Q24 / 100 · BITSAT 2024 (Memory Based Paper 3) · Chemistry

If for a first order reaction, the value of $A$ and $E_a$ are $4 \times 10^{13} \mathrm{~s}^{-1}$ and $98.6 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively, then at what temperature will its half life period be 10 minutes?

  • A
    330 K
  • B
    300 K
  • C
    330.95 K
  • Correct answer
    D
    311.15 K

Solution

According to Arrhenius equation, $\log k=\log A-\frac{E_a}{2.303 R T}...(i)$ For $1^{\text {st }}$ order reaction, $k=\frac{0.693}{t_{1 / 2}}=\frac{0.693}{600 s}=1.1 \times 10^{-3} \mathrm{~s}^{-1}$ Substitute the value of $k$ in Eq. (i) $log \left(1.1 \times 10^{-3}\right)=\log \left(4 \times 10^{13}\right)-\frac{98.6 \times 10^3}{2.303 \times 8.314 \times T}$ Solving for $T$, $T=311.15 \mathrm{~K}$

Hence, the correct answer is option: 'D'.

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