# Ideal gas law

The ideal gas law relates the pressure, temperature, and volume of an ideal gas. Many common gases exhibit behavior very close to that of an ideal gas at ambient temperature and pressure. The ideal gas law was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law.

The ideal gas law is expressed as :
$\mathrm{PV}=\mathrm{nRT}$

where:

P is the pressure of the gas.

V is the volume of the gas.

n is the amount of substance of gas (also known as number of moles).

T is the temperature of the gas (measured in Kelvin).

R is the ideal, or universal, gas constant.

The universal, gas constant (R) is a numerical value made up of the combination of atandard pressure (1 atmosphere or 760 torr), stanard temperature (273 K), and the fact that 1 mole of a gas occupies a volume of 22.4 liters at STP.

Values of R |
---|

0.082057 L atm mol^{-1} K^{-1} |

62.364 L Torr mol^{-1} K^{-1} |

8.3145 m3 Pa mol^{-1} K^{-1} |

8.3145 J mol^{-1} K^{-1} |

Example 1:

What is the temperature (in Kelvin) of the gas, if 2 moles of the gas ocuupy 50 liters at a pressure of 3 atmospheres?

$\mathrm{PV}=\mathrm{nRT}$

$T=\frac{\mathrm{PV}}{\mathrm{nR}}=\frac{3\mathrm{atmospheres}x50\mathrm{liters}}{2\mathrm{mol}x0.082\frac{\mathrm{atmosphere}x\mathrm{liters}}{\mathrm{mol}xk}}=914.63K$

Example 2:

What is the pressure in the container, if a 10 liter container holds 5 moles of hydrogen gas (H2) at 40 °C?

Celsius temperature must be changed to Kelvin (40 + 273 = 313K).

$\mathrm{PV}=\mathrm{nRT}$

$V=\frac{\mathrm{nRT}}{V}=\frac{5\mathrm{moles}x0.082x313}{10\mathrm{liters}}=12.833\mathrm{atm}$

Ideal gas law is based upon absolute temperature. The absolute temperature is calculated by adding 273 to the temperature in Celsius scale. 10°C is equiavalent to 283 K.

${T}_{}=10\mathrm{\xb0C}+273=283K$