Jan 12, 2015

The mathematical expression for Avogadro's law is

$\text{V"/"n" = "constant}$, where

$V$ - the volume of the ideal gas;
$n$ - 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

$P V = n R T \implies V = \frac{n R T}{P} \implies \frac{V}{n} = \frac{R T}{P} = \text{constant}$, 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 Avogadro's law; however, it could be, if you take into account the fact that

$N = n \cdot {N}_{A}$, where

$N$ - the number of molecules of gas present;
$n$ - the number of moles of gas;
${N}_{A}$ - Avogadro's number - $6.022 \cdot {10}^{23}$ $\text{molecules/mol}$

If you multiply the ideal gas equation by ${N}_{A} / {N}_{A}$ on the right-hand side, you'll get

$P V = n \cdot {N}_{A} / {N}_{A} \cdot R T = n \cdot {N}_{A} \cdot \frac{R}{N} _ A \cdot T = N \cdot \frac{R}{N} _ A \cdot T$,

where $\frac{R}{N} _ A = k$ - Boltzmann's constant = $1.38 \cdot {10}^{- 23}$ $\text{J/K}$

So, in this form, $P V = N k T$, so you could write Avogadro's law using

$\frac{V}{N} = \frac{k T}{P} = \text{constant}$