Topic 6 · page 2 of 15

Enthalpy level diagrams

An enthalpy level diagram is a picture of ΔH. Reactants and products sit on two levels, and an arrow from reactants to products carries the sign and the size of the change.

10 min read6.3

Read first: Enthalpy change and its sign

Reading a level diagram 6.3

Enthalpy goes on the vertical axis. Each substance, or group of substances, sits on a horizontal line at its enthalpy. The height of a line has no scale you can read off; only the difference between two lines matters, and that difference is ΔH.

Two enthalpy level diagrams side by side. Left, exothermic: methane plus oxygen on the upper level, carbon dioxide plus liquid water on the lower level, a downward arrow labelled delta c H equals minus 890 kilojoules per mole. Right, endothermic: nitrogen plus oxygen on the lower level, nitrogen monoxide on the upper level, an upward arrow labelled delta r H equals plus 181 kilojoules per mole.
Exothermic: products below reactants, arrow down. Endothermic: products above reactants, arrow up.

The arrow always starts at the reactants and ends at the products. That is why its direction gives the sign: down is negative, up is positive.

Interpreting a diagram means saying what it shows in words: "The products are 890 kJ mol⁻¹ lower in enthalpy than the reactants, so heat is given out to the surroundings and the reaction is exothermic."

Drawing one 6.3

MethodConstructing an enthalpy level diagram

  1. Label the vertical axis enthalpy (or H). Draw two horizontal lines.
  2. Put the reactants on one line and the products on the other. Write the formulae with state symbols, balanced as in the equation.
  3. Make the products lower if ΔH is negative, higher if ΔH is positive.
  4. Draw a vertical arrow from the reactants' line to the products' line.
  5. Label the arrow with ΔH, its sign and its units, for example ΔH = −890 kJ mol⁻¹.

Worked exampleA diagram for the decomposition of calcium carbonate

Draw a level diagram for CaCOX3(s)→CaO(s)+COX2(g)\ce{CaCO3(s) -> CaO(s) + CO2(g)}, ΔH = +178 kJ mol⁻¹.

  1. The sign is positive, so the reaction is endothermic and the products are on the upper line.
  2. Lower line: CaCO₃(s). Upper line: CaO(s) + CO₂(g).
  3. Arrow up from CaCO₃(s) to CaO(s) + CO₂(g), labelled ΔH = +178 kJ mol⁻¹.
  4. Axis labelled enthalpy, no scale needed.

Scaling and reversing 6.3

ΔH belongs to the equation as written. Change the equation and you change the arrow.

Two enthalpy level diagrams drawn to the same scale. Left: nitrogen plus three hydrogen on the upper level, two ammonia on the lower level, downward arrow minus 92 kilojoules per mole. Right: half nitrogen plus one and a half hydrogen on the upper level, one ammonia on the lower level, a downward arrow half as long labelled minus 46 kilojoules per mole.
Halve the equation and the arrow halves. Doubling the equation doubles it.

Both ideas are used again in Hess's Law, so check you can do them now.

Check yourself

  1. Describe an enthalpy level diagram for an exothermic reaction.
  2. For N₂(g) + O₂(g) → 2NO(g), ΔH = +181 kJ mol⁻¹. State ΔH for (a) ½N₂(g) + ½O₂(g) → NO(g); (b) 2NO(g) → N₂(g) + O₂(g); (c) 2N₂(g) + 2O₂(g) → 4NO(g).
  3. A student draws the arrow for an exothermic reaction pointing up from the lower level. Give two things wrong with the diagram.
  4. A diagram shows the reactants at a higher level than the products by 120 kJ mol⁻¹. State the type of reaction and the value of ΔH.
  5. Draw (describe) a level diagram for C(s)+OX2(g)→COX2(g)\ce{C(s) + O2(g) -> CO2(g)}, ΔH = −393.5 kJ mol⁻¹.

Answers cover these until you have tried the questions

  1. The vertical axis is enthalpy. The reactants are on an upper line and the products on a lower line, both labelled with formulae and state symbols. A downward arrow runs from the reactants' line to the products' line, labelled ΔH, negative, with units kJ mol⁻¹.
  2. (a) Halve the equation, halve ΔH: +90.5 kJ mol⁻¹. (b) Reverse the equation, change the sign: −181 kJ mol⁻¹. (c) Double the equation, double ΔH: +362 kJ mol⁻¹.
  3. (1) An upward arrow shows a positive ΔH, which is wrong for an exothermic reaction. (2) The arrow starts on the lower line, but the reactants of an exothermic reaction are on the upper line. It must start at the reactants and point down.
  4. Products lower than reactants, so the reaction is exothermic and ΔH = −120 kJ mol⁻¹.
  5. Axis labelled enthalpy. Upper line: C(s) + O₂(g). Lower line: CO₂(g). A downward arrow from the upper line to the lower line, labelled ΔH = −393.5 kJ mol⁻¹.