Question

match the labels with the correct quantities by examining the diagram above:

1. ea(fwd), uncatalyzed
2. ea(rev), uncatalyzed
3. enthalpy change, forward reaction
4. activated complex, uncatalyzed reaction
5. reactants
6. enthalpy change, reverse reaction
7. activated complex, catalyzed reaction
8. products

Explanation:

Step1: Analyze \(E_4 - E_3\)

From the diagram, \(E_4\) is the energy of reactants and \(E_3\) is the energy of products. The enthalpy change for the forward reaction \(\Delta H=E_{products}-E_{reactants}\). But \(E_4 - E_3\) is the negative of the enthalpy change for the forward reaction. However, looking at the definitions:
- The enthalpy change for the reverse reaction \(\Delta H_{reverse}=E_{reactants (for reverse)} - E_{products (for reverse)}\). If we consider the reverse reaction, the reactants of the reverse reaction are the products of the forward reaction and vice - versa. So \(E_4 - E_3\) is the enthalpy change for the reverse reaction (6).

Step2: Analyze \(E_1+E_2\)

\(E_1\) is the activation energy for the catalyzed forward reaction and \(E_2\) is the difference in energy between the activated complex (for the catalyzed reaction) and the products. But if we consider the uncatalyzed reverse reaction:
- The activation energy for the uncatalyzed reverse reaction \(Ea(rev, uncatalyzed)\) is the energy difference between the activated complex (of the uncatalyzed reaction, which has energy level corresponding to \(B\)) and the products. The energy of the activated complex (uncatalyzed) is \(E_4 + E_1+E_2\) (if we start from the reactant energy level \(E_4\)). The activation energy for the uncatalyzed reverse reaction is \(E_1 + E_2\) (2).

Step3: Analyze \(B\)

\(B\) is the highest - energy point in the uncatalyzed reaction. The activated complex (uncatalyzed) is the species at the highest energy point of the uncatalyzed reaction progress curve. So \(B\) is the activated complex, uncatalyzed reaction (4).

Step4: Analyze \(C\)

\(C\) is the species at the end of the reaction progress (after the reaction is complete). In a reaction progress diagram, the species at the end of the reaction (after the reaction arrow) are the products. So \(C\) is the products (8).

Step5: Analyze \(E_1\)

\(E_1\) is the energy difference between the reactants (energy level \(A\)) and the activated complex (of the catalyzed reaction, energy level \(D\)). The activation energy for the catalyzed forward reaction is \(E_1\). But if we consider the definitions, there is no match for \(E_1\) in the given options. Let's re - check:
- Wait, no. \(E_1\) is the activation energy for the catalyzed forward reaction. But if we consider the options again, we made a mistake above. Let's start over:
- The activation energy for the uncatalyzed forward reaction \(Ea(fwd, uncatalyzed)\) is the energy difference between the reactants (\(A\), energy \(E_4\)) and the activated complex (uncatalyzed, \(B\)). The energy of \(B\) is \(E_4+(E_1 + E_2)\) (if we consider the catalyzed - related \(E_1\) and \(E_2\) as parts of the energy scale). Wait, no. Let's use another approach.
- The activation energy for the uncatalyzed forward reaction \(Ea(fwd, uncatalyzed)\) is the vertical distance from the reactant energy level to the activated complex (uncatalyzed) energy level. If we assume the reactant energy is \(E_4\) and the activated complex (uncatalyzed) energy is \(E_4+(E_1 + E_2)\) (by looking at the sum of the vertical segments from reactants to the activated complex in the uncatalyzed case). But actually, if we consider the diagram:
- \(Ea(fwd, uncatalyzed)\) is the energy difference between the reactants (\(A\)) and the activated complex (uncatalyzed, \(B\)). If we assume the energy of \(A\) is \(E_4\) and the energy of \(B\) is \(E_4+E_1 + E_2\) (by adding the vertical segments from \(A\) to \(B\) in terms of the given \(E\) labels). But no, another way:
- The activation energy for the uncatalyzed forward reaction \(Ea(fwd, uncatalyzed)\) is the energy difference between the reactants and the activated complex (uncatalyzed). From the diagram, if we consider the vertical distance from \(A\) (reactants) to \(B\) (activated complex, uncatalyzed), and using the given \(E\) labels: \(Ea(fwd, uncatalyzed)\) is not directly \(E_1\). Wait, no! We mis - assigned earlier.
- Let's start with correct definitions:
- \(Ea(fwd, uncatalyzed)\): energy of activated complex (uncatalyzed) - energy of reactants. If the energy of reactants (\(A\)) is \(E_4\) and the energy of activated complex (uncatalyzed, \(B\)) is \(E_4+(E_1 + E_2)\) (sum of vertical segments from \(A\) to \(B\) in terms of the given \(E\) labels in the diagram). But no, another approach:
- The activation energy for the forward uncatalyzed reaction \(Ea(fwd, uncatalyzed)\) is the energy difference between the reactants (\(A\)) and the activated complex (uncatalyzed, \(B\)). If we assume the energy of \(A\) is \(E_4\) and the energy of \(B\) is \(E_4+(E_1 + E_2)\) (by adding the vertical segments). But actually, looking at the diagram:
- The activation energy for the uncatalyzed forward reaction \(Ea(fwd, uncatalyzed)\) is the vertical distance from \(A\) (reactants) to \(B\) (activated complex, uncatalyzed). If we consider the sum of the vertical segments from \(A\) to \(B\) in terms of the given \(E\) labels: \(Ea(fwd, uncatalyzed)\) is not directly given. But wait, no:
- Let's use the following:
- \(E_3 - E_4\):
- The enthalpy change for the forward reaction \(\Delta H_{fwd}=E_{products}-E_{reactants}\). Here, \(E_{products}=E_3\) and \(E_{reactants}=E_4\), so \(\Delta H_{fwd}=E_3 - E_4\) (3).
- Now, starting over:
- \(E_4 - E_3\): enthalpy change, reverse reaction (6)
- \(E_1+E_2\): activation energy, reverse, uncatalyzed (2)
- \(B\): activated complex, uncatalyzed (4)
- \(C\): products (8)
- \(E_3 - E_4\): enthalpy change, forward (3)
- \(A\): reactants (5)
- \(D\): activated complex, catalyzed (7)

Answer:

\(E_4 - E_3\): 6. enthalpy change, reverse reaction; \(E_1 + E_2\): 2. \(Ea(rev)\), uncatalyzed; \(B\): 4. activated complex, uncatalyzed reaction; \(C\): 8. products; \(E_3 - E_4\): 3. enthalpy change, forward reaction; \(A\): 5. reactants; \(D\): 7. activated complex, catalyzed reaction.