## Problem 11.10

#### (a) How does the average kinetic energy of molecules compare with the average energy of attraction between molecules in solids, liquids, and gases?

The physical state of a substance (solid/liquid/gas) is determined by the magnitude of the average kinetic energy of the particles which make up the substance vs. the magnitude of the attractive forces which operate between the particles. In a solid, the energy of attraction between particles is so large that the particles are not free to move - rather, they are held in place and have very very little (or no) kinetic energy. In a liquid, attractive forces are still considerable, but are large enough to lock particles in an ordered structure. In a liquid, particles form large 'clusters' or aggregates and these clusters can move. Thus, in a liquid, we would state that kinetic energy of particles is much greater than in a solid, and attractive forces are weaker than in a solid. In a gas, particles are free to move - particles do not encounter each other very often, and when they do, we view the collisions as being perfectly elastic - particles collide and bounce off one another. Thus, in a gas, kinetic energy is much greater in magnitude than attractive forces.

(b) Why does increasing the temperature cause a solid substance to change in succession from a solid to a liquid to a gas?

One of the main results of the kinetic molecular theory is that the average kinetic energy of a particle is directly proportional to absolute temperature. Thus, the higher the abolsute temperature, the faster, on average, the particles which make up a substance will move. Since the physical state of a substance is a balance between attractive forces and kinetic energy, as we increase the temperature on a solid, we eventually increase the KE of the particles to the point where their KE overcomes the attractive forces, and the solid melts to form a liquid. Likewise, if we heat a liquid, we increase the KE of the constituent particles to the point where the attractive forces are overcome, and the particles enter the gas phase.

(c) What happens to a gas if you put it under extremenly high pressure? The easiest way to think about this is to picture a piston- cylinder arrangement:

The gas is contained in the cylinder, and the piston is movable. If we compress the gas by pushing down on the piston, we are decreasing the available volume in which the gas molecules can move; the molecules undergo a much larger number of collisions, and are forced to stick together, forming a liquid phase.