JEE Main 2026 — Chemical Kinetics Question with Solution

The given reaction is $A(g)\to B(g)+C(g)$

At $t=0$, the initial pressure of A is $p_i$ and the pressures of B and C are $0$.

At time $t$, let the decrease in pressure of A be $x$.
Pressure of A $=p_i-x$
Pressure of B $=x$
Pressure of C $=x$

Total pressure at time $t$ is $p_t=(p_i-x)+x+x=p_i+x$

From this, we get $x=p_t-p_i$

The partial pressure of A at time $t$ is $P_A=p_i-x=p_i-(p_t-p_i)=2p_i-p_t$

For a first order reaction, the rate constant $k$ is given by

$k=\frac{1}{t}\ln \frac{P_{A,0}}{P_A}$

Substituting the values, we get

$k=\frac{1}{t}\ln \frac{p_i}{2p_i-p_t}$

Answer: $\frac{1}{t}\ln \frac{p_i}{2p_i-p_t}$