Verified Solution • 2025–26 Session moderate

QJEEM22Ch4556: JEE Main 2022 Chemistry - Class 12 JEEM22Ch4556 Solution: For the reaction P B, the values of frequency factor A and…

For the reaction P →\to B, the values of frequency factor A and activation energy EA are 4 ×\times 1013 s −- 1 and 8.3 kJ mol −- 1 respectively. If the reaction is of first order, the temperature at which the rate constant is 2 ×\times 10 −- 6 s −- 1 is _____________ ×\times 10 −- 1 K.

(Given : ln 10 = 2.3, R = 8.3 J K −- 1 mol −- 1, log2 = 0.30)

Step-by-Step Verified Solution

amp;k=Ae−EaRTamp;ln⁡k=ln⁡A−EaRTamp;⇒log⁡(2×10−6)=log⁡(4×1013)−8.3×1038.3×T×2.3amp;⇒log⁡(2)−6=2×log⁡(2)+13−8.3×1038.3×T×2.3amp;⇒−19.3=−103T×2.3⇒T=225×10−1 K\begin{aligned}&k=A \mathrm{e}^{\frac{-E_{a}}{R T}} \\\\&\ln k=\ln A-\frac{E_{a}}{R T} \\\\&\Rightarrow \log \left(2 \times 10^{-6}\right)=\log \left(4 \times 10^{13}\right)-\frac{8.3 \times 10^{3}}{8.3 \times T \times 2.3} \\\\&\Rightarrow \log (2)-6=2 \times \log (2)+13-\frac{8.3 \times 10^{3}}{8.3 \times T \times 2.3} \\\\&\Rightarrow-19.3=-\frac{10^{3}}{T \times 2.3} \Rightarrow T=225 \times 10^{-1} \mathrm{~K}\end{aligned}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring