Chemical Energetics I – Rapid Review

Thermochemistry: study of heat changes accompanying chemical/physical processes.
System: part of universe examined; surroundings: everything else.
Heat flows from higher $T$ to lower $T$ until equilibrium.
Enthalpy $H$ : energy content at constant pressure (KE + PE); only changes $\Delta H$ measurable.
Sign convention: $\Delta H<0$ exothermic, $\Delta H>0$ endothermic.
Standard conditions: $P=1\,\text{bar},\;T=298\,\text{K},\;[\;]=1\,\text{mol dm}^{-3}$ ; denote by $^{\circ}$ .

$\Delta H_{r}^{\circ}$ : reaction (stoichiometric amounts).
$\Delta H_{f}^{\circ}$ : formation (1 mol compound from elements, standard states).
$\Delta H_{c}^{\circ}$ : combustion (complete burn of 1 mol substance).
$\Delta H{neut}^{\circ}$ : neutralisation (forming 1 mol $\text{H}2\text{O}$ ).
$\Delta H_{at}^{\circ}$ : atomisation (gaseous atoms from element/compound).
Bond energy $\text{BE}$ : average energy to break 1 mol covalent bonds (gaseous).
Ionic terms:
• Ionisation energy $\text{IE}$ (endothermic).
• Electron affinity $\text{EA}$ (1st usually exo, 2nd endo).
• Lattice energy $\text{LE}$ (gaseous ions $\rightarrow$ solid; exothermic).
• $\Delta H{hyd}^{\circ}$ : hydration of gaseous ion (exo). • $\Delta H{sol}^{\circ}$ : solution of ionic solid.

Calorimetry uses $Q = mc\Delta T$ (or $Q=C\Delta T$ ).
$\Delta H = -\dfrac{Q}{n}$ for exothermic, $+\dfrac{Q}{n}$ for endothermic; $n$ = moles as defined.
Assumptions: negligible heat losses, density $\approx$ $1\,\text{g cm}^{-3}$ , $c\approx4.18\,\text{J g}^{-1}\text{K}^{-1}$ .
Temperature correction via extrapolated $T{max}/T{min}$ to account for losses.
Combustion calorimetry: heat water; adjust for efficiency.

For gaseous reactions: $\Delta H^{\circ}=\sum \text{BE(bonds broken)}-\sum \text{BE(bonds formed)}$ .
For diatomic gas $X2$ : $\text{BE}(X-X)=2\,\Delta H{at}^{\circ}(X2)$ (only if $X2$ is gaseous at 298 K).

Lattice energy magnitude $\propto \dfrac{q^{+}q^{-}}{r^{+}+r^{-}}$ .
• Higher charge, smaller radii $\Rightarrow$ more exothermic $\text{LE}$ .
Hydration energy $\left|\Delta H_{hyd}^{\circ}\right| \uparrow$ with higher charge density.
$\Delta H{sol}^{\circ}=\Delta H{hyd}^{\circ}(\text{cation})+\Delta H{hyd}^{\circ}(\text{anion})-\text{LE}$ . • Negative $\Delta H{sol}^{\circ}$ favours solubility.

Enthalpy change independent of path: sum round any cycle $=0$ .
Useful identities:
• $\Delta H{r}^{\circ}=\sum \Delta H{f}^{\circ}(\text{products})-\sum \Delta H{f}^{\circ}(\text{reactants})$ • $\Delta H{r}^{\circ}=\sum \Delta H{c}^{\circ}(\text{reactants})-\sum \Delta H{c}^{\circ}(\text{products})$
• $\Delta H{sol}^{\circ}=\big[\Delta H{hyd}^{\circ}(\text{ions})\big]-\text{LE}$
Apply via energy cycles, energy-level diagrams, algebraic manipulation.

Atomise elements: $\Delta H{at}^{\circ}(M)+\tfrac12\Delta H{at}^{\circ}(X_2)$ .
Ionise metal: $\text{IEs}$ .
Add electrons to non-metal: $\text{EAs}$ .
Lattice formation: $\text{LE}$ .
Overall: $\Delta H{f}^{\circ}=\sum \Delta H{at}^{\circ}+\sum \text{IE}+\sum \text{EA}+\text{LE}$ .

Heat: $Q=mc\Delta T$ .
Reaction enthalpy (gaseous, bonds): $\Delta H=\Sigma BE{break}-\Sigma BE{form}$ .
Solution: $\Delta H{sol}^{\circ}=\Delta H{hyd}^{\circ}(+) + \Delta H_{hyd}^{\circ}(-) - \text{LE}$ .
Lattice trends: more exothermic with $\uparrow q$ , $\downarrow r$ .

Negative $\Delta H{f}^{\circ}$ or more exothermic $\text{LE}$ / $\Delta H{hyd}$ $\Rightarrow$ higher thermodynamic stability.
Less negative or positive $\Delta H_{f}^{\circ}$ implies relative instability toward elemental decomposition.