Question

For a certain reaction, \(E_{\mathrm{a}}\) is \(135 \mathrm{~kJ}\) and \(\Delta H=45 \mathrm{~kJ} .\) In the presence of a catalyst, the activation energy is \(39 \%\) of that for the uncatalyzed reaction. Draw a diagram similar to Figure 11.14 but instead of showing two activated complexes (two humps) show only one activated complex (i.e., only one hump) for the reaction. What is the activation energy of the uncatalyzed reverse reaction?

Short answer

Question: Calculate the activation energy of the uncatalyzed reverse reaction, given that the activation energy of the uncatalyzed forward reaction is 135 kJ and the change in enthalpy is -45 kJ. Answer: The activation energy of the uncatalyzed reverse reaction is 90 kJ.

Step-by-step solution

Calculate the Activation Energy of the Catalyzed Reaction

Using the provided percentage, calculate the activation energy of the catalyzed reaction. For the catalyzed reaction, the activation energy is 39% of the uncatalyzed reaction. So, \(E_\text{a (catalyzed)} = 0.39 * E_\text{a (uncatalyzed)}\) Given, the uncatalyzed reaction's activation energy, \(E_\text{a (uncatalyzed)} = 135\) kJ, \(E_\text{a (catalyzed)} = 0.39 * 135 \mathrm{kJ} = 52.65 \mathrm{kJ}\)

Draw the Energy Diagram with One Hump

Draw the energy diagram using the given activation energies for the uncatalyzed and catalyzed reactions. 1. Draw a horizontal line representing the reaction coordinate (x-axis), and a vertical line representing the energy (y-axis). 2. On the y-axis, mark the energy levels for the reactants, activated complex, and products. 3. The reactants' energy level is marked at the y-axis origin and the products' energy level is marked at an energy of 45 kJ below the reactants (as \(\Delta H = -45\) kJ). 4. Above the reactants, draw two levels - one for the uncatalyzed activation energy (135 kJ) and another for the catalyzed activation energy (52.65 kJ). 5. Draw the energy profile showing a single activated complex (one hump) for the catalyzed reaction and another for the uncatalyzed reaction.

Calculate the Activation Energy of the Uncatalyzed Reverse Reaction

Considering that the change in enthalpy, \(\Delta H\), is constant for backward and forward reactions, we can write the following relation: \(E_\text{a (reverse)} = E_\text{a (forward)} - \Delta H\) Given that \(E_\text{a (forward)} = 135 \mathrm{kJ}\) and \(\Delta H = 45 \mathrm{kJ}\), we can calculate the activation energy for the uncatalyzed reverse reaction: \(E_\text{a (reverse)} = 135 \mathrm{kJ} - 45 \mathrm{kJ} = 90 \mathrm{kJ}\) The activation energy of the uncatalyzed reverse reaction is 90 kJ.