For a first order reaction, the plot of ( [ A ]₀ [ A ] ) versus time t (in seconds) is a straight line with a slope of 4.62 10⁻³ s ⁻¹ . The time required for the concentration of the reactant to reduce to 1 64 of its initial value is ______

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For a first order reaction, the plot of ( [ A ]₀ [ A ] ) versus time t (in seconds) is a straight line with a slope of 4.62 10⁻³ s ⁻¹ . The time required for the concentration of the reactant to reduce to 1 64 of its initial value is ________ minutes.

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Correct answer: 15

For a first order reaction, the integrated rate law is: ( [ A ]₀ [ A ] ) = kt The plot of ( [ A ]₀ [ A ] ) versus t is a straight line passing through the origin with slope equal to the rate constant k . Thus, k = 4.62 10⁻³ s ⁻¹ . The half-life of the reaction is: t_ 1/2 = 0.693 k = 0.693 4.62 10⁻³ = 150 s The concentration reduces to 1 64 of its initial value. Since 1 64 = ( 1 2 )^6 , this corresponds to 6 half-lives. Total time required = 6 t_ 1/2 = 6 150 s = 900 s . Converting the time into minutes: t = 900 60 m

For a first order reaction, the plot of ( [ A ]₀ [ A ] ) versus time t (in seconds) is a straight line with a slope of 4.62 10⁻³ s ⁻¹ . The time required for the concentration of the reactant to reduce to 1 64 of its initial value is ________ minutes.

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