Answer
There are $2.49\times 10^{19}$ molecules in $1.0~cm^3$ of air.
Work Step by Step
We can convert the average molecular mass to units of $kg$:
$m = 29.0~u\times \frac{1.66\times 10^{-27}~kg}{1~u} = 4.814\times 10^{-26}~kg$
We can find the mass of $1.0~cm^3$ of air:
$1.2~kg/m^3\times \frac{1~m^3}{10^6~cm^3} = 1.2\times 10^{-6}~kg/cm^3$
We can find the number of molecules in $1.0~cm^3$ of air:
$\frac{1.2\times 10^{-6}~kg/cm^3}{4.814\times 10^{-26}~kg/molecule} = 2.49\times 10^{19}~molecules/cm^3$
There are $2.49\times 10^{19}$ molecules in $1.0~cm^3$ of air.
