72 Hour Transit US>PEK>SEL

Hello! I think I'm overthinking this, but just trying to see if I qualify for the 72 hour visa for the arrival part of my trip...
I am a US citizen traveling from US to Beijing (arriving on a Friday) and I plan to stay over night Friday and leave for Seoul Saturday evening. I will return to Beijing 9 days later (following Monday) from Seoul to US (same day travel).