A slightly bruised apple will rot extensively in about 2.5 days at room temperature (25.0°C). If it is kept in the refrigerator at 0.5°C, the same extent of rotting takes about 17 days. What is the activation energy for the rotting reaction?

Activation energy for the rotting reaction is 4.805 x 10⁻⁶ kJ/mol

Explanation:

Use the Arrhenius equation applied for two temperatures:

Ea = R· ln(k2/k1) · (1/T1 – 1/T2)

Where

R= 8.314x10-3kJ/(mol.K)

k2/k1 = 2.5/17 = 0.147    ∴    ln(k2/k1) = - 1.92

(1/T1 – 1/T2) = 1/298K – 1/273.5K = - 0.000301 K-1

Ea = 8.314x10⁻³ x (- 1.92) x (- 0.000301 K-1)

      = 4.805 x 10⁻⁶ kJ/mol