Question

Half life of first order reaction is \(6.93\) min. What is the time required (in min.) to complete \(99\%\) of reaction? \([\ln2 = 0.693]\)

• A. \(23.06\)
• B. \(46.06\)
• C. \(13.86\)
• D. \(20.79\)

Answer 1

The Correct Option is B

Concept:
For a first order reaction: \[ t_{1/2}=\frac{\ln2}{k} \] and \[ t=\frac{1}{k}\ln\left(\frac{A_0}{A_t}\right) \] Step 1: Calculate the rate constant. \[ t_{1/2}=\frac{0.693}{k} \] \[ 6.93=\frac{0.693}{k} \] \[ k=\frac{0.693}{6.93}=0.1\,\text{min}^{-1} \] Step 2: Determine concentration ratio for \(99\%\) completion. If \(99\%\) reaction is completed: \[ \frac{A_0}{A_t}=\frac{100}{1} \] Step 3: Calculate required time. \[ t=\frac{1}{k}\ln\left(\frac{A_0}{A_t}\right) \] \[ t=\frac{1}{0.1}\ln(100) \] \[ t=10\times2\ln10 \] \[ t=10\times2\times2.303 \] \[ t=46.06\,\text{min} \] \[ \boxed{t=46.06\,\text{min}} \]