The isomerization of methyl isocyanide, CH₃NC  CH₃CN, follows first-order kinetics.The half-lives were found to be 161 min at 199°C and 12.5 min at 230°C. Calculate the activation energy for this reaction.

Question

Quizplus · Accepted Answer

We can use the Arrhenius equation to calculate the activation energy:

k = Aexp(-Ea/RT)

where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

Taking the natural logarithm of both sides and rearranging, we get:

ln(k) = ln(A) - Ea/RT

Plotting ln(k) vs. 1/T should give us a straight line with slope equal to -Ea/R. We can then use the half-lives given to find k at each temperature, and solve for the activation energy.

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

ln(2) = Ea/R (1/230 - 1/199)

Ea = -ln(2) * R / (1/230 - 1/199)

Plugging in the values for R and solving gives:

Ea = 163 kJ/mol

Therefore, the answer is (E).

The Isomerization of Methyl Isocyanide, CH3NC  CH3CN, Follows

The Isomerization of Methyl Isocyanide, CH₃NC  CH₃CN, Follows