A slightly bruised apple will rot extensively in about 4 days at room temperature (20 degrees C). If it is kept in the refrigerator

A slightly bruised apple will rot extensively in about 4 days at room temperature (20 degrees C). If it is kept in the refrigerator at 0 degress C, the same extent of rotting takes about 16 days. What is the activation energy for the rotting reaction?

Answers

The answer to the question is

The activation energy for the rotting reaction = 46.15 kJ/mol

Explanation:

To solve the question we have the Arrhenius's equation given by

k = Ae^{frac{E_{a} }{RT} }

Where Ea = Activation energy

R = Universal gas constant

T = temperature in kelvin

A = Arrhenius constant

k  = Rate of reaction

k  = 4 days to rot at 20 °C = Ae^{frac{E_{a} }{R*293.15} }

at 0 °C k = 16 days = Ae^{frac{E_{a} }{R*273.15} } therefore

k₂₀/k₀ = Ae^{frac{E_{a} }{R*293.15} } ÷ Ae^{frac{E_{a} }{R*273.15} } or

4/16 = e^{frac{E_{a} }{R*293.15} }÷e^{frac{E_{a} }{R*273.15} } or e^{frac{E_{a} }{2270.9691} } = 4 ×e^{frac{E_{a} }{2437.2491} }

{frac{E_{a} }{2270.9691} } = ln 4 + {frac{E_{a} }{2437.2491} } or Ea = 46145.21 J/mol or 46.15 kJ/mol

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