We’re being asked to **determine the activation energy (E _{a})** of the processes responsible when food rots. We’re given the ratio of rates at two different temperatures.

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 30 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. not enough information is given

b. -124000 kJ/mol

c. 124000 kJ/mol

d. -124 kJ/mol

e. 124 kJ/mol

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