The mathematical expression for Avogadro's law is
"V"/"n" = "constant"Vn=constant, where
VV - the volume of the ideal gas;
nn - the amount of gas - expressed in moles;
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 ideal gas law, implies that
PV = nRT => V = (nRT)/P => V/n = (RT)/P = "constant"PV=nRT⇒V=nRTP⇒Vn=RTP=constant, since
RR, PP, and TT are all constants in this case.
To answer your question, Avogadro's number is not used in the formula for Avogadro's law; however, it could be, if you take into account the fact that
N = n*N_AN=n⋅NA, where
NN - the number of molecules of gas present;
nn - the number of moles of gas;
N_ANA - Avogadro's number - 6.022*10^(23)6.022⋅1023 "molecules/mol"molecules/mol
If you multiply the ideal gas equation by N_A/N_ANANA 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 * TPV=n⋅NANA⋅RT=n⋅NA⋅RNA⋅T=N⋅RNA⋅T,
where R/N_A = kRNA=k - Boltzmann's constant = 1.38*10^(-23)1.38⋅10−23 "J/K"J/K
So, in this form, PV = NkTPV=NkT, so you could write Avogadro's law using
V/N = (kT)/P = "constant"VN=kTP=constant