For the reversible reaction \(\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D},\) the enthalpy change of the forward reaction is \(+21 \mathrm{kJ} / \mathrm{mol}\) The activation energy of the forward reaction is \(84 \mathrm{kJ} / \mathrm{mol}.\) (a) What is the activation energy of the reverse reaction? (b) In the manner of Figure 14-10, sketch the reaction profile of this reaction.

To calculate the activation energy for the reverse reaction, we use the relationship between the activation energies for the forward and reverse reactions and the enthalpy change. This relationship is defined by the equation: \( E_a^{reverse} = E_a^{forward} + \Delta H \), where \(\Delta H\) is the enthalpy change of the reaction. Using the given values for the forward activation energy, \(84 \mathrm{kJ/mol}\), and the enthalpy change, \(+21 \mathrm{kJ/mol}\), the activation energy for the reverse reaction can be calculated as: \( E_a^{reverse} = 84 \mathrm{kJ/mol} + 21 \mathrm{kJ/mol} = 105 \mathrm{kJ/mol}\).

The reaction profile is a diagram that shows the energy of the reactants and products and the activation energy for the forward and reverse reactions. On the y-axis is the energy, and on the x-axis is the reaction progress. The reactants \(A + B\) start at a certain energy level, and the products \(C + D\) end at a higher energy level due to the positive enthalpy change (\(+21 \mathrm{kJ/mol}\)). The peak of the forward reaction represents the activation energy of the forward reaction (\(84 \mathrm{kJ/mol}\)). The peak of the reverse reaction (from products to reactants) represents the activation energy of the reverse reaction (\(105 \mathrm{kJ/mol}\)). So, the forward reaction curve starts at the energy level of the reactants, goes up to the forward reaction activation energy, and then comes down to the energy level of the products. The reverse reaction curve starts at the energy level of the products, goes up to the reverse reaction activation energy, and then comes down to the energy level of the reactants.