Chemistry Q57 – JEE-MAIN 2026

Home Chemistry Chemical KineticsQuestion #262

Consider the first order reaction R

\to

P. The fraction of molecules decomposed in the given first order reaction can be expressed as

Clue 1 of 3: First-Order Kinetics

Recall the integrated rate law for a first-order reaction.

🧠 Full Solution Path

● Video Walkthrough

Step 1: Recall the integrated rate law for a first-order reaction✦ Active

For a first-order reaction $R \to P$ , the concentration of reactant $R$ at time $t$ , $[R]_{t}$ , is related to its initial concentration, $[R]_{0}$ , by the equation:

[R]_{t} = [R]_{0} e^{- k t}

where $k$ is the rate constant.

Step 2: Define the fraction of molecules decomposed○ Expand

The fraction of molecules decomposed is the ratio of the amount of reactant consumed to the initial amount of reactant.

Fraction decomposed = \frac{[R]_{0} - [R]_{t}}{[R]_{0}}

Step 3: Substitute the integrated rate law into the fraction decomposed expression○ Expand

Substitute $[R]_{t} = [R]_{0} e^{- k t}$ into the expression for the fraction decomposed:

Fraction decomposed = \frac{[R]_{0} - [R]_{0} e^{- k t}}{[R]_{0}} = \frac{[R]_{0} (1 - e^{- k t})}{[R]_{0}} = 1 - e^{- k t}

Thus, the fraction of molecules decomposed is $1 - e^{- k t}$ .

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

Chemistry Question 57 – JEE-MAIN 2026

Clue 1 of 3: First-Order Kinetics

🧠 Full Solution Path