Answer
Yes, gas is mostly empty space.
Work Step by Step
As the problem suggests, assume an ideal gas at STP.
Calculate the volume occupied by one mole of gas particles, assuming a volume of $\mathcal{l}^3$.
$$V_{molecules}=(6.02\times10^{23})(0.3\times10^{-9}m)^3)$$
Divide this by the molar volume of 22.4 L.
$$\frac{ V_{molecules}}{V_{container}}=\frac{(6.02\times10^{23})(0.3\times10^{-9}m)^3)}{22.4\times10^{-3}m^3}=7.3\times10^{-4}$$
The volume taken up by the molecules is a tiny fraction of the container's volume. The gas is mostly empty space.
