Draw energy diagrams analogous to Figure 1 for simple addition of \(\mathrm{H}^{+}\) to 1,3 -pentadiene and 1,4 -pentadiene so as to give the most stable carbonium ions possible. It turns out that the 1,3 -isomer is both the more reactive and the more energetically stable diene. Explain how this information can be used to deduce the relative stabilities of the carbonium ions formed from these dienes.

First, we need to draw the structures of 1,3-pentadiene and 1,4-pentadiene. 1,3-pentadiene: It has a carbon-carbon double bond between the first and second carbon atoms and another double bond between the third and fourth carbon atoms. 1,4-pentadiene: It has a carbon-carbon double bond between the first and second carbon atoms and another double bond between the fourth and fifth carbon atoms.

Now, we will add the \(\mathrm{H}^{+}\) in such a way that we form the most stable carbonium ions for both the dienes. 1,3-pentadiene forms a tertiary carbocation when the \(\mathrm{H}^{+}\) adds to the double bond between carbons 1 and 2. 1,4-pentadiene also forms a tertiary carbocation when the \(\mathrm{H}^{+}\) adds to the double bond between carbons 1 and 2.

In this step, we will draw energy diagrams for both reactions. The energy diagrams plot energy on the y-axis and reaction progress on the x-axis. For 1,3-pentadiene reaction: - The reactants have a certain energy level. - The reaction proceeds with the formation of the tertiary carbocation, and the energy level decreases. For 1,4-pentadiene reaction: - The reactants have a certain energy level. - The reaction proceeds with the formation of the tertiary carbocation, and the energy level decreases, but with a lower decrease compared to 1,3-pentadiene reaction.

Now, let's analyze the energy diagrams for stability and reactivity. It was given that the 1,3-isomer is both the more reactive and the more energetically stable diene. From energy diagrams, we can deduce the following: 1. Since the energy diagram of 1,3-pentadiene shows a greater decrease in energy level, it means that the carbonium ion formed from 1,3-pentadiene is more energetically stable compared to the carbonium ion formed from 1,4-pentadiene. 2. The greater decrease in energy level for 1,3-pentadiene also indicates that the reaction is more exothermic (releases more energy) than the reaction of 1,4-pentadiene, thus making it more reactive. Based on this analysis, we can conclude that the carbonium ions formed from 1,3-pentadiene are more stable and reactive compared to the carbonium ions formed from 1,4-pentadiene.