What would happen to the density of a mass of air that is heated? Would that mass of air rise above and float on top of cooler air above it or would it sink down below cooler air below it? (Assume that the majority of the masses do not mix.)

As air is heated its density decreases because its mass remains constant but its volume increases. As air is cooled, its density increases because its mass remains constant but its volume decreases. ... The decrease in density as air is heated causes it to rise above cooler, more dense air. Hope this helped.