How does mixing water and alcohol show that atoms have a lot of empty space?
This happens because water has an open structure (like ice) and the tails of the alcohol molecules bond or go in and lodge into the open water molecules thus reducing the volume
When you fill up a glass with 500 mL of water and fill another one with 500 mL of alcohol, it's noticeable that the glass with 500 mL of alcohol visually seems to be less than the water and when you mix them such as 250 mL of water and 250 mL of alcohol and add that to a glass you can also see that the level of the liquid on the glass seems to be lower than the water. This shows that there are empty spaced between atoms since you can visually see the levels of both liquids change.
I would watch this video to help you visualize it