Question

This questic concerns a tablet that

has remained in storage for 2 years
since manufacture. From the drug
monograph the decomposition
rate constant (k) was found to be 6
x 10-2 year-1. The degradation
reaction is known to proceed via
first-order kinetics. Which one of
the following is the remaining
percentage of the original drug
? concentration​

Answer 1

The remaining percentage of drug concentration is about 88.7% 2 years after manufacture.

Step-by-step explanation:

Recall the formula for the decay of a substance at an initial
`N_0` concentration at manufacture:

`N(t)=N_0\,e^(-k\,\,t)`

where k is the decay rate (in our case 0.06/year), and t is the elapsed time in years. Therefore, after 2 years since manufacture we have:

`N=N_0\,e^(-0.06\,\,(2))\\N=N_0\,e^(-0.12)\\N/N_0=e^(-0.12)\\N/N_0=0.8869`

This in percent form is 88.7 %. That is, the remaining percentage of drug concentration is about 88.7% 2 years after manufacture.