Why is water denser in the liquid state than in the solid state. I know it has something to do with hydrogen bonding and the particles sliding past each other. Can someone please explain.

Take a look at the structure of water. The H-O-H bond angle shows you everything you need to know. Remember, when water is in a solid state the H is attracted to the O of another water molecule. If you draw it out, the answer will appear for you immediately.

so is it because in a solid, the nonpolar bonds are less dense compared to a liquid as the particles vibrate in place

so is it because in a solid, the nonpolar bonds are less dense compared to a liquid as the particles vibrate in place

 

Nope. Think again. What exactly is density? It is a measurement of Mass divided by volume. A bond can't have density since a bond isn't really a mass. That's like trying to calculate the density of the word "bug". It's just not logically possible.

 

So back to your question. The density of a substance is the measurement of how much mass exists in a fixed volume. Your comment on vibration does begin to lead you down the right path. What is the difference between the intermolecular/interatomic interactions in a liquid and in a solid? If you can answer this question, as well as draw out a few water molecules, the answer should be pretty evident.