Summarizing the Ideal Gas Law

Summary

• The ideal gas law relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas.
• The ideal gas law can be written in terms of the number of molecules of gas:

  \(\text{PV}=\text{NkT},\)

  where \(P\) is pressure, \(V\) is volume, \(T\) is temperature, \(N\) is number of molecules, and \(k\) is the Boltzmann constant

  \(k=1\text{.}\text{38}×{\text{10}}^{–\text{23}}\phantom{\rule{0.25em}{0ex}}\text{J/K}.\)

• A mole is the number of atoms in a 12-g sample of carbon-12.
• The number of molecules in a mole is called Avogadro’s number \({N}_{\text{A}}\),

  \({N}_{\text{A}}=6\text{.}\text{02}×{\text{10}}^{\text{23}}\phantom{\rule{0.25em}{0ex}}{\text{mol}}^{-1}.\)

• A mole of any substance has a mass in grams equal to its molecular weight, which can be determined from the periodic table of elements.
• The ideal gas law can also be written and solved in terms of the number of moles of gas:

  \(\text{PV}=\text{nRT},\)

  where \(n\) is number of moles and \(R\) is the universal gas constant,

  \(R=8\text{.}\text{31}\phantom{\rule{0.25em}{0ex}}\text{J/mol}\cdot \text{K}.\)

• The ideal gas law is generally valid at temperatures well above the boiling temperature.

Glossary

ideal gas law

the physical law that relates the pressure and volume of a gas to the number of gas molecules or number of moles of gas and the temperature of the gas

Boltzmann constant

\(k\) , a physical constant that relates energy to temperature; \(k=\text{1.38}×{\text{10}}^{\text{–23}}\phantom{\rule{0.25em}{0ex}}\text{J/K}\)

Avogadro’s number

\({N}_{\text{A}}\) , the number of molecules or atoms in one mole of a substance; \({N}_{\text{A}}=6\text{.}\text{02}×{\text{10}}^{\text{23}}\) particles/mole

mole

the quantity of a substance whose mass (in grams) is equal to its molecular mass