Q. A reaction follows first-order kinetics with k = 0.0231 min⁻¹. The time taken for the concentration to fall to one-eighth of its initial value is:

एक प्रतिक्रिया k = 0.0231 min⁻¹ के साथ प्रथम-क्रम गतिकी का अनुसरण करती है। सांद्रता को उसके प्रारंभिक मूल्य के आठवें हिस्से तक गिरने में लगने वाला समय है:

15 min
15 मिनट

30 min
30 मि

60 min
60 मिनट

90 min
90 मिनट

$\frac{[A]}{[A]_0} = \frac{1}{8} = 2^{-3}$

For first order:

\ln \frac{[A]_0}{[A]} = kt

\ln 8 = 0.0231 \times t \Rightarrow 2.079 = 0.0231 t

t = \frac{2.079}{0.0231} = 90 \, \text{min}

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