Why is atmospheric pressure generally lower beneath a mass of warm air than beneath a mass of cold air?

It is so because warm air is lighter than cold air. Cold air means the molecules are not moving as much, so they will feel like sticking together and will not jump around as molecules in warm air will(higher temp. means higher KE). Think of a solid, colder solids are much heavier than warmer ones(think of ice-starts melting).

I’m not sure what your trying to say here.. can you clarify again?