All of these problems involve preparation and use of a vaccine solution that con

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.

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

First, let's determine the constant k
k = ln2 / t1/2
k = ln2/8.4 h
k = 0.0825 h-1

C = Co exp(-kt)
C = 20 exp(-0.0825 * 4)
C = 14.38 ug/L

The vaccine should not be used, because is under the minimum concentration

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