Q46 / 200 · Manipal (MET) 2014 · Chemistry

Raw milk sours in about 4 h at $27^{\circ} \mathrm{C}$, but in about 48 h in a refrigerator at $17^{\circ} \mathrm{C}$. What is the activation energy for souring of milk?

  • Correct answer
    A
    $78.3 \mathrm{~kJ} \mathrm{~mol}^{-1}$
  • B
    $46.21 \mathrm{~kJ} \mathrm{~mol}^{-1}$
  • C
    $23.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$
  • D
    $80.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} & K \propto \frac{1}{t} \\ & \log \frac{k_2}{k_1}=\log \frac{t_1}{t_2}=\frac{E_a}{R}\left(\frac{T_2-T_1}{T_1 \cdot T_2}\right) \\ & \log \frac{48}{4}=\frac{E_a}{8.314}\left(\frac{10}{300 \times 290}\right) \\ & E_a=78.0 \mathrm{~kJ} \mathrm{~mol}^{-1}\end{aligned}$

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

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