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JEE Main 202431 JanuaryMorning Shift
Exam
JEE Main
Year
2024
Date
31 January
Shift
Morning Shift
Subject
Chemistry
Chapter
Chemical Kinetics

JEE Main 2024 · 31 January · Morning Shift · Chemistry · Chemical Kinetics

Integrated rate law equation for a first order gas phase reaction...

Integrated rate law equation for a first order gas phase reaction is given by (where Pi{P}_{i} is initial pressure and Pt{P}_{t} is total pressure at time tt)

Options

  1. Ak = \dfrac{2 . 303}{t} \times log\dfrac{{P}_{i}}{\left(2{P}_{i} - {P}_{t}\right)}
  2. Bk = \dfrac{2 . 303}{t} \times log\dfrac{2{P}_{i}}{\left(2{P}_{i} - {P}_{t}\right)}
  3. Ck = \dfrac{2 . 303}{t} \times log\dfrac{\left(2{P}_{i} - {P}_{t}\right)}{{P}_{i}}
  4. Dk = \dfrac{2 . 303}{t} \times \dfrac{{P}_{i}}{\left(2{P}_{i} - {P}_{t}\right)}

Correct answer

A. k = \dfrac{2 . 303}{t} \times log\dfrac{{P}_{i}}{\left(2{P}_{i} - {P}_{t}\right)}

Step-by-step solution

A→B+CA \to B + C

Pi00{P}_{i}00

Pi−xxx{P}_{i} - xxx

The formula used here is:

k=2.303tlogPiPtk = \dfrac{2 . 303}{t}log\dfrac{{P}_{i}}{{P}_{t}}

Pt=Pi+x{P}_{t} = {P}_{i} + x

Pi−x=Pi−Pt+Pi{P}_{i} - x = {P}_{i} - {P}_{t} + {P}_{i}

=2Pi−Pt= 2{P}_{i} - {P}_{t}

k=2.303t×logPi(2Pi−Pt)k = \dfrac{2 . 303}{t} \times log\dfrac{{P}_{i}}{\left(2{P}_{i} - {P}_{t}\right)}

Hence, the answer is option A.

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