# Difference between revisions of "Ideal Gas Law"

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− | The '''ideal gas law''', is an | + | The '''ideal gas law''', is an equation of state for an ideal gas. It combines three [[gas]] laws ([[Dalton's Law of Partial Pressures|Dalton's Law]], [[Boyle's Law]] and [[Charles' Law]]) into one equation: |

− | :PV = nRT | + | :<math>PV = nRT</math> |

where | where | ||

− | *P is the [[pressure]] of gas; | + | *<math>P</math> is the [[pressure]] of gas; |

− | *V the [[volume]] the gas occupies; | + | *<math>V</math> the [[volume]] the gas occupies; |

− | *T the absolute [[temperature]] (meaning it must be in [[Kelvin]] or [[Rankine]]); | + | *<math>T</math> the absolute [[temperature]] (meaning it must be in [[Kelvin]] or [[Rankine]]); |

− | *n is the number of [[Mole (chemistry)|moles]] of the gas | + | *<math>n</math> is the number of [[Mole (chemistry)|moles]] of the gas; |

− | *R is the | + | *<math>R</math> is the ideal gas constant. |

− | The gas constant can be expressed in any number of units, but the most common representations are <math>0.0821\,L \cdot atm \cdot mole^{-1} \cdot K^{-1}</math> or <math>8.314\,J \cdot mole^{-1} \cdot K^{-1}</math> | + | It can also be expressed in terms of the number of [[molecules]], <math>N</math> and the Boltzmann constant, <math>k_B</math> as: |

+ | :<math>PV = N k_B T</math> | ||

+ | |||

+ | The ideal gas constant can be expressed in any number of units, but the most common representations are <math>0.0821\,L \cdot atm \cdot mole^{-1} \cdot K^{-1}</math> or <math>8.314\,J \cdot mole^{-1} \cdot K^{-1}</math> | ||

==Ideal Gas== | ==Ideal Gas== | ||

− | The equation is valid only for an ideal gas, the hypothetically perfect embodiment of a gas in which the particles ([[atom]]s or [[molecule]]s) in the gas are | + | |

+ | The equation is valid only for an ideal gas, the hypothetically perfect embodiment of a gas in which the particles ([[atom]]s or [[molecule]]s) in the gas are point particles (have no [[volume]]) and experience no intermolecular forces. All collisions between the particles or the particles and the container are perfectly elastic. | ||

Since this is just a model, real gases only obey the ideal gas law approximately, not perfectly. Generally, the ideal gas assumption is accurate for unreactive gases at high temperature and/or low pressure. A good rule of thumb is that the assumption can be used above room temperature and below 1 [[atmosphere]] of pressure. | Since this is just a model, real gases only obey the ideal gas law approximately, not perfectly. Generally, the ideal gas assumption is accurate for unreactive gases at high temperature and/or low pressure. A good rule of thumb is that the assumption can be used above room temperature and below 1 [[atmosphere]] of pressure. | ||

− | == | + | ==Density== |

− | With the molar mass (M), the ideal gas law can be used to calculate the [[density]] of a gas, | + | With the molar mass (''M''), the ideal gas law can be used to calculate the [[density]] of a gas, <math>\rho</math>. |

+ | |||

+ | :<math>PM= \rho RT</math> | ||

− | + | ==See also== | |

+ | *[https://en.wikiversity.org/wiki/Ideal_gas_law Ideal Gas Law] | ||

− | [[ | + | [[Category:Physics]] |

− | [[ | + | [[Category:Thermodynamics]] |

+ | [[Category:Chemistry Laws and Principles]] |

## Latest revision as of 20:51, 15 January 2017

The **ideal gas law**, is an equation of state for an ideal gas. It combines three gas laws (Dalton's Law, Boyle's Law and Charles' Law) into one equation:

where

- is the pressure of gas;
- the volume the gas occupies;
- the absolute temperature (meaning it must be in Kelvin or Rankine);
- is the number of moles of the gas;
- is the ideal gas constant.

It can also be expressed in terms of the number of molecules, and the Boltzmann constant, as:

The ideal gas constant can be expressed in any number of units, but the most common representations are or

## Ideal Gas

The equation is valid only for an ideal gas, the hypothetically perfect embodiment of a gas in which the particles (atoms or molecules) in the gas are point particles (have no volume) and experience no intermolecular forces. All collisions between the particles or the particles and the container are perfectly elastic.

Since this is just a model, real gases only obey the ideal gas law approximately, not perfectly. Generally, the ideal gas assumption is accurate for unreactive gases at high temperature and/or low pressure. A good rule of thumb is that the assumption can be used above room temperature and below 1 atmosphere of pressure.

## Density

With the molar mass (*M*), the ideal gas law can be used to calculate the density of a gas, .