JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Chemical Kinetics

For the given first order reaction

A \to B

the half life of the reaction is 0.3010 min. The ratio of the initial concentration of reactant to the concentration of reactant at time 2.0 min will be equal to

____

. (Nearest integer)

Answer: 100

Solution

For a first-order reaction, the rate constant is:

k = \frac{0.693}{t _{1/2}} = \frac{0.693}{0.3010} = 2.303 min^{- 1}

Using the first-order integrated rate law:

k = \frac{2.303}{t} lo g (\frac{A _{0}}{A _{t}})

Substituting k and t = 2.0 min:

2.303 = \frac{2.303}{2} lo g (\frac{A _{0}}{A _{t}})

lo g (\frac{A _{0}}{A _{t}}) = 2

\frac{A _{0}}{A _{t}} = 1 0^{2} = 100

Answer: 100

JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Integer answer

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