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The decomposition of a drug in human was found to be a first order process. The activation energy for the decomposition is (3100R x In 2) and pre-exponential factor $A = 4096 {hr}^{- 1}$ . How long will it take the concentration of the drug in the blood to fall to half of its initial value at 310K?
(Given: In 2 = 0.7)

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10.5 hr

10.5 min

0.175 min

0.175 sec

answer is C.

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Detailed Solution

It take the concentration of the drug in the blood to fall to half of its initial value at 310 K will be:

$\begin{array}{l} \frac{\ln 2}{t_{1 / 2}} = 4096 e^{- \frac{3100 R \times \ln 2}{310 R}} \\ \frac{\ln 2}{t_{1 / 2}} = \frac{4096}{2^{10}} \Rightarrow t_{1 / 2} = \frac{\ln 2}{4} hr = 10.5 \min \end{array}$

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