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BITSAT 2024
Exam
BITSAT
Year
2024
Subject
Chemistry
Chapter
Chemical Kinetics

BITSAT 2024 · Chemistry · Chemical Kinetics

If for a first order reaction, the value of A and E_a are 4 × 10^...

If for a first order reaction, the value of AA and EaE_a are 4×1013s−14 \times 10^{13} \mathrm{ s}^{-1} and 98.6kJmol−198.6 \mathrm{ kJ} \mathrm{ mol}^{-1} respectively, then at what temperature will its half life period be 10 minutes?

Options

  1. A330 K
  2. B300 K
  3. C330.95 K
  4. D311.15 K

Correct answer

D. 311.15 K

Step-by-step solution

According to Arrhenius equation, log⁡k=log⁡A−Ea2.303RT...(i)\log k=\log A-\frac{E_a}{2.303 R T}...(i) For 1st 1^{\text{st }} order reaction, k=0.693t1/2=0.693600s=1.1×10−3s−1k=\frac{0.693}{t_{1/2}}=\frac{0.693}{600 s}=1.1 \times 10^{-3} \mathrm{ s}^{-1} Substitute the value of kk in Eq. (i) log⁡(1.1×10−3)=log⁡(4×1013)−98.6×1032.303×8.314×T\log \left(1.1 \times 10^{-3}\right)=\log \left(4 \times 10^{13}\right)-\frac{98.6 \times 10^3}{2.303 \times 8.314 \times T} Solving for TT, T=311.15KT=311.15 \mathrm{ K}
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