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Chemistry Question 57 – JEE-MAIN 2026

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

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

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

For a first-order reaction R→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]0e−kt

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=[R]0−[R]t[R]0
Step 3: Substitute the integrated rate law into the fraction decomposed expression○ Expand

Substitute [R]t=[R]0e−kt into the expression for the fraction decomposed:

Fraction decomposed=[R]0−[R]0e−kt[R]0=[R]0(1−e−kt)[R]0=1−e−kt

Thus, the fraction of molecules decomposed is 1−e−kt.

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