There certainly is time. Whenever I'm flying thru BCN with 5 or any more hrs transit I always go into the city, even if it is just for a walk, tapa or coffee - for me, I can feel history in every street corner. If the train is due (30mins apart, and you at T2 - the older terminal), that takes you to Sants, or better in many ways is to take the bus from either Terminal (runs more often, and cheaper too) which arrives in Plaza España and then explore the cities "non-tourist" areas like the Fira ("Fair") Barcelona Montjuic. If your flight is in the evening go up to the roof of the Arenas ("Sands") shopping mall to catch the sunset and the lights of the city. Don't eat at the airport, better to sample some street food, and then picnic in the park or visit the museums at the Fair. You can check their schedules online so as not to miss any events being hosted.