Topic 4.1: Energetics II

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4.1 (a) Enthalpy of atomisation, enthalpy of hydration and lattice enthalpy
The lattice enthalpy of an ionic crystal is the enthalpy change when 1 mole of the crystal is formed from widely separated gaseous ions.  It is the enthalpy change for the following process:     M+(g) + X-(g) --->M+X-(s) ; enthalpy of reaction = DHlatt[M+X-(s)]
The enthalpy of atomisation of an element is the enthalpy change when one mole of gaseous atoms of an element are formed from an element is its standard state.  E.g. It is the enthalpy change for the following process:
1/2Cl2(g) ----> Cl(g) ; enthalpy change = DHa[1/2Cl2(g)]
The enthalpy of hydration is the enthalpy change when 1 mol of aqueous ions is formed from gaseous ions.  It is the enthalpy change for the following process:
M+(g) + aq ---> M+(aq) ; enthalpy change = DHhyd[M+(g)]

4.1 (b) Born-Haber cycle
Lattice enthalpies cannot be determined directly and are found instead by cycles, called the Born-Haber cycles, which is similar to the cycles used for determining enthalpy changes using Hess's law.  e.g. The reaction between sodium and chlorine may be considered to take place in a series of steps and the enthalpy changes involved in these steps may be determined.  These steps may now be put into the Born-Haber cycle, with endothermic steps shown by upward arrows and exothermic reactions shown as downward arrows.  Building up the Born Haber Cycle.  (Needs Powerpoint.)

       ___________________ Na+(g) + Cl(g) _______________
       /\                                                                 | 1st electron affinity
       | enthalpy of atomisation of chlorine              | of chlorine
       |                                                                   |
       |____Na+(g) + 1/2Cl2(g)____                           \/  ____Na+(g) + Cl-(g)____
       /\                                                                 |
       |  1st ionisation enthalpy of sodium               | lattice enthalpy of sodium chloride
       |                                                                  |
       |____Na(g) + 1/2Cl2(g)____                         |
       /\                                                                 |
       | enthalpy of atomisation of sodium              |
       |                                                                  |
       |____Na(s) + 1/2Cl2(g)____                                |
       |                                                                  |
       | enthalpy of formation of sodium chloride |
       |                                                                  |
       \/_____________________ NaCl(s) ____ \/________________

4.1 (c) Experimental and theoretical lattice energies

compound Lattice enthalpy value based on theoretical ionic model Lattice enthalpy value based on experiment
sodium chloride -766.1 kJmol-1 -776.4 kJmol-1
silver chloride -768.6 kJmol-1 -916.3 kJmol-1
Good fit e.g. sodium chloride, indicates strongly ionic compound.
Poor fit e.g. silver chloride, indicates some covalent nature in compound.

4.1 (d) Factors influencing lattice enthalpy
The lattice enthalpy of an ionic compound is affected by the size and charge on the ions which make it up.  
A decrease in the size of any ion increases the lattice enthalpy. (more negative/exothermic)
This is because small ions can be close together and the smaller distance of separation the larger the attractive force between the ions.
An increase in charge also increases lattice enthalpy. (makes it more negative/exothermic)  This is because the force of attraction between ions increases as the charge on the ion increases.

4.1 (e) Explaining solubilities of hydroxides and sulphates of group 2
Before a compound dissolves, its lattice has to be broken down. A high lattice enthalpy tends to leave an unbroken lattice which will mean an insoluble compound.  The energy needed to break the lattice is taken from the hydration process. 
A high hydration enthalpy for an ion tends to give a soluble compound.  Hydration enthalpy increases as the size of an ion decreases and as the charge on an ion increases.  This is because both of these factors create a high charge density and cause the ion to attract more water molecules making hydration more exothermic.
As we go down group 2, the increase in cationic size decreases the hydration enthalpy, tending to make all compounds less soluble.  Also as we descend the group the same increasing cationic size reduces the lattice enthalpy, tending to make compounds more soluble.
The solubility of the sulphates decreases down the group because the large sulphate ion makes the lattice enthalpy changes less than hydration enthalpy.  The hydration enthalpy is therefore dominant.
The solubility of the hydroxides increases down the group because the small hydroxide ion makes the lattice enthalpy change more than hydration enthalpy.  The lattice energy is therefore dominant.