Does anyone have any information on incorporating vitamin C serum and going to the gym in the morning?

I go to work right after the gym so I don’t have a lot of time in the locker room to put on the serum and wait 20 minutes before putting on the rest of my routine. I figure I can put it on at home, then go to the gym, work out for an hour, take a shower, and put on the rest of my routine.

1) wash face with gentle Cetaphil cleanser 2) apply toner and vitamin C serum 3) Eat breakfast, about 20 minutes later, apply Aveeno moisturizer with sunscreen, go to the gym 4) About 45 minutes after vitamin C serum, work out (sweat) 5) Shower, Neo-gen Green tea cleansing stick, toner, essence, moisturizer with sunscreen again

tl;dr: Is it bad to work out then wash my face 45 minutes after putting on vitamin C serum? Has all the vitamin C already sunken in or am I reducing its efficacy by sweating or washing my face after ~ an hour?