JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Chemical Kinetics

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

]

Answer: 10

Solution

A half-life quoted without reference to the starting concentration fixes the order as one, so

k = \frac{ln 2}{t _{1/2}} = \frac{0.69}{1} = 0.69 mi n^{- 1}

99.9%

completion the fraction of reactant left is

1 0^{- 3}

, and for first order decay

t = \frac{1}{k} ln \frac{[ A ] _{0}}{[ A ]} = \frac{ln 1 0 ^{3}}{0.69} = \frac{3 ( 2.3 )}{0.69} = 10

The reaction reaches

99.9%

completion in

10

min.

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Integer answer