Enthalpy of combustion of propan-1-ol: a spirit burner that gives 72 per cent
A student determines the enthalpy of combustion of propan-1-ol with a spirit burner. The burner is weighed before and after heating 200 g of water in a copper can: 186.42 g before, 185.17 g after. The water temperature rises from 22.0 °C to 58.5 °C. The student calculates a value for the enthalpy of combustion and finds it much smaller in magnitude than the Data Booklet value. The teacher notes soot on the base of the can and a draught in the laboratory, and asks the student to check the result against a value calculated from standard enthalpies of formation: propan-1-ol(l), -302 kJ mol-1; carbon dioxide(g), -394 kJ mol-1; water(l), -286 kJ mol-1. The student must also decide whether the measured value can be used to estimate a C-C bond enthalpy in propan-1-ol, and the teacher warns that there is more than one reason why it cannot.
1. Calculate the enthalpy of combustion from the measurements, calculate the value from the standard enthalpies of formation, and express the shortfall as a percentage.
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Heat gained by water: q = mc(delta T) = 200 x 4.18 x 36.5 = 30 514 J = 30.5 kJ. Mass of propan-1-ol burned = 186.42 - 185.17 = 1.25 g; Mr(C3H8O) = 60.1, so n = 1.25 / 60.1 = 2.08 x 10^-2 mol.
Experimental enthalpy change = -(30.5 / 2.08 x 10^-2) = -1467 kJ mol-1, i.e. about -1470 kJ mol-1.
From formation enthalpies: C3H8O(l) + 4.5O2(g) -> 3CO2(g) + 4H2O(l) delta H = [3(-394) + 4(-286)] - (-302) = (-1182 - 1144) + 302 = -2024 kJ mol-1.
Shortfall = 2024 - 1467 = 557 kJ mol-1. Percentage of the theoretical value released = 1467 / 2024 x 100 = 72.5 per cent, so the measurement is about 27.5 per cent too small in magnitude. The discrepancy is far too large to be random error; it is systematic and one-directional.
2. Identify the assumptions behind the calculation and explain, for each, whether it makes the measured value more or less exothermic than the true value. Suggest two improvements and predict their effect.
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Assumptions and their effects (all make the measured value less exothermic, i.e. too small in magnitude):
- All heat released warms the water. In reality the copper can, the thermometer, the air and the draught all take heat. Heat loss means the water's temperature rise understates the heat released.
- Combustion is complete and goes to CO2 and H2O. The soot shows partial combustion to CO and carbon, which releases less energy per mole.
- The mass lost from the burner is all fuel that burned. Some propan-1-ol evaporates from the wick without burning, so a falsely large number of moles is used in the denominator, shrinking the calculated magnitude further.
- The reaction is under standard conditions and the water is weighed accurately; stirring and thermometer errors are small by comparison.
Improvements: fit a draught shield and lid and lag the can, and ensure complete combustion with a good air supply. Both reduce heat loss and incomplete combustion, so the water temperature rise increases and the calculated value becomes more negative, closer to -2024 kJ mol-1. Using a larger temperature rise and a lid also improves the precision of the reading.
3. Explain why the measured value, even after correction, cannot be used to obtain a reliable C-C bond enthalpy for propan-1-ol.
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Several independent problems arise.
First, the combustion is of the liquid, while bond enthalpies refer to gaseous species. A Hess cycle would need the enthalpy of vaporisation of propan-1-ol (about +47 kJ mol-1) and the enthalpy of atomisation of oxygen before any bonds can be counted, and each added term carries its own uncertainty.
Second, bond enthalpies are average values taken over many compounds. The C-C and C-H bonds in propan-1-ol are not identical to the statistical averages quoted for C-C and C-H, so no calculation can extract a specific bond enthalpy for that molecule; it can only return an average.
Third, the experimental value itself is unreliable: even the corrected figure is only valid if the heat loss is quantified, which the simple apparatus cannot do.
A better route is to use Hess's law with standard enthalpies of formation or combustion of a suitable set of compounds, accepting that the result is an average bond enthalpy, and to state that limitation explicitly.