The first-order rearrangement of CH3NC is measured to have a rate constant of 3.61 x 10-15 s-1 at 298 K and a rate constant of 8.66 × 10-7 s-1 at 425 K. Determine the activation energy for this reaction. The first-order rearrangement of CH3NC is measured to have a rate constant of 3.61 x 10-15 s-1 at 298 K and a rate constant of 8.66 × 10-7 s-1 at 425 K. Determine the activation energy for this reaction. 127 kJ/mol 338 kJ/mol 240. kJ/mol 160. kJ/mol 417 kJ/mol

The correct answer is 160.37 KJ/mol.

Explanation:

To find the activation energy in the given case, there is a need to use the Arrhenius equation, which is,  

k = Ae^-Ea/RT

k1 = Ae^-Ea/RT1 and k2 = Ae^-Ea/RT2

k2/k1 = e^-Ea/R (1/T2-1/T1)

ln(k2/k1) = Ea/R (1/T1-1/T2)

The values of rate constant k1 and k2 are 3.61 * 10^-15 s^-1 and 8.66 * 10^-7 s^-1.  

The temperatures T1 and T2 are 298 K and 425 K respectively.  

Now by filling the values we get:  

ln (8.66*10^-7/3.61*10^-15) = Ea/R (1/298-1/425)

19.29 = Ea/R * 0.001

Ea = 160.37 KJ/mol

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