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ChemistryMultiple correct+4 / -1Question 41 of 54

JEE Advanced 2026 · Paper 2, Chemistry question 5

For a first-order reaction R⟶P\mathbf R\longrightarrow\mathbf P at a given temperature, kk is the rate constant. For this reaction, at the given temperature, the concentrations of R\mathbf R and P\mathbf P at a time tt are [R][\mathbf R] and [P][\mathbf P], respectively. The correct graphical representation(s) for this reaction is(are)

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Answer and worked solution

Official answer: C, D

For a first-order reaction, [R]=[R]0e−kt[\mathbf R]=[\mathbf R]_0e^{-kt} and [P]=[R]0(1−e−kt)[\mathbf P]=[\mathbf R]_0\left(1-e^{-kt}\right).

  • (A) [P][\mathbf P] rises with decreasing slope (concave down) to [R]0[\mathbf R]_0; the graph is concave up. False.
  • (B) d[R]dt=−k[R]\dfrac{d[\mathbf R]}{dt}=-k[\mathbf R] is a line of negative slope; the graph has positive slope. False.
  • (C) d[P]dt=k[R]0e−kt\dfrac{d[\mathbf P]}{dt}=k[\mathbf R]_0e^{-kt} decays exponentially from its maximum at t=0t=0. True.
  • (D) kk is constant at fixed temperature. True.
Topics:Integrated rate equationsRate of reaction and rate law
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