Question

Half life for a first order reaction is \(6.93\) min. What is the time required (in min) to complete \(90\%\) of reaction? (Nearest integer)

Answer 1

Correct Answer: 23

Concept: For a first order reaction, \[ t_{1/2}=\frac{0.693}{k} \] and \[ t=\frac{2.303}{k}\log\frac{[A]_0}{[A]} \] Step 1: Find rate constant \[ t_{1/2}=6.93 \] \[ 6.93=\frac{0.693}{k} \] \[ k=\frac{0.693}{6.93} \] \[ k=0.1\ \text{min}^{-1} \] Step 2: For 90\% completion \[ [A]=0.1[A]_0 \] \[ t=\frac{2.303}{0.1}\log\frac{[A]_0}{0.1[A]_0} \] \[ t=23.03\log(10) \] \[ \log(10)=1 \] \[ t=23.03\ \text{min} \] Step 3: Nearest integer \[ t \approx 23\ \text{min} \]