JEE Main · 2024 · Shift-ImediumCK-053

Integrated rate law equation for a first order gas phase reaction is given by (where Pi is initial pressure and Pt is…

Chemical Kinetics · Class 12 · JEE Main Previous Year Question

Question

Integrated rate law equation for a first order gas phase reaction is given by (where $P_i$ is initial pressure and $P_t$ is total pressure at time $t$ ):

Options

a
$k = \frac{2.303}{t} \times \log\frac{P_i}{(2P_i - P_t)}$
✓
b
$k = \frac{2.303}{t} \times \log\frac{2P_i}{(2P_i - P_t)}$
c
$k = \frac{2.303}{t} \times \log\frac{(2P_i - P_t)}{P_i}$
d
$k = \frac{2.303}{t} \times \frac{P_i}{(2P_i - P_t)}$

Correct Answera

$k = \frac{2.303}{t} \times \log\frac{P_i}{(2P_i - P_t)}$

Detailed Solution

For a first order gas phase reaction $\mathrm{A(g) \rightarrow B(g) + C(g)}$ :

Let initial pressure of A = $P_i$ , decrease in pressure = $p$ .

At time $t$ : $P_A = P_i - p$ , total pressure $P_t = (P_i - p) + p + p = P_i + p$

So $p = P_t - P_i$ , and $P_A = P_i - (P_t - P_i) = 2P_i - P_t$

For first order: $k = \frac{2.303}{t}\log\frac{P_i}{P_A} = \frac{2.303}{t}\log\frac{P_i}{2P_i - P_t}$

Answer: Option (1)

Practice this question with progress tracking

Want timed practice with adaptive difficulty? Solve this question (and hundreds more from Chemical Kinetics) inside The Crucible, our adaptive practice platform.

Practice in The Crucible →Browse Chemical Kinetics chapter →

More JEE Main Chemical Kinetics PYQs

2025medium

Reaction A(g) - 2B(g) + C(g) is a first order reaction. It was started with pure A. | t/min | Pressure of system at time t/mm Hg | |---|---| | 10 | 160 | | | 240 | Which of the following option is…

2025medium

In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are t1 and t2 (s), respectively. The ratio t1t2…

2022medium

For a first order reaction, the time required for completion of 90% reaction is 'x' times the half life of the reaction. The value of 'x' is (Given: 10 = 2.303 and 2 = 0.3010)

2022medium

At 30°C, the half life for the decomposition of AB2 is 200 s and is independent of the initial concentration of AB2. The time required for 80% of the AB2 to decompose is (Given: 2 = 0.30; 3 = 0.48)

2020hard

A flask contains a mixture of compounds A and B. Both compounds decompose by first-order kinetics. The half-lives for A and B are 300 s and 180 s, respectively. If the concentrations of A and B are…

View all 51 Chemical Kinetics PYQs →