Question:
Raw milk sours in about 4 h at 27$^\circ$C, but in about 48 h in a refrigerator at 17$^\circ$C. What is the activation energy for souring of milk?
Raw milk sours in about 4 h at 27$^\circ$C, but in about 48 h in a refrigerator at 17$^\circ$C. What is the activation energy for souring of milk?
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Lower temperature → slower rate → higher time.
Updated On: Apr 23, 2026
- 78.3 kJ mol$^{-1}$
- 46.21 kJ mol$^{-1}$
- 23.5 kJ mol$^{-1}$
- 80.8 kJ mol$^{-1}$
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The Correct Option is A
Solution and Explanation
Concept:
Arrhenius equation:
\[
\ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)
\]
Step 1: Rate $\propto$ $\dfrac{1}{\text{time}}$.
\[ \frac{k_2}{k_1} = \frac{t_1}{t_2} = \frac{4}{48} = \frac{1}{12} \]
Step 2: Temperatures: \[ T_1 = 300\text{ K}, \quad T_2 = 290\text{ K} \]
Step 3: Substitute in Arrhenius equation: \[ \ln(1/12) = \frac{E_a}{8.314}\left(\frac{1}{300} - \frac{1}{290}\right) \]
Step 4: Activation energy: \[ E_a \approx 78.3\ \text{kJ mol}^{-1} \] Conclusion:
Activation energy = 78.3 kJ mol$^{-1}$
Step 1: Rate $\propto$ $\dfrac{1}{\text{time}}$.
\[ \frac{k_2}{k_1} = \frac{t_1}{t_2} = \frac{4}{48} = \frac{1}{12} \]
Step 2: Temperatures: \[ T_1 = 300\text{ K}, \quad T_2 = 290\text{ K} \]
Step 3: Substitute in Arrhenius equation: \[ \ln(1/12) = \frac{E_a}{8.314}\left(\frac{1}{300} - \frac{1}{290}\right) \]
Step 4: Activation energy: \[ E_a \approx 78.3\ \text{kJ mol}^{-1} \] Conclusion:
Activation energy = 78.3 kJ mol$^{-1}$
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