Bottled straight-chain alkanes can be used as fuels, including heptane and octane . heptane and octane have a ??°comb (kJ/mol) -4871.0 and -5430.0 respectively and liquid Denisty (g/mL) 0.684 ,0.703 respectively.By how much are the fuel values of heptane and octane difference? Give the magnitude of the difference (the absolute value).
Answer
🔥 Comparing Fuel Values of Heptane and Octane
🔍 Given Data
| Property | Heptane | Octane |
|---|---|---|
| ΔHcomb (kJ/mol) | −4871.0 | −5430.0 |
| Density (g/mL) | 0.684 | 0.703 |
| Molar Mass (g/mol) | 100.20 | 114.23 |
📐 Step 1: Calculate Fuel Value (kJ/mL)
Fuel value per mL is the energy released per mL of liquid fuel. Formula:
Fuel Value = (ΔHcomb / Molar Mass) × Density
🔹 Heptane:
= (−4871.0 / 100.20) × 0.684
= (−48.63) × 0.684 ≈ −33.29 kJ/mL
= (−48.63) × 0.684 ≈ −33.29 kJ/mL
🔹 Octane:
= (−5430.0 / 114.23) × 0.703
= (−47.52) × 0.703 ≈ −33.42 kJ/mL
= (−47.52) × 0.703 ≈ −33.42 kJ/mL
🧮 Step 2: Find the Absolute Difference
|−33.42 − (−33.29)| = |−0.13| = 0.13 kJ/mL
✅ Final Answer
The magnitude of the difference in fuel value is 0.13 kJ/mL.
💡 Tip: Fuel value per volume is critical in assessing fuel efficiency in engines. Though heptane and octane differ in molar mass and enthalpy, their energy densities per mL are very similar.