when working with the particle theory,

for which changes of state does the volume increase?
and Decrease?

volume changes greatly when going to the gas state.

what part of the system is missing

When working with the particle theory, the volume of a substance can change during changes of state, which refer to the transitions between solid, liquid, and gas phases.

1. Changes of state with increasing volume:
When a substance undergoes a change of state from a solid to a liquid or from a liquid to a gas, the volume usually increases. This is because the particles in a solid are closely packed together and have less freedom to move. However, when heat is added, the particles gain energy and start to move more vigorously, causing the substance to expand and occupy a larger volume.

For example, when ice (solid) melts into water (liquid), the volume of the water increases. Similarly, when water (liquid) evaporates and turns into steam (gas), the volume of the steam is larger than the volume of the liquid water.

2. Changes of state with decreasing volume:
When a substance undergoes a change of state from a gas to a liquid or from a liquid to a solid, the volume generally decreases. This is because the particles lose energy and slow down, causing them to move less and be closer together. As a result, the substance becomes more compact and occupies a smaller volume.

For instance, when steam (gas) condenses into liquid water, the volume decreases. Similarly, when liquid water freezes and turns into ice (solid), the volume of the ice is usually smaller than that of the liquid.

Now, regarding your question about what part of the system is missing, it seems to be unrelated to the topic at hand. Could you please provide more context or clarify what you mean by "what part of the system is missing"?