Aspartame has the chemical formula C14H18N2O5 and undergoes combustion by the following unbalanced reaction: C14H18N2O5 + O2 → CO2 + H2O + N2. Using bond dissociation energies, calculate the amount of energy released upon combustion of 35 pounds of aspartame: C14H18N2O5 + 1.5O2 → 4CO2 + 5H2O + N2. C-C = 347 kJ/mol, C-H = 413 kJ/mol, C-N = 305 kJ/mol, N-N = 163 kJ/mol, C=O = 799 kJ/mol, O-H = 463 kJ/mol, N-H = 391 kJ/mol. Given that aspartame is often used as a substitute for sucrose (C12H22O11), determine the heat of combustion for 35 pounds of sucrose. Compare the two values and decide which one has the higher caloric content (1 kcal = 4.184 kJ).
The Correct Answer and Explanation is:
To compare the energy released by the combustion of 35 pounds of aspartame versus 35 pounds of sucrose, first calculate the combustion energy using bond dissociation energies (BDEs).
Step 1: Molar Masses
- Aspartame (C₁₄H₁₈N₂O₅)
= 14(12.01) + 18(1.008) + 2(14.01) + 5(16.00) = 294.30 g/mol - Sucrose (C₁₂H₂₂O₁₁)
= 12(12.01) + 22(1.008) + 11(16.00) = 342.30 g/mol
Step 2: Mass in grams
- 35 pounds = 35 × 453.592 = 15,875.72 grams
Step 3: Moles of each substance
- Aspartame: 15,875.72 / 294.30 ≈ 53.94 mol
- Sucrose: 15,875.72 / 342.30 ≈ 46.38 mol
Step 4: Energy per mole via bond energies (approximate estimate)
Bonds broken (in reactants, per mole of Aspartame):
Let’s estimate approximately:
- 14 C–H: 14 × 413 = 5782
- 6 C–C: 6 × 347 = 2082
- 4 C–N: 4 × 305 = 1220
- 4 N–H: 4 × 391 = 1564
- 5 C=O: 5 × 799 = 3995
- 5 O–H: 5 × 463 = 2315
- Total bonds broken (energy input) ≈ 16,958 kJ/mol
Bonds formed (products):
- 14 CO₂ (C=O): 28 C=O × 799 = 22,372
- 9 H₂O: 18 O–H × 463 = 8,334
- 1 N₂ (N≡N): 1 × 946 = 946
- Total bonds formed (energy released) ≈ 31,652 kJ/mol
Net energy released per mole:
31,652 − 16,958 = 14,694 kJ/mol
Step 5: Total energy for 53.94 mol Aspartame
= 53.94 × 14,694 ≈ 792,492 kJ
= 792,492 ÷ 4.184 ≈ 189,414 kcal
Step 6: Heat of combustion for sucrose (known)
Standard enthalpy of combustion for sucrose ≈ −5645 kJ/mol
- Total energy = 46.38 × 5645 ≈ 261,773 kJ
- In kcal = 261,773 ÷ 4.184 ≈ 62,545 kcal
Conclusion:
- Aspartame (35 lb): ~189,414 kcal
- Sucrose (35 lb): ~62,545 kcal
Aspartame releases significantly more energy per 35 pounds than sucrose, showing a higher caloric content by mass.
