Answer
$\frac{N}{V}=2.5\times 10^{25}\frac{molecules}{m^3}$
Work Step by Step
We can find number of molecules per unit volume$\frac{N}{V}$ as
$\frac{N}{V}=\frac{nN_A}{V}$..............eq(1)
From ideal gas equation $PV=nRT$, we find
$\frac{n}{V}=\frac{P}{RT}$
Substituting this formula in eq(1), we obtain:
$\frac{N}{V}=N_A(\frac{P}{RT})$
We plug in the known values to obtain:
$\frac{N}{V}=6.02\times 10^{23}(\frac{1.01\times 10^5}{8.31(293)})=2.5\times 10^{25}\frac{molecules}{m^3}$
