Question

The isomerization of cyclopropane follows first order kinetics. the rate constant at 700 k is 6.20 × 10–4 min–1 , and the half-life at 760 k is 29.0 min. calculate the activation energy for this reaction.

a) 5.07 kj/mol
b) 60. kj/mol
c) 27.0 kj/mol
d) 270. kj/mol
e) 50.7 kj/mol

Answer 1

The activation energy for the isomerization of cyclopropane can be calculated using the Arrhenius equation and the given data. The activation energy for this reaction is approximately 27.0 kJ/mol. option d is correct.

Step-by-step explanation:

The isomerization of cyclopropane follows first order kinetics. In a first order reaction, the rate of the reaction depends on the concentration of only one reactant. The reaction rate can be determined using the equation: rate = k[Cyclopropane], where k is the rate constant and [Cyclopropane] is the concentration of cyclopropane.

To calculate the activation energy for the isomerization of cyclopropane, we can use the Arrhenius equation: k = A * e^(-Ea/RT). The rate constant (k) at a given temperature (T) can be determined using the half-life of the reaction. The activation energy (Ea) can then be calculated.

Using the given data: the rate constant at 700 K is 6.20 x 10^-4 min^-1 and the half-life at 760 K is 29.0 min, we can plug these values into the Arrhenius equation to solve for Ea. The activation energy for this reaction is approximately 27.0 kJ/mol.