What is the relationship between the ideal gas law and the Avogadro's law?

Question

Naomi Aronson · Accepted Answer

According to Avogadro's law, equal volumes of gases at constant pressure and temperature contain the same number of molecules, regardless of their physical or chemical makeup. This means that, at constant temperature and pressure, a gas's volume is directly proportional to the number of moles present.

This number of molecules is #6.022 * 10^23# and is known as Avogadro's number, #N_A#.

Avogadro's law can be expressed mathematically in this way:

#V/n = const#, or, better yet, #V_1/n_1 = V_2/n_2#.

Avogadro's law, as well as Boyle's law and Charles' law, are special cases of the ideal gas law, #PV = nRT#. If temperature and pressure are kept constant, and knowing that #R# is of course constant, then

#PV = nRT -> (PV)/n = RT -> V/n = (RT)/P = const#, which represents Avogadro's law.

The ideal gas law can also be written to incorporate #N_A#, since the number of moles are actually the number of molecules divided by Avogadro's number

#PV = N/N_A *RT#, where #N# represents the number of molecules.

Caleb Adams · Answer

undefined The relationship between the ideal gas law and Avogadro's law is that both laws describe the behavior of gases. Avogadro's law states that at constant temperature and pressure, equal volumes of gases contain equal numbers of molecules. The ideal gas law, on the other hand, relates the pressure, volume, temperature, and number of moles of a gas, assuming ideal behavior. Avogadro's law is a special case of the ideal gas law when pressure and temperature are constant.