Chemistry Q57 – JEE-MAIN 2026

Home Chemistry Chemical KineticsQuestion #267

First order gas phase reaction

A \to B + C

p_{i}

= initial pressure of gas A,

p_{t}

= total pressure of the reaction mixture at time t Expression of rate constant (k) is

Clue 1 of 3: Reaction Stoichiometry

Understand how the partial pressures of reactants and products change over time based on the reaction stoichiometry.

🧠 Full Solution Path

Step 1: Set up pressure table for the reaction✦ Active

For the first-order gas phase reaction $A \to B + C$ , let $p_{i}$ be the initial pressure of A. At time $t$ , let $x$ be the pressure of A that has reacted.

\begin{array}{lccc} Reaction: & A & \to & B & + & C \\ Initial pressure: & p_{i} & 0 & 0 \\ Pressure at time t : & p_{i} - x & x & x \end{array}

Step 2: Relate total pressure to initial pressure and reacted pressure○ Expand

The total pressure of the reaction mixture at time $t$ , $p_{t}$ , is the sum of the partial pressures of all components:

p_{t} = P_{A} + P_{B} + P_{C} = (p_{i} - x) + x + x = p_{i} + x

From this, we can express $x$ in terms of $p_{i}$ and $p_{t}$ : $x = p_{t} - p_{i}$ . Now, substitute $x$ back into the expression for the partial pressure of A at time $t$ , $P_{A}$ :

P_{A} = p_{i} - x = p_{i} - (p_{t} - p_{i}) = 2 p_{i} - p_{t}

💡 Teacher's Secret Hint

Ensure correct algebraic manipulation when substituting $x$ .

Step 3: Apply the integrated rate law for a first-order reaction○ Expand

For a first-order gas phase reaction, the rate constant $k$ is given by the integrated rate law:

k = \frac{1}{t} \ln \frac{P_{A} (i n i t i a l)}{P_{A} (a t t i m e t)}

Substitute $P_{A} (i n i t i a l) = p_{i}$ and $P_{A} (a t t i m e t) = 2 p_{i} - p_{t}$ into the equation:

k = \frac{1}{t} \ln \frac{p_{i}}{2 p_{i} - p_{t}}

This expression matches option 1.

💡 Teacher's Secret Hint

Remember that for gas phase reactions, partial pressures are used instead of concentrations in the rate law.

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Chemistry Question 57 – JEE-MAIN 2026

Clue 1 of 3: Reaction Stoichiometry

🧠 Full Solution Path