Question

A drug solution decomposes via first-order kinetics with a rate constant, \( k \), of \( 0.0077 \, \text{days}^{-1} \). What is the half-life of the drug in solution?

• A. 0.033 day
• B. 33 days
• C. 70 days
• D. 90 days
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Hint:

A drug solution decomposes via first-order kinetics with a rate constant, k , of 0.0077 days . What is the half-life of the drug in solution?

Answer 1

The Correct Option is D

Step 1: Understanding the first-order half-life formula. - The half-life (\( t_{1/2} \)) for a first-order reaction is given by: \[ t_{1/2} = \frac{0.693}{k} \] where: - \( k = 0.0077 \, \text{days}^{-1} \).

Step 2: Substituting the given values. \[ t_{1/2} = \frac{0.693}{0.0077} \]

Step 3: Performing the calculation. \[ t_{1/2} = 90 \] \bigskip