Is the Avogadro constant used in the Avogadro's law formula?

The mathematical expression for is

##"V"/"n" = "constant"##, where

##V## - the volume of the ideal gas; ##n## - the amount of gas - expressed in ;

So, what that above equation suggests is that there is a relationship between the volume a gas occupies and how much of that gas is present; this takes place for constant temperature and constant pressure, which, using the , implies that

##PV = nRT => V = (nRT)/P => V/n = (RT)/P = "constant"##, since

##R##, ##P##, and ##T## are all constants in this case.

To answer your question, Avogadro's number is not used in the formula for ; however, it could be, if you take into account the fact that

##N = n*N_A##, where

##N## - the number of molecules of gas present; ##n## - the number of moles of gas; ##N_A## - Avogadro's number - ##6.022*10^(23)## ##"molecules/mol"##

If you multiply the ideal gas equation by ##N_A/N_A## on the right-hand side, you'll get

##PV = n*N_A/N_A *RT = n*N_A * R/N_A * T = N * R/N_A * T##,

where ##R/N_A = k## - Boltzmann's constant = ##1.38*10^(-23)## ##"J/K"##

So, in this form, ##PV = NkT##, so you could write Avogadro's law using

##V/N = (kT)/P = "constant"##