All of these problems involve preparation and use of a vaccine solution that con
ID: 973207 • Letter: A
Question
All of these problems involve preparation and use of a vaccine solution that contains an active agent in an aqueous solution. The active agent in the vaccine degrades in aqueous solutions with first-order kinetics. The half-life of the active agent in water 25o C is 8.4 hours. The vaccine should be administered at a concentration of at least 20 g/L to be fully effective.
3. (25 pts) The half-life of the active agent is measured at 4o C and found to be 11.5 hours. What is the activation energy for the degradation reaction?
4. (25 pts) A stock solution of the vaccine is prepared at 8:30 am and stored in a refrigerator at 4o C. It will be used for all of the patients with morning appointments between 9:00 am – 12:00 noon. However, the last patient of the morning was delayed and did not arrive until 12:30 pm. What is the concentration of the active agent in the stock solution at that time? Can the vaccine still be used?
Explanation / Answer
i. k1 = 0.693 / t1/2 = 0.693 / 8.4 = 0.0825 h-1 at 25 degree C
ii. k2 = 0.693 / 11.5 = 0.0603 h -1 at 4 degree C
iii. Arrhenius equation,
Log k2/k1 = (Ea / 2.303 R)[(1/T1) - (1/T2)]
Log(0.0603/0.0825) = (Ea / 2.303x8.314) [(1/298) - (1/277)]
- 0.136 = (Ea) ( - 0.000133)
Ea = 10226 J
Ea = 10.226 kJ