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NEET 2024
Exam
NEET
Year
2024
Subject
Chemistry
Chapter
Chemical Kinetics

NEET 2024 · Chemistry · Chemical Kinetics

The rate of a reaction quadruples when temperature changes from 27^...

The rate of a reaction quadruples when temperature changes from 27∘C27^{\circ} \mathrm{C} to 57∘C57^{\circ} \mathrm{C}. Calculate the energy o activation. Given R=8.314 J K−1 mol−1,log⁡4=0.6021\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}, \log 4=0.6021

Options

  1. A380.4 kJ/mol380.4 \mathrm{~kJ} / \mathrm{mol}
  2. B3.80 kJ/mol3.80 \mathrm{~kJ} / \mathrm{mol}
  3. C3804 kJ/mol3804 \mathrm{~kJ} / \mathrm{mol}
  4. D38.04 kJ/mol38.04 \mathrm{~kJ} / \mathrm{mol}

Correct answer

D. 38.04 kJ/mol38.04 \mathrm{~kJ} / \mathrm{mol}

Step-by-step solution

log⁡(k2k1)=Ea2.303R(1 T1−1 T2)log⁡(41)=Ea2.303R(1300−1330)Ea=(log⁡(4))×2.303×8.314×300×33030=3.804×104 J/mol=38.04 kJ/mol\begin{aligned} & \log \left(\frac{\mathrm{k}_2}{\mathrm{k}_1}\right)=\frac{\mathrm{E}_{\mathrm{a}}}{2.303 \mathrm{R}}\left(\frac{1}{\mathrm{~T}_1}-\frac{1}{\mathrm{~T}_2}\right) \\ & \log \left(\frac{4}{1}\right)=\frac{\mathrm{E}_{\mathrm{a}}}{2.303 \mathrm{R}}\left(\frac{1}{300}-\frac{1}{330}\right) \\ & \mathrm{E}_{\mathrm{a}}=\frac{(\log (4)) \times 2.303 \times 8.314 \times 300 \times 330}{30} \\ & =3.804 \times 10^4 \mathrm{~J} / \mathrm{mol} \\ & =38.04 \mathrm{~kJ} / \mathrm{mol}\end{aligned}
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