AP® Chemistry · Unit 6 · Topic 6.9
Enthalpy Cycles and Diagrams
An enthalpy cycle draws two different paths between the same starting and ending substances on an energy diagram, so the total enthalpy change around the closed loop must equal zero and any unknown step can be solved for.
Enthalpy is a state function: it only depends on where you start and end, not on the road you took. That means if you draw a reaction going straight from reactants to products, and also draw a longer detour through intermediate steps that reaches the same products, both paths must add up to the same total enthalpy change. Put those two paths together and you get a closed loop, and a closed loop that returns to its starting point has to sum to zero. That one fact is Hess's law in picture form, and it is what lets you solve for a step you cannot measure directly.
A Born-Haber cycle applies this to forming an ionic solid, like NaCl, straight from its elements. Instead of one direct step, it breaks the formation into pieces you can measure: subliming solid sodium into gas, ionizing that gas atom, breaking the Cl-Cl bond, attaching the electron to chlorine, and finally letting the gaseous ions collapse into a crystal lattice. Each arrow is a separate enthalpy change, and the direct formation arrow closes the loop. Since the loop sums to zero, the formation enthalpy equals the sum of every other step plus the lattice energy, so lattice energy is whatever makes the books balance.
This connects directly to Hess's law from earlier in the unit: adding reaction steps to get a target reaction, and adding their enthalpies to get its enthalpy. Enthalpy cycles are just that idea drawn as a shape instead of stacked equations, which makes it easier to see which step is missing and solve for it algebraically.
Key terms
- State function
- A property, like enthalpy, that depends only on initial and final states, not the path taken.
- Hess's law
- The enthalpy of a reaction equals the sum of the enthalpies of any set of steps that add up to it.
- Born-Haber cycle
- An enthalpy cycle that breaks the formation of an ionic solid into sublimation, ionization, bond breaking, electron affinity, and lattice energy steps.
- Lattice energy
- The enthalpy change when gaseous ions combine to form one mole of a solid ionic crystal.
- Closed loop
- A cycle on an enthalpy diagram that starts and ends at the same substance, so its arrows must sum to zero.
Watch it explained
- How it worksDraw an enthalpy cycle that gets from elements to products by two different paths.
- How it worksHow does a Born-Haber style cycle break the formation of NaCl into separate energy steps?
- Worked exampleFind the lattice energy of NaCl from the steps of its formation cycle.
- Common mistakeWhy isn't the sum of the arrows around a closed enthalpy loop anything other than zero?
Check yourself
End of topic.