Calorimeter Types

Bomb Calorimeter (constant volume): Used to measure $\Delta U$ for combustion reactions. The rigid steel bomb prevents volume change ($\Delta V = 0$, $w = 0$). Heat measured is $q_v = \Delta U$. To obtain $\Delta H$: apply correction $\Delta H = \Delta U + \Delta n_g RT$.

Apparatus reference:

Coffee-Cup Calorimeter (constant pressure): Operates at atmospheric pressure. Heat measured is $q_p = \Delta H$ directly. Used for solution-phase reactions (acid-base, dissolution).

Enthalpy Level Diagrams

For an exothermic reaction, the product energy level is lower than the reactant energy level. For an endothermic reaction, the product energy level is higher. The activation energy (kinetics) is separate from $\Delta H$ (thermodynamics).

Enthalpy diagram reference: Energy Profile Diagrams

Exothermic ($\Delta H$ < 0) Enthalpy H Reactants Products Ea $\Delta H$ < 0 Endothermic ($\Delta H$ > 0) Reactants Products Ea $\Delta H$ > 0

Hess's Law Cycle Diagram

The Born-Haber cycle for NaCl formation is a classic application of Hess's law to an ionic compound:

$\text{Na(s) + }\frac{1}{2}\text{Cl}_2\text{(g)} \rightarrow \text{NaCl(s)}$

Steps: Sublimation of Na → Ionization of Na → Dissociation of $Cl_{2}$ → Electron gain by Cl → Lattice formation. The net enthalpy is the same regardless of which path is taken (direct synthesis or via Born-Haber cycle).

Thermodynamic Spontaneity Diagram

For the four spontaneity cases, a $\Delta G$ vs. $T$ graph shows:

• Case 1 ($\Delta H < 0$, $\Delta S > 0$): line entirely below the x-axis → always spontaneous
• Case 2 ($\Delta H > 0$, $\Delta S < 0$): line entirely above → never spontaneous
• Cases 3 and 4: lines cross the x-axis at $T = \Delta H/\Delta S$ → spontaneous only one side

Reversible vs Irreversible Expansion

For P-V diagrams, reversible expansion follows a curve ($PV = nRT$) enclosing maximum area (maximum work). Irreversible expansion against constant $P_{ext}$ forms a rectangle of smaller area (less work).