We’re being asked to determine the activation energy (E_{a}) for the process responsible when food rots about 50 times more rapidly at 25 °C than when it is stored at 6 °C.

This means we need to use the ** two-point form of the Arrhenius Equation**:

$\overline{){\mathbf{ln}}{\mathbf{}}\frac{{\mathbf{k}}_{\mathbf{2}}}{{\mathbf{k}}_{\mathbf{1}}}{\mathbf{=}}{\mathbf{-}}\frac{{\mathbf{E}}_{\mathbf{a}}}{\mathbf{R}}\mathbf{[}\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{2}}}\mathbf{-}\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{1}}}\mathbf{]}}$

where **k _{1}** = rate constant at T

**k _{2}** = rate constant at T

**E _{a}** = activation energy (in J/mol)

**R** = gas constant (8.314 J/mol•K)

**T _{1} and T_{2}** = temperature (in K)

Food rots about 50 times more rapidly at 25 °C than when it is stored at 6 °C. Determine the overall activation energy for the processes responsible for its decomposition.

A. 30 kJ/mol

B. 142 kJ/mol

C. -30 kJ/mol

D. -142 kJ/mol

E. not enough information given

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