As a teacher, I show students the particle model as an explanation of solids, liquids and gases, and changes of state. I did this today, explaining that the bonds in the solid break because the kinetic energy of the particles has increased so much that it overcomes the bonds between the particles. The bonds between the molecules in the liquid state are weaker. But... if this is true, then how come the level of kinetic energy that broke apart the solid bonds, is not also able to break apart the liquid bonds? Are the liquid bonds in fact stronger?
The bonds between the molecules in the liquid state are weaker.
The bonds in the solid are the same kind of bond as in a liquid. We know the liquid still has bonds between particles because liquids have a constant volume. It would be better to say that the solid turns into a liquid because there are fewer bonds, or bonds break continuously (with the current neighbor) and form continuously (with the new neighbor). In solid and liquid water, we have hydrogen bonds between molecules. In solid and liquid sodium chloride, we have ionic bonds between ions. In solid and liquid iron, we have metallic bonds between atoms.
Here is a simulation of ice melting. Notice the change in density as you pass zero degrees celsius, water molecules starting to rotate as the temperature increases, and rare switches in position (you would have to play this faster to see diffusion of water molecules in the liquid).
[...] how come the level of kinetic energy that broke apart the solid bonds, is not also able to break apart the liquid bonds?
If I want to buy a house, and then buy furniture for it, the house will be more expensive than the furniture. However, if I have just enough money to buy the house, I can't buy the furniture until I get more money because I already spent it on the house.
So at the melting point, we put in sufficient energy to switch from continuous bonds between neighboring particles to bonds that break every now and then, allowing particles to move but not to escape (become a gas). To turn this liquid into a gas, we need to break all the intermolecular bonds, which has an additional energetic cost.
Often, the energy required to go from solid to liquid is lower than the energy required to go from liquid to gas. For example, in ice, each water molecule makes 4 hydrogen bonds. In liquid water, each water molecule makes between 3 and 4 hydrogen bonds. In steam, each water molecule makes about zero hydrogen bonds (except for the rare and fleeting instances where it collides with another water molecule).
Are the liquid bonds in fact stronger?
No, bond by bond they are of similar strength. If the liquid has a lower density thant the solid, the particles are a bit further apart from each other, so the bond will be slightly weaker. Also, averaged over time, there will be a lower number of bonds.
As a teacher, I tell my students that in a solid the atoms are vibrating around a central point. The higher the temperature, the stronger they vibrate. But, if the vibration energy is too high, it is like with a rubber band or an elastic, the bond is broken, and the system acquires a new degree of freedom : translation. The solid becomes a liquid. I know it is oversimplified, but for my high school students, it is sufficient