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A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min. respectively. Starting from an equimolar non reactive mixture of A and B, the time taken for the concentration of A to become 16 times that of B is ______ min.
(Round off to the nearest integer)
    Correct answer is '108'. Can you explain this answer?
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    A and B decompose via first order kinetics with half-lives 54.0 min an...
    Concept: First-order kinetics, Half-life, Equimolar mixture

    Solution:

    Let the initial concentration of A and B be 'x' mol/L each.

    After time 't', the concentrations of A and B can be given as:

    [A] = x.e^(-kt) (1)

    [B] = x.e^(-kt/3) (2)

    where 'k' is the rate constant.

    Given, half-life of A = 54.0 min

    Hence, k = ln(2)/54.0 = 0.0128 min^(-1)

    Similarly, half-life of B = 18.0 min

    Hence, k = ln(2)/18.0 = 0.0386 min^(-1)

    Now, we need to find the time taken for [A] to become 16 times that of [B].

    i.e., [A]/[B] = 16

    Substituting equations (1) and (2) in the above equation, we get:

    e^(kt/3) = 16e^(kt)

    Taking natural logarithm on both sides, we get:

    kt/3 = ln(16) + kt

    Solving for 't', we get:

    t = 108.2 min

    Rounding off to the nearest integer, the time taken for [A] to become 16 times that of [B] is 108 min.

    Therefore, the answer is 108.
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    A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min. respectively. Starting from an equimolar non reactive mixture of A and B, the time taken for the concentration of A to become 16 times that of B is ______ min.(Round off to the nearest integer)Correct answer is '108'. Can you explain this answer?
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    A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min. respectively. Starting from an equimolar non reactive mixture of A and B, the time taken for the concentration of A to become 16 times that of B is ______ min.(Round off to the nearest integer)Correct answer is '108'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min. respectively. Starting from an equimolar non reactive mixture of A and B, the time taken for the concentration of A to become 16 times that of B is ______ min.(Round off to the nearest integer)Correct answer is '108'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min. respectively. Starting from an equimolar non reactive mixture of A and B, the time taken for the concentration of A to become 16 times that of B is ______ min.(Round off to the nearest integer)Correct answer is '108'. Can you explain this answer?.
    Solutions for A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min. respectively. Starting from an equimolar non reactive mixture of A and B, the time taken for the concentration of A to become 16 times that of B is ______ min.(Round off to the nearest integer)Correct answer is '108'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
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