JEE Main · 2025 · Shift-IhardCK-140

A person's wound was exposed to some bacteria and then bacteria growth started to happen at the same place. The wound…

Chemical Kinetics · Class 12 · JEE Main Previous Year Question

Question

A person's wound was exposed to some bacteria and then bacteria growth started to happen at the same place. The wound was later treated with some antibacterial medicine and the rate of bacterial decay (r) was found to be proportional with the square of the existing number of bacteria at any instance. Which of the following set of graphs correctly represents the 'before' and 'after' situation of the application of the medicine?

[Given: N = No. of bacteria, t = time, bacterial growth follows Ist^{\text{st}} order kinetics.]

Options
  1. a

    image

  2. b

    image

    ✓
  3. c

    image

  4. d

    image

Correct Answerb

image

Detailed Solution

Step 1: Analyse bacterial growth (Before medicine)

Bacterial growth follows first order kinetics:

dAdt=k[A]\frac{dA}{dt} = k[A]

AA0=ekt\frac{A}{A_0} = e^{kt}

This gives an exponential growth curve (N/N₀ vs t is exponential, concave up).

Step 2: Analyse bacterial decay (After medicine)

Rate of decay r=−dAdt∝[A]2r = -\tfrac{dA}{dt} \propto [A]^2 (second order in bacteria)

r=k[A]2r = k[A]^2

So rr vs NN is a parabola (y=kx2y = kx^2).

Step 3: Match with graphs

  • Before: N/N0N/N_0 vs tt → exponential growth (starts slow, then rapid) ✓
  • After: rr vs NN → parabola (second order) ✓

Graph (b) shows: Before = exponential growth curve, After = parabolic r vs N relationship.

Answer: (b)

Practice this question with progress tracking

Want timed practice with adaptive difficulty? Solve this question (and hundreds more from Chemical Kinetics) inside The Crucible, our adaptive practice platform.

Practice in The Crucible →Browse Chemical Kinetics chapter →

More JEE Main Chemical Kinetics PYQs

2023medium

For a chemical reaction A + B Product, the order is 1 with respect to A and B. | Rate mol\,L-1\,s-1 | [A]\,mol\,L-1 | [B]\,mol\,L-1 | |:---:|:---:|:---:| | 0.10 | 20 | 0.5 | | 0.40 | x | 0.5 | | 0.80…

2023medium

A student has studied the decomposition of a gas AB3 at 25°C. He obtained the following data: | p\,(mm\,Hg) | Relative t1/2\,(s) | |:---:|:---:| | 50 | 4 | | 100 | 2 | | 200 | 1 | | 400 | 0.5 | The…

2021hard

For the following graphs: Choose from the options given below, the correct one regarding order of reaction is:

2020medium

The graph which represents the following reaction is: {(C_6H_5)_3C{-}Cl} {{OH^-/Pyridine}} {(C_6H_5)_3C{-}OH}

2020medium

The results given in the below table were obtained during kinetic studies of the following reaction: {2A + B C + D} | Experiment | [A]\,/\,mol\,L-1 | [B]\,/\,mol\,L-1 | Initial rate mol\,L-1\,min-1 |…

View all 51 Chemical Kinetics PYQs →
A person's wound was exposed to some bacteria and then bacteria growth started to happen at the… (JEE Main 2025) | Canvas Classes