Hess's law

AS Level Chemistry · Chemical energetics. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

Hess's law says that the enthalpy change of a reaction depends only on the starting substances and the final substances. It does not depend on the route taken between them.

This lets you find an enthalpy change that cannot be measured directly. You build an energy cycle: the direct route is one side, and an indirect route through a common set of substances is the other. The common substances are the elements if you have formation data, the combustion products if you have combustion data, or separate gaseous atoms if you have bond energies.

The enthalpy change is the same by both routes. When you travel against an arrow in the cycle, you change the sign of its value.

Rules to remember

Common mistake

Students use 'products − reactants' with combustion data. That order is for formation data; with combustion data it is reactants − products.

Worked example

Standard enthalpy changes of formation in kJ mol−1: CaCO3(s) −1207, CaO(s) −635, CO2(g) −394. What is ΔH for CaCO3(s) → CaO(s) + CO2(g)?

  1. Formation data, so ΔH = sum of ΔHf of products − sum of ΔHf of reactants.
  2. Products: (−635) + (−394) = −1029 kJ.
  3. ΔH = −1029 − (−1207) = −1029 + 1207 = +178 kJ mol−1.

Answer: ΔH = +178 kJ mol−1 (endothermic)

Practice questions

Try each one, then open the answer.

1. The enthalpy change of solution of anhydrous MgSO4 is −91 kJ mol−1 and that of MgSO4·7H2O is +16 kJ mol−1. What is ΔH for MgSO4(s) + 7H2O(l) → MgSO4·7H2O(s)?

  1. A
    +75 kJ mol−1
  2. B
    −75 kJ mol−1
  3. C
    +107 kJ mol−1
  4. D
    −107 kJ mol−1
Show answer

Answer: D. Both salts dissolve to give the same solution, so the direct route (anhydrous salt to solution, −91) equals hydration (ΔH) followed by dissolving the hydrate (+16). ΔH + 16 = −91, so ΔH = −107 kJ mol−1. Simply adding the two values gives the wrong −75.

2. Which statement is Hess's law?

  1. A
    the enthalpy change of a reaction depends only on the initial and final states, not on the route taken
  2. B
    the enthalpy change of a reaction is always negative
  3. C
    the total bond energy of the reactants equals the total bond energy of the products
  4. D
    the enthalpy change of a reaction equals its activation energy
Show answer

Answer: A. Hess's law follows from conservation of energy: whichever route is taken from reactants to products, the overall ΔH is the same. It lets us find enthalpy changes that cannot be measured directly.

3. Bond energies in kJ mol−1: C–H 413, Cl–Cl 242, C–Cl 346, H–Cl 431. What is ΔH for CH4(g) + Cl2(g) → CH3Cl(g) + HCl(g)?

  1. A
    +122 kJ mol−1
  2. B
    −122 kJ mol−1
  3. C
    −777 kJ mol−1
  4. D
    −535 kJ mol−1
Show answer

Answer: B. Bonds broken: one C–H and one Cl–Cl = 413 + 242 = 655 kJ. Bonds formed: one C–Cl and one H–Cl = 346 + 431 = 777 kJ. ΔH = 655 − 777 = −122 kJ mol−1.

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