Question

The activation energy for the isomerization of cyclopropane to propene is 274 kJ/mol. By what factor does the rate of this reaction increase as the temperature rises from 257 to 280 degree C? The factor is the ratio of the rates. Since rate is directly proportional to rate constant, the factor is also ratio of rate constants Make sure your units are correct and cancel properly and use the correct expression: k= Ae^-E_a/RT A catalyst decreases the activation energy of a particular exothermic reaction by 38 kJ/mol, to 63 kJ/mol. Assuming that the mechanism has only one step, and that the products are 97 kJ lower in energy than the reactants, sketch approximate energy-level diagrams for the catalyzed and unanalyzed reactions. What is the activation energy for the unanalyzed reverse reaction? The problem is easy if you follow instructions and draw a sketch.

Answer 1

Answer 7.

Expression for rate constant of given reaction (Arrhenius equation) can be written as follows:

Where, k = Rate constant

A = Arrhenius factor

Ea = activation energy = 274 kJ/mol

R = Universal gas constant = 0.008314 kJ/(mol.K)

T = temperature in Kelvin

Thus, expression for rate constant at two temperatures can be written as follows:

Where, k1 is the rate constant at temperature T1 and k2 is the rate constant at temperature T2

T1 = 257^oC = (257 + 273.15) K = 530.15 K

T2= 280^oC = (280 + 273.15) K = 553.15 K

Thus, the factor by which rate of reaction increases i.e. ratio of K2/K1 can be written as follows:

$\frac{k_{2}}{k_{1}} = e^{(-Ea/RT_{2})+(Ea/RT_{1})}$

$\frac{k_{2}}{k_{1}} = e^{(-274/(0.008314)(553.15))+(274/(0.008314)(530.15))}$

$\frac{k_{2}}{k_{1}} = e^{(-59.58)+(62.16)}$

$\frac{k_{2}}{k_{1}} = e^{(2.58)}$

$\frac{k_{2}}{k_{1}} = 13.2$

Thus, the factor by which rate of reaction increases is 13.2

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Answer 8.

The approximate energy level diagram for catalyzed and uncatalyzed reaction can be shown as follows:

It can be seen from above diagram, the activation energy for uncatalyzed forward reaction is 101kJ/mol. The uncatalyzed reverse reaction will be endothermic reaction and its activation energy will be 198 kJ/mol as shown in above diagram.