Thermodynamics of Ionic Lattices

Recap of AS

At AS Level we defined the term standard enthalpy change as

the heat energy absorbed or evolved during a reaction under standard conditions (temperature of 298K, pressure of 100kPa) and with all substances in their standard states under these conditions (solid carbon, liquid water, gaseous ammonia etc.)

We looked at endothermic reactions, in which heat is absorbed and the standard enthalpy change is positive, and exothermic reactions, in which heat is evolved and the standard enthalpy change is negative.

We then applied this definition to various enthalpy changes:

standard enthalpy of reaction: the enthalpy change when a reaction takes place in equation proportions under standard conditions

standard enthalpy of formation: the enthalpy change when one mole of a compound is formed from its elements under standard conditions (note that, by definition, the enthalpy of formation of an element is zero)

standard enthalpy of combustion: the enthalpy change when one mole of a compound is burned completely in excess oxygen under standard conditions (note that this is always negative)

We then began to consider calculating enthalpy changes for reactions in which it was impossible to measure directly. For example, methane does not form from carbon and hydrogen readily under standard conditions. We used Hess's Law in order to overcome this obstacle. Hess's Law states that

the overall enthalpy change of a reaction is independent of the route by which it occurs, provided that the initial and final conditions are the same.

For example, consider the reaction

A(g) + 2B(g) --> 3C(g) + D(g)

Given the following enthalpies of formation:

A = +60 kJ/mol

B = -34 kJ/mol

C = -115 kJ/mol

D = +52 kJ/mol

We can calculate the enthalpy of reaction by using Hess's Law. In this case, drawing a cycle would lead us to the calculation

60 + 2*(-34) + x = 3*(-115) + 52

We can solve this to give x = -285 kJ/mol, showing this is a strongly exothermic reaction.

We will now apply these techniques to ionic lattices.

Some definitions

bond dissociation enthalpy: the enthalpy change when one mole of gaseous bonds of a given type are broken to give separated atoms under standard conditions (note that this is always positive - bond breaking is endothermic)

standard enthalpy of atomisation: the enthalpy change when one mole of gaseous atoms is formed from the element in its standard state under standard conditions (note that this is always positive)

first ionisation energy: the enthalpy change when one electron is removed from each of one mole of gaseous atoms to produce one mole of unipositive gaseous ions (note that this is always positive and is given by the equation)

X(g) --> X+(g) + e-

nth ionisation energy: the enthalpy change whe one electron is removed from each of one mole of gaseous ions of charge +(n-1) to produce one mole of gaseous ions with charge +n (note that this is also always positive)

first electron affinity: the enthalpy change…