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Ratio of times for different percentage completions of a first-order reaction

This type of question, asked 7 times: 2021 Paper 22, 14 Jun 2022, 28 Jun 2022, 13 Apr 2023, 27 Jan 2024, 6 Apr 2024, 28 Jan 2026 S1. All 7 questions below, oldest first.

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  1. Question 1

    2021 Paper 22

    56
    For a first order reaction, the ratio of the time for 75%75\% completion of a reaction to the time for 50%50\% completion is ____\_\_\_\_. (Integer answer)

  2. Question 2

    14 Jun 2022

    125
    For a first order reaction, the time required for completion of 90%90\% reaction is ' xx ' times the half life of the reaction. The value of ' xx ' is (Given: ln⁡10=2.303\ln10 = 2.303 and log⁡2=0.3010\log2 = 0.3010 )

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  3. Question 3

    28 Jun 2022

    58
    For a first order reaction A→BA \rightarrow B, the rate constant, k=5.5×10−14 s−1k = 5.5 \times10^{- 14}{\text{ }s}^{- 1}. The time required for 67%67\% completion of reaction is x×10−1x \times10^{- 1} times the half life of reaction. The value of xx is (Nearest integer) (Given: log⁡3=0.4771\log3 = 0.4771 )

  4. Question 4

    13 Apr 2023

    58
    t87.5t_{87.5} is the time required for the reaction to undergo 87.5%87.5\% completion and t50t_{50} is the time required for the reaction to undergo 50%50\% completion. The relation between t87.5t_{87.5} and t50t_{50} for a first order reaction is t87.5=x×t50t_{87.5}= x \times t_{50} The value of xx is _________(Nearest integer)

  5. Question 5

    27 Jan 2024

    143
    Time required for completion of 99.9%99.9\% of a First order reaction is ____ times of half life (t1/2)\left( t_{1/2} \right) of the reaction.

  6. Question 6

    6 Apr 2024

    53
    Time required for 99.9%99.9\% completion of a first order reaction is______ time the time required for completion of 90%90\% reaction. (nearest integer).

  7. Question 7

    28 Jan 2026 S1

    32
    An organic compound undergoes first order decomposition. The time taken for decomposition to (18)th \left( \frac{1}{8} \right)^{\text{th~}} and (110)th \left( \frac{1}{10} \right)^{\text{th~}} of its initial concentration are t1/8t_{1/8} and t1/10t_{1/10} respectively. What is the value of t1/8t1/10×10\frac{t_{1/8}}{t_{1/10}}\times 10 ?
    (log⁡2=0.3)(\log2 = 0.3)

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