15.2 Born-Haber Cycle
Our calculations of enthalpies so far have involved covalent substances. Now we need to look at the enthalpy changes involved in the formation of giant ionic lattices. Lattice enthalpy is defined as either the:
'the enthalpy change that occurs when one mole of a solid ionic crystal is broken into its ions in the gaseous state, at standard temperature and pressure. Because all the bonds in the ionic lattice are broken, it is an endothermic process, ∆H is positive.' The IB uses this definition. M+ (g)
'the enthalpy change that occurs when one mole of a solid ionic crystal is formed form its ions in the gaseous state, at standard temperature and pressure. Because all the bonds in the ionic lattice are made, it is an exothermic process, ∆H is negative.'
[Remember that bond breaking is endothermic and bond making is exothermic] Standard lattice enthalpy values for ionic solids are found in the IB Chemistry data booklet.
Sodium Chloride ionic lattice
Born-Haber Cycles (named after Fritz Haber and Max Born) are simply energy / enthalpy cycles that show how ionic compounds are formed from their constituent elements. They are useful because they allow lattice enthalpies to be calculated theoretically using empirical data (observations and data collected from experiments).
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Definitions involved in calculation of lattice enthalpy of NaCl ∆Hf° standard enthalpy of formation of sodium chloride. The enthalpy change when one mole of a NaCl is formed from its elements under standard conditions. They are exothermic because new bonds are being made between the atoms of the elements sodium and chlorine. Na(s) + ½ Cl2 (g)
∆Hf° (NaCl) = - 411 kJmol-1
∆H1° standard enthalpy of atomization of chlorine. The energy required to change one mole of gaseous chlorine molecules into one mole of gaseous chlorine atoms. Endothermic because the bonds between the Cl-Cl atoms are being broken.
½ Cl2 (g) → Cl (g)
∆H1° (Cl2) = +121 kJmol-1
∆H2° standard enthalpy of first electron affinity of chlorine. The energy released when one mole of gaseous chlorine atoms gains one mole of electrons to form a -1 charged ion. Exothermic because the gaseous atom needs to release energy in order to slow down sufficiently to attract and an electron.
Cl (g) + e- → Cl- (g) ∆H2° (Cl) = -364 kJmol-1
NOTE: Non-metal elements with -2 ions have two electron affinities. For example oxygen and sulfur form -2 ions and have a first and second electron affinity. The second electron affinity is endothermic and is defined as the energy absorbed when one mole of electrons is gained by a -1 ion. Energy is absorbed because the negative ion is gaining a negative electron. Because both the ion and the electron are negatively charged they repel each other so energy needs to be absorbed in order for the process to take place.
O (g) + e- → O- (g) ∆H°1st electron affinity = - kJmol-1 O- (g) + e- → O2- (g) ∆H°2nd electron affinity = + kJmol-1
∆H1° standard enthalpy of atomization of sodium. The energy required to change one mole of solid sodium atoms into one mole of gaseous atoms. Endothermic, energy needs to be absorbed to change the state from a solid to a gas.
Na (s) → Na (g)
∆H1° (Na) = +108 kJmol-1
∆H4° first ionization energy of sodium. The enthalpy change when one mole of electrons is removed from a gaseous metal atom. Endothermic, energy needs to be absorbed to remove the electron.
Na (g) → Na+(g) + e-
∆H4° (Na) = +500 kJmol-1
The second ionisation energy is the energy absorbed when a second electron is released from a gaseous ion. Endothermic.
X+ (g) → X2+ + e-(g)
∆H4° = + kJmol-1
∆H5° lattice enthalpy of sodium chloride. The enthalpy change when one mole of ions in a solid ionic lattice is broken. Endothermic, because the ionic bonds between the sodium and chloride ions need to absorb energy in order to...
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