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AIIMS 2016
Exam
AIIMS
Year
2016
Subject
Chemistry
Chapter
Chemical Kinetics

AIIMS 2016 · Chemistry · Chemical Kinetics

A first order reaction, which is 30 \% complete in 30 minutes has a...

A first order reaction, which is 30%30 \% complete in 30 minutes has a half-life period of

Options

  1. A102.2 min102.2 \mathrm{~min}
  2. B58.2 min58.2 \mathrm{~min}
  3. C24.2 min24.2 \mathrm{~min}
  4. D120.2 min120.2 \mathrm{~min}

Correct answer

B. 58.2 min58.2 \mathrm{~min}

Step-by-step solution

For first order reaction, t=2.303klog⁡aa−x⇒t30%t50%=2.303klog⁡100100−302.303klog⁡100100−50⇒30t1/2=log⁡107log⁡2⇒30t1/2=0.15490.3010⇒t1/2=0.3010×300.1549=58.29 min\begin{aligned} & t=\frac{2.303}{k} \log \frac{a}{a-x} \Rightarrow \frac{t_{30 \%}}{t_{50 \%}}=\frac{\frac{2.303}{k} \log \frac{100}{100-30}}{\frac{2.303}{k} \log \frac{100}{100-50}} \\ & \Rightarrow \frac{30}{t_{1/2}}=\frac{\log \frac{10}{7}}{\log 2} \Rightarrow \frac{30}{t_{1/2}}=\frac{0.1549}{0.3010} \\ & \Rightarrow t_{1/2}=\frac{0.3010 \times 30}{0.1549}=58.29 \mathrm{~min}\end{aligned}
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