# Energetics (II)

## 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

## 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