Question 7.1: Heat of Reaction from Bond Energies Estimate the ΔH (in kcal......
Heat of Reaction from Bond Energies
Estimate the ΔH (in kcal/mol) for the reaction of hydrogen and oxygen to form water:
2 H_2 + O_2 \xrightarrow[]{} 2 H_2O ΔH = ?
ANALYSIS The individual bond energies from Table 7.1 can be used to calculate the total bond energies of reactants and products. ΔH can then be calculated as
ΔH = ∑(Bond dissociation energies)_{reactants} – ∑(Bond dissociation energies)_{products}
BALLPARK ESTIMATE The average H — H bond energy is ~100 kcal/mol and the O \xlongequal[]{} O bond energy is ~120 kcal/mol. Thus, the total energy needed to break reactant bonds is ~ (200 + 120) = 320 kcal/mol. The O — H bonds are ~110 kcal/mol, so the total energy released when product bonds are formed is ~440 kcal/mol. Based on these estimates, ΔH ~ -120 kcal/mol.
TABLE 7.1 Average Bond Dissociation Energies
| Bond | Bond Dissociation
Energy (kcal/mol, kJ/mol) |
Bond | Bond Dissociation
Energy (kcal/mol, kJ/mol) |
Bond | Bond Dissociation
Energy (kcal/mol, kJ/mol) |
| C — H | 99,413 | N — H | 93,391 | C \xlongequal[]{} C | 147,614 |
| C — C | 83,347 | N — N | 38,160 | C\equivC | 201,839 |
| C — N | 73,305 | N — Cl | 48,200 | C\xlongequal[]{}O^* | 178,745 |
| C — O | 86,358 | N — O | 48,201 | O \xlongequal[]{} O | 119,498 |
| C — Cl | 81,339 | H — H | 103,432 | N \xlongequal[]{} O | 145,607 |
| Cl—Cl | 58,243 | O — H | 112,467 | C \equiv N | 213,891 |
| H — Cl | 102,427 | O — Cl | 49,203 | N \equiv N | 226,946 |
*The C=O bond dissociation energies in CO_2 are 191 kcal/mol (799 kJ/mol).
ΔH = ∑(Bond dissociation energies)_{reactants} – ∑(Bond dissociation energies)_{products}
= (2(H — H) + (O \xlongequal[]{} O)) – (4(O — H))
= (2(103 kcal/mol) + (119 kcal/mol)) – (4(112 kcal/mol)) = -123 kcal/mol
BALLPARK CHECK Our estimate was -120 kcal/mol, within 3% of the calculated answer.