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Two first-order reactants with different half-lives: when do their concentrations reach a given ratio

The same question, asked 2 times: 26 Jun 2022*, 3 Apr 2025. Every wording below, oldest first.

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  1. Question 1

    26 Jun 2022

    54
    A flask is filled with equal moles of AA and B. The half lives of AA and BB are 100 s100\text{ }s and 50 s50\text{ }s respectively and are independent of the initial concentration. The time required for the concentration of AA to be four times that of BB is s. (Given: ln⁡2=0.693\ln2 = 0.693 )
  2. Question 2

    3 Apr 2025

    30
    In a reaction A+B→CA + B \rightarrow C, initial concentrations of AA and BB are related as [A]0=8[B]0\lbrack A\rbrack_{0}= 8\lbrack B\rbrack_{0}. The half lives of AA and BB are 10 min and 40 min . respectively. If they start to disappear at the same time, both following first order kinetics, after how much time will the concentration of both the reactants be same?

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