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

1 Answer
Jan 12, 2015

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=nRTV=nRTPVn=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=nNA, 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)6.0221023 "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=nNANART=nNARNAT=NRNAT,

where R/N_A = kRNA=k - Boltzmann's constant = 1.38*10^(-23)1.381023 "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