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CUET · CHEMISTRY · PYQ PAPER 2023

If time taken for a first order reaction to get \(90\%\) complete is \(24\ min\), its \(t_{99.9\%}\) will be:

  1. A 240 min
  2. B 48 min
  3. C 120 min
  4. D 72 min
Verified Solution

Answer & Solution

Correct Answer

(D) 72 min

Step-by-step Solution

Detailed explanation

\(k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}\) \(k = \frac{2.303}{24} \log \frac{1}{0.1} = \frac{2.303}{24} \times 1\) \(t_{99.9\%} = \frac{2.303}{k} \log \frac{1}{0.001}\) \(t_{99.9\%} = \frac{2.303}{\frac{2.303}{24}} \log 1000\) \(t_{99.9\%} = 24 \times 3 = 72 \text{ min}\)
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