JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Chemical Kinetics

For the first order reaction

A \to 2 B

, 1 mole of reactant A gives 0.2 moles of B after 100 minutes. The half life of the reaction is

____

min. (Round off to the Nearest Integer).
[Use :

ln 2 = 0.69, ln 10 = 2.3

Properties of logarithms :

ln x^{y} = y ln x; ln (\frac{x}{y}) = ln x - ln y

]

Answer: 655

Solution

A \to 2 B

, 0.2 mol of B means 0.1 mol of A has reacted, so

0.9

mol of A remains from the initial

1

mol. For a first-order reaction

k = \frac{1}{t} ln \frac{[ A ] _{0}}{[ A ]} = \frac{1}{100} ln \frac{1}{0.9} = \frac{l n ( 10/9 )}{100} \approx 1.054 \times 1 0^{- 3} min^{- 1}

. Then

t_{1/2} = \frac{l n 2}{k} = \frac{0.69}{1.054 \times 1 0 ^{- 3}} \approx 655 min

JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Integer answer