Answer
$\frac{25 molecules}{cm^3}$
Work Step by Step
We know that
$PV=nRT$
which can be rearranged as $n=\frac{PV}{RT}$...eq(1)
Also, $V=1 cm^3=1\times10^{-6}m^3$
We then substitute the values of $P$,$V$,$R$ and $T$ in eq(1) to find $n$:
$n=\frac{1.01\times10^{-13}(1\times10^{-6})}{8.31(293)}=4.1\times10^{-23}$
We also know that
$N=nN_a$ where $N_a$ is Avogadro's number and $N_a=6.023\times10^{23}$
We now find $N$ by substituting the values of $n$ and $N_a$ in the above formula:
$N=4.1\times10^{23}\times6.023\times10^{-23}=25$
As a result, the number of molecules per cubic centimeter are:
$\frac{N}{V}=\frac{25 molecules} {cm^3}$
