## Thermodynamics

- Lattice energy
- Energy change when one mole of the solid is formed from its constituent gaseous ions that start infinitely apart (to avoid attraction).
- There are multiple definitions of lattice eergy, the one used by Edexcel means that the value is always exothermic (negative)
- \begin{align}ions_{(g)} \rightarrow Ionic\ lattice_{(s)}\end{align}

## Born-Haber cycle

The formation of an ionic compound

##### Hess’s law diagram here

##### Or else we can use this style:

## Factors affecting lattice enthalpy

Theoretical lattice enthalpy assumes that the substances are **completely ionic**, which is in almost every situation incorect.
As a result, high differences between experimental and theoretical values can occur. The relevent factors are:

- Extent of covalency
- Cation
- High charge – higher polarising ability
- Small radius – higher polarising ability
- Charge density

- Anion
- High charge – more easily polarised
- Large radius – more easily polarised

- Covalency is indicated by large differences between theoretical & experimental values

### Magnitude of lattice enthalpy

- Down a group LE decreases as cation gets bigger
- Down a group LE decreases as anion gets bigger
- Charge on an ion increases LE
**Repulsion becomes significant when difference in ion size increases, particularly with large anions (smaller value)**

### Strength of the force depends on:

- Magnitude of charge
- Sum of cation & anion radii
- Arrangement of ions in the lattice
- Relative size of ions
- Extent of covalency
- Charge density

## Enthalpy changes of hydration

- Hydrated ions form
- In sodium chloride hypothetically gaseous sodium & gaseous chloride ions become hydrated, by breaking up the lattice
- In the lattice they are all discreetly organised; but in solution they are in disarray
- Defined as the
**enthalpy change when one mole of gaseous ions forms a solution of aqueous ions in standard condition** - A higher charge density gives a higher enthalpy of hydration

- \begin{align}NaCl_{\left(s\right)}\ +\ \left(aq\right)\rightarrow Na^+{(aq)}\ +\ Cl^-_{(aq)}\end{align}
- The energy change here is the enthalpy change of solution
- It is the enthalpy change when one mole of a compound dissolves to form a “infinitely dilute” solution in water

\begin{align}NaCl_{s}\rightarrow Na_{g}^++Cl_{g}^-\end{align}
This is the *Lattice disassociation enthalpy*; the opposite of our known lattice enthalpy

## Spontaneity

A change will occur spontaneously if one state is more probable than the initial state.
The universe tends towards **minimum energy** & **maximum entropy**

In some cases, an endothermic strange reaction can occur: the final state has a lower enthalpy than initial & is more disordered.

### \begin{align}\Delta G\end{align}

The free energy change for a reaction under a set of conditions, $\Delta G^\ominus$ denotes the standard free-energy change at $pH 7.0$.

- Negative: spontaneous
- 0: crossover
- Positive: doesn’t happen

For a reaction to occur spontaneously, it needs a $\Delta S$ positive – although it doesn’t give any indication of rate. If negative, **does not occur at this temperature**.

\begin{align}\Delta S_{universe}=\Delta S_{surrondings}+\Delta S_{system}\end{align} If you substitute $\Delta S_{surrondings}=\frac{\Delta H}{T}$ you get: \begin{align}\Delta S_{universe}=\frac{\Delta H}{T}+\Delta S_{system}\end{align}

\begin{align}-T\Delta S_{universe}=\frac{T\Delta H}{T} - T\Delta S_{system}\end{align} We can then substitute $\Delta G=-T\Delta S_{universe}$ to give: \begin{align}\Delta G = \Delta H-T\Delta S_{system}\end{align} If $\Delta G$ is negative then the universe must be positive. The only variable in the $\Delta G$ calculation is temperature.

Enthalpy change | Entropy change | Gibbs energy | Spontaneous? |
---|---|---|---|

Positive | Positive | Depends on T | Yes, if temperature high enough |

Negative | Positive | Always negative | Always |

Negative | Negative | Depends on T | Yes, if temperature is low enough |

Positive | Negative | Always positive | Never |