Question

As a gas is compressed the molecules gain energy. If this energy is not taken away by an outside source, how is it used by the gas molecules?

Answer 1

Actually, if you compress something its pressure increases and temperature decreases, hence it will change into different state of matter.

So, if you compress a gas it will change into liquid or solid according to the amount of pressure  given in.

In this process the kinetic energy of the gas molecules is converted to potential energy (as you know energy is neither created nor destroyed, but can be converted to another form)

Conclusion : this means the energy is used by the gas molecules to convert to other state of matter.