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Chapter 20: Problem 101

Use bond energies (see Table 8.4) to show that the preferred products for the decomposition of \(\mathrm{N}_{2} \mathrm{O}_{3}\) are \(\mathrm{NO}_{2}\) and \(\mathrm{NO}\) rather than \(\mathrm{O}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}\). (The \(\mathrm{N}-\mathrm{O}\) single bond energy is 201 \(\mathrm{kJ} / \mathrm{mol}\).) (Hint: Consider the reaction kinetics.)

Short Answer

Expert verified
The preferred products for the decomposition of N₂O₃ are NO₂ and NO rather than O₂ and N₂O. This is shown by comparing the net energy changes for each reaction. For the first reaction, N₂O₃ → NO₂ + NO, the net energy change is 406 kJ/mol. For the second reaction, N₂O₃ → O₂ + N₂O, the net energy change is 635 kJ/mol. Since the first reaction has a lower net energy change, it is the preferred pathway due to the release of more energy.

Step by step solution

01

1. Write down the decomposition reactions

We have two possible reactions for the decomposition of N₂O₃: Reaction 1: N₂O₃ → NO₂ + NO Reaction 2: N₂O₃ → O₂ + N₂O
02

2. Calculate the required bond energies to break the molecules

We will use Table 8.4 to find the bond energies of the involved molecules. For N₂O₃, there are 2 N-O single bonds and 1 N=O double bond. The N-O single bond energy is given as 201 kJ/mol, and from Table 8.4, the N=O double bond energy is 607 kJ/mol. Therefore, the total energy required to break the N₂O₃ molecule will be: Energy (N₂O₃) = 2 × 201 kJ/mol + 1 × 607 kJ/mol = 1009 kJ/mol
03

3. Calculate the bond energies released in the formation of products

For Reaction 1, we form 1 NO₂ molecule and 1 NO molecule. The bond energies released will be the sum of the N-O single bond and the N=O double bond in both molecules: Energy (NO₂ + NO) = 1 × 201 kJ/mol + 2 × 607 kJ/mol = 1415 kJ/mol For Reaction 2, we form 1 O₂ molecule and 1 N₂O molecule. From Table 8.4, the O=O double bond energy is 498 kJ/mol. For N₂O, there is 1 N≡N triple bond (945 kJ/mol according to Table 8.4) and 1 N-O single bond, so: Energy (O₂ + N₂O) = 1 × 498 kJ/mol + 1 × 945 kJ/mol + 1 × 201 kJ/mol = 1644 kJ/mol
04

4. Compare the net energy changes

To find the net energy change for each reaction, we need to subtract the energy required to break the molecules from the energy released in the formation of products: Net energy (Reaction 1) = 1415 kJ/mol - 1009 kJ/mol = 406 kJ/mol Net energy (Reaction 2) = 1644 kJ/mol - 1009 kJ/mol = 635 kJ/mol
05

5. Determine the preferred decomposition reaction

Since Reaction 1 has the lower net energy change (406 kJ/mol) compared to Reaction 2 (635 kJ/mol), it is the preferred reaction because it releases more energy: N₂O₃ → NO₂ + NO Therefore, we have shown that the preferred products for the decomposition of N₂O₃ are NO₂ and NO rather than O₂ and N₂O, based on the bond energies.

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