JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Chemical Kinetics

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A \to B

The above reaction is of zero order. Half life of this reaction is 50 min . The time taken for the concentration of A to reduce to one-fourth of its initial value is

____

min.
(Nearest integer)

Answer: 75

Solution

For a zero-order reaction the concentration falls linearly,

[A] = [A]_{0} - k t

. The half-life

t_{1/2} = \frac{[ A ] _{0}}{2 k} = 50

min fixes the rate constant as

k = \frac{[ A ] _{0}}{100}

. To reach one-fourth of the initial value,

\frac{[ A ] _{0}}{4} = [A]_{0} - k t

, so

k t = \frac{3 [ A ] _{0}}{4}

and

t = \frac{3 [ A ] _{0}}{4 k} = \frac{3 [ A ] _{0}}{4} \times \frac{100}{[ A ] _{0}}

. The time required is

75

min.

JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Integer answer

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