of moles of gas, directly proportional to the temperature, and inversely proportional to the pressure.**

V = \frac{R n T}{P}

PV = nRT

The proportional constant R is called the gas constant.

For one mole gas: PV = RT

The numerical valu of R is calculated from the law and it depends on the unit of both V and P.

R = \frac{PV}{nT}

At STP: one mole of any gas occupies 22.4 L so by appling this:

The value R changes with any change of P or V units the following table represents the units and value of R:

R | Unit |

0.082 | L-atm K^-1mol^-1 |

82.1 | ml-atm K^-1mol^-1 |

62.3 | L-mmHg K^-1mol^-1 |

8.314 x 10^7 | erg K^-1mol^-1 |

8.314 | Joule K^-1mol^-1 |

1.987 | cal K^-1mol^-1 |

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