Answer
$n_0=2.7 \times 10^{25} m^{-3}$
Work Step by Step
From the ideal gas law,
$P = \frac{NkT }{V} $
We want to solve for molecules per cubic meter, so
$P = n_okT$
Rearrange the equation
$n_o =\frac{ P}{kT}$
Where
$P = (1.00) atm \times 1.0\times 10^5 Pa/atm $
$P= 1.0\times 10^5 Pa$
$k = 1.38 \times 10^{-23} J/K$
$T= 0^o C + 273 K$
$ T = 273 K$
so
$n_o =\frac{1.0\times 10^5 Pa}{(1.38 \times 10^{-23} J/K)(273 K)}$
$n_0=2.7 \times 10^{25} m^{-3}$
