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.

2. Suppose a stock solution of the vaccine with a concentration of 25 g/L is prepared in a clinic at 8:30 am. The clinic plans to store this solution at 25o C and use it for all of the patients that are seen for morning appointments between 9:00 am – 12:00 noon. Is this a good practice? Justify your answer. Will the vaccine be effective for all of these patients? If not, at what time will the concentration of the active agent fall below the effective level?

Explanation / Answer

The governing equation of 1st order :-

k*t = ln{[A0]/[A]}

Also, k = ln2/t1/2 = 0.0825 hr-1

where k = rate constant , t = time ; [A0] = initial concentration , [A] = concentration after time 't'

Thus, at 9:00 AM , 0.0825*0.5 = ln(25/[A])

or, [A] = 23.99 g/L

At 12 noon, 0.0825*3.5 = ln(25/[A])

or, [A] = 18.73 g/L

Thus, this is not a good practice

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