Chemistry Q72 – JEE-MAIN 2025

Home Chemistry Chemical KineticsQuestion #280

For the reaction A

\to

products. The concentration of A at 10 minutes is _______

\times 10^{- 3}

mol L

^{- 1}

(nearest integer). The reaction was started with 2.5 mol L

^{- 1}

of A. The graph shows

t_{1 / 2}

(min) vs

[A]_{0}

(mol L

^{- 1}

) is a straight line with slope = 76.92.

Enter Calculated Numerical Value:

Clue 1 of 3: Reaction Order Identification

Analyze the relationship between half-life and initial concentration from the given graph to determine the order of the reaction.

🧠 Full Solution Path

● Video Walkthrough

Step 1: Determine Reaction Order and Rate Constant✦ Active

The graph shows that $t_{1 / 2}$ is directly proportional to $[A]_{0}$ , i.e., $t_{1 / 2} = slope \times [A]_{0}$ . This relationship is characteristic of a zero-order reaction.

For a zero-order reaction, the half-life is given by $t_{1 / 2} = \frac{[A]_{0}}{2 k}$ . Comparing the two expressions, we get:

\frac{[A]_{0}}{2 k} = slope \times [A]_{0} ⟹ \frac{1}{2 k} = slope

Given slope = 76.92 min (mol L $^{- 1}$ ) $^{- 1}$ . Therefore, the rate constant $k$ is:

k = \frac{1}{2 \times slope} = \frac{1}{2 \times 76.92} = \frac{1}{153.84} \approx 0.00650026 {mol L}^{- 1} {min}^{- 1}

Step 2: Calculate Concentration at 10 minutes○ Expand

The integrated rate law for a zero-order reaction is $[A]_{t} = [A]_{0} - k t$ . Given $[A]_{0} = 2.5$ mol L $^{- 1}$ and $t = 10$ minutes, we can calculate $[A]_{10}$ :

[A]_{10} = 2.5 - (0.00650026 {mol L}^{- 1} {min}^{- 1} \times 10 min)

[A]_{10} = 2.5 - 0.0650026 = 2.4349974 {mol L}^{- 1}

Step 3: Convert to Required Units and Round○ Expand

The question asks for the concentration in $\times 10^{- 3}$ mol L $^{- 1}$ (nearest integer). Convert the calculated concentration:

2.4349974 {mol L}^{- 1} = 2.4349974 \times 1000 \times 10^{- 3} {mol L}^{- 1}

= 2434.9974 \times 10^{- 3} {mol L}^{- 1}

Rounding to the nearest integer gives 2435.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Chemistry Question 72 – JEE-MAIN 2025

Clue 1 of 3: Reaction Order Identification

🧠 Full Solution Path