Verified Solution • 2025–26 Session moderate

QJEEM21Chdaf3: JEE Main 2021 Chemistry - Class 12 JEEM21Chdaf3 Solution: A reaction has a half life of 1 min. The time required for…

A reaction has a half life of 1 min. The time required for 99.9% completion of the reaction is _________ min. (Round off to the Nearest Integer). [Use : ln 2 = 0.69; ln 10 = 2.3]

Step-by-Step Verified Solution

Given t1/2 = 1 min

∴\therefore K=ln⁡2t1/2=ln⁡21K = {{\ln 2} \over {{t_{1/2}}}} = {{\ln 2} \over 1}

From formula we know,

Kt=ln⁡(100100−x)Kt = \ln \left( {{{100} \over {100 - x}}} \right)

⇒ln⁡21=1tln⁡(1000.1)\Rightarrow {{\ln 2} \over 1} = {1 \over t}\ln \left( {{{100} \over {0.1}}} \right)

⇒0.3=1tln⁡(103)\Rightarrow 0.3 = {1 \over t}\ln \left( {{{10}^3}} \right)

⇒0.3=1t×3\Rightarrow 0.3 = {1 \over t} \times 3

⇒t=10\Rightarrow t = 10 min

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