Calorimetry: Heat of reaction, heat of mixing, heat of anything.

The change in enthalpy of reaction ΔHrxn is one of the two critical quantities — alongside TΔS — that together determine reaction spontaneity through the Gibbs energy framework established above. It is also one of the most directly measurable quantities in all of thermodynamics.

ΔH_rxn is measured in a reaction calorimeter operating at constant pressure and temperature — typically 1 atm and 25°C for standard conditions. The reaction proceeds inside the calorimeter and the heating or cooling required to maintain constant temperature is measured. That quantity is ΔHrxn. Negative values correspond to an exothermic reaction — the system releases energy and the calorimeter must remove it to hold temperature constant. Positive values correspond to an endothermic reaction — the system absorbs energy and the calorimeter must supply it.

It is worth noting the distinction between this constant-pressure calorimeter and the bomb calorimeter, which operates at constant volume. The constant-pressure calorimeter measures ΔH — the enthalpy change. The bomb calorimeter measures ΔU — the change in internal energy. The two differ by the PV work term, as established in the enthalpy section above. Both are valid and useful; the choice depends on the conditions of interest.

Now consider what physically happens during a reaction to cause a heat effect — a non-zero ΔHrxn. The events that lead to a heat effect involve the rearrangement of both atoms and electrons, specifically:

• Orbital electron rearrangement — the dominant contribution in most chemical reactions. When electrons move from higher-energy orbitals in the reactants to lower-energy orbitals in the products, potential energy is released and converted to kinetic energy of the surrounding atoms. This is the atomic-level source of exothermic heat release. The reverse — electrons moving to higher-energy orbitals — absorbs energy and produces endothermic cooling.
• Change in intramolecular potential energies — bond lengths and angles change between reactants and products, altering the vibrational and rotational energy stored within molecules.
• Change in intermolecular potential energies — the attractive and repulsive interactions between molecules change as reactants become products, particularly relevant when phase change accompanies reaction or when solution-phase reactions involve significant changes in molecular interactions.
• Change in volume at constant pressure — the PV work term that distinguishes ΔH from ΔU. If the reaction produces a net change in volume against a constant external pressure, that mechanical work is included in the enthalpy change.

All of these events result in a change in the internal energy of the system — both kinetic and potential contributions — which at constant pressure manifests as the measurable heat effect quantified by ΔHrxn.

The challenge now in front of us is connecting these microscopic events to the macroscopic composite properties built upon ΔHrxn — particularly the change in Gibbs energy, which governs reaction spontaneity, maximum work, and equilibrium. Can these connections be made exact? Can they be parsed into one-to-one micro-to-macro connections that illuminate the physical meaning of TΔS? These questions will be addressed in later chapters.

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