Calculate the activation energy (ea in kj/mol for a reaction if the rate constant (k is 2.7 × 10-4 (m−1sec−1 at 600 k and 3.5 × 10−3 (m−1sec−1 at 650 k.

Below are the choices:

a. −166 kJ/mol 
b. 166 kJ/mol 
c. 1.64 kJ/mol 
d. 1.66 × 10^5 kJ/mol

To calculate the activation energy of a reaction, we use the Arrhenius equation.  You may want to look it up to see how and why it works.  In the problem you posted, there are two temperatures and two rate constants.  After some rearranging and substitution of the Arrhenius equation, we have Ea = R T1 T2/(T1-T2) ln(k1/k2) = 8.314 J/mol K (600 K)(650 K)/(600 K-650 K) ln(2.7×10^-4 M^−1sec^−1/3.5×10^−3 M−^1sec^−1) = 166145 J/mol = 166 kJ/mol => choice b

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