Fast train from Beijing to Zhengzhou after 7 am

I am coming to Beijing on 12/24/2011 at 5 am. I want to take fast train to Zhenzhou same day. I see one at 7 am and I do not know it I can make it from airport or not. If I buy this ticket and I do not make it can I take the 2nd train or I will loss my money. What time the train schedules and how much? Do you know if the train is going to buy full in that day? Can I buy the ticket from the train station when I get there? I want to know when is the first train and the 2nd train and 3ed train after 7 am like 8 or 9 or 10 AM and what time will get there in Zhengzhou. What about slow train?