Draw a rough sketch of the energy profile for each of the following cases: a. \(\Delta E=+10 \mathrm{kJ} / \mathrm{mol}, E_{\mathrm{a}}=25 \mathrm{kJ} / \mathrm{mol}\) b. \(\Delta E=-10 \mathrm{kJ} / \mathrm{mol}, E_{\mathrm{a}}=50 \mathrm{kJ} / \mathrm{mol}\) c. \(\Delta E=-50 \mathrm{kJ} / \mathrm{mol}, E_{\mathrm{a}}=50 \mathrm{kJ} / \mathrm{mol}\)

For each case, draw the energy profile using a graph with the x-axis representing the progress of the reaction and the y-axis representing the energy. Identify the initial and final energy levels based on the given \(\Delta E\), and mark the transition state energy level by adding the activation energy, \(E_\text{a}\), to the initial energy level. Then, sketch curves connecting these points: a. Initial energy level below final energy level, transition state at \(25 \mathrm{kJ/mol}\) above the initial level. b. Initial energy level above final energy level, transition state at \(50 \mathrm{kJ/mol}\) above the initial level. c. Initial energy level above final energy level, transition state at \(50 \mathrm{kJ/mol}\) above the initial level.