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Rate constant or half-life of a first-order reaction from amounts at two times

This type of question, asked 4 times: 2021 Paper 12, 2021 Paper 17, 30 Jan 2024, 4 Apr 2026 S2. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 12

    34
    PCl5→PCl3+Cl2PCl_{5}\rightarrow PCl_{3}+Cl_{2} The above first order reaction has initial moles as 10 and after 20 min⁡20\text{ }\min final moles are 2. Find the rate constant. (Given: log⁡5=0.693\log5 = 0.693 )

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  2. Question 2

    2021 Paper 17

    59
    For the first order reaction A→2 B,1A \rightarrow 2\text{ }B,1 mole of reactant A gives 0.2 moles of BB after 100 minutes. The half life of the reaction is ____\_\_\_\_ min. (Round off to the nearest integer). [Use: ln⁡2=0.69,ln⁡10=2.3\ln2 = 0.69,\ln10 = 2.3 Properties of logarithms: ln⁡xy=ylnx\ln x^{y}= ylnx;
     ln⁡(xy)=ln⁡x−ln⁡y]\left. \ \ln\left( \frac{x}{y} \right)= \ln x - \ln y \right\rbrack
    (Round off to the nearest integer)

  3. Question 3

    30 Jan 2024

    51
    The rate of first order reaction is 0.04 mol L−1 s−10.04\text{ }mol{\text{ }L}^{- 1}{\text{ }s}^{- 1} at 10 minutes and 0.03 mol L−1 s−10.03\text{ }mol{\text{ }L}^{- 1}{\text{ }s}^{- 1} at 20 minutes after initiation. Half life of the reaction is ____ minutes. (Given log⁡2=0.3010,log⁡3=0.4771\log2 = 0.3010,\log3 = 0.4771 )

  4. Question 4

    4 Apr 2026 S2

    49
    For a first order reaction A→BA \rightarrow B
    tt/min[A][A]/M
    00.6500
    xx0.0650
    200.00065
    x=x = ____\_\_\_\_ min. (Nearest integer)