Question

A doctor prescribes a drug to his patient in order to control his allergies. The patient must take $25mg$ of this drug every $24$ hours to maintain effectiveness. The drug is metabolized as a first order reactant with a half-life of $18$ hours.
What is the rate constant, $k$, for this drug?

• A. $0.029hour{s}^{-1}$
• B. $0.039hour{s}^{-1}$
• C. $1.4mg/hour$
• D. $450mg\cdot hours$

Answer 1

The correct option is B $0.039hour{s}^{-1}$

It is a first order reaction

$\therefore t_{1/2}=\frac{\ln 2}{K}\therefore K=\frac{\ln 2}{t_{1/2}}=\frac{0.693}{18}=0.039hour{s}^{-1}$