2.5 year old with big emotions

My oldest daughter is 2.5 years old and SO emotional. The highs are very high and the lows are *very* low. Once she gets upset about something and starts crying, there's no reasoning with her at all. She can't hear us because she's too busy crying her heart out. I wouldn't even say that she throws tantrums excessively, she just feels emotions very intensely. Is this normal behavior for this age? I don't know how to manage it, and my youngest is almost 1 so I'm feeling very overwhelmed right now.