Some enthalpy changes cannot be measured: you cannot make methane by mixing carbon and hydrogen in a calorimeter. Hess's law lets you go the long way round, through reactions you can measure, and still get the right answer.
Hess's law: the total enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions are the same. Build a cycle with the unknown change along the top and a route through measurable changes. With formation data the common point is the elements below: ΔHr = ΣΔHf(products) − ΣΔHf(reactants). With combustion data the common point is the combustion products below: ΔHr = ΣΔHc(reactants) − ΣΔHc(products). Multiply each value by its coefficient and reverse the sign of any arrow you travel against.
Build the methane cycle in the simulator. Try both routes from the elements to the combustion products and confirm they give the same total.
When you have enthalpies of formation, products minus reactants works because every substance can be made from the same elements.
| Substance | ΔHf / kJ mol−1 | Substance | ΔHc / kJ mol−1 |
|---|---|---|---|
| CO2(g) | −394 | C(s) | −394 |
| H2O(l) | −286 | H2(g) | −286 |
| CH4(g) | −75 | CH4(g) | −890 |
| O2(g) | 0 | C2H4(g) | −1411 |
| C2H6(g) | −1560 | ||
| C2H5OH(l) | −1367 |
Combustion of methane from formation data: ΔH = [−394 + 2(−286)] − [−75 + 0] = −966 + 75 = −891 kJ mol−1.
Hydrogenation of ethene from combustion data: ΔH = [−1411 + (−286)] − [−1560] = −137 kJ mol−1.
Four quick checks. Each correct answer earns XP and records this skill on your profile.
Hess's law states that the enthalpy change for a reaction:
Using formation data, ΔHr equals:
Using combustion data, ΔHr equals:
Why can ΔHf of methane not be measured directly?
Calcium carbonate only decomposes above about 800 °C, so its ΔH cannot be found in a cup calorimeter. React both CaCO3 and CaO with hydrochloric acid instead.
The two formula shortcuts have opposite orders: formation is products minus reactants, combustion is reactants minus products. If unsure, draw the cycle and follow the arrows, changing the sign whenever you travel against one. Never forget to multiply by the coefficients, and remember that elements have ΔHf = 0.
Unlocks once the four checks above are done. Worth more XP, written to AS Paper 1 and Paper 2 standard.
Use ΔHc: C(s) −394, H2(g) −286, C2H5OH(l) −1367 kJ mol−1 to find ΔHf of ethanol.
Use ΔHf: CO2 −394, H2O(l) −286, CH4 −75 kJ mol−1 to calculate ΔHc of methane.
Use ΔHc: C2H4 −1411, H2 −286, C2H6 −1560 kJ mol−1 to find ΔH for C2H4 + H2 → C2H6.
CaCO3 + 2HCl has ΔH1 = −17 kJ mol−1; CaO + 2HCl has ΔH2 = −195 kJ mol−1. What is ΔH for CaCO3 → CaO + CO2?
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