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

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

What the calorimeter measures

ΔH_rxn is measured in a reaction calorimeter operating at constant pressure — typically 1 atm and 25°C for standard conditions. The reaction proceeds inside the calorimeter and the thermal energy exchanged with the surroundings to maintain constant temperature is measured or calculated from the temperature response of the calorimeter. That quantity is ΔH_rxn. Negative values correspond to an exothermic reaction — the system releases energy and the calorimeter removes it to hold temperature constant. Positive values correspond to an endothermic reaction — the system absorbs energy and the calorimeter supplies 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 Chapter 11. Both are valid and useful; the choice depends on the conditions of interest.

What physically causes a heat effect

Consider what actually happens during a reaction at the atomic level to cause a heat effect. The contributing events fall into two broad categories.

The first is the rearrangement of orbital electrons — 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. This electron rearrangement is the primary event; everything else follows from it.

The second category encompasses changes in the structural and configurational energy of the system as reactants become products:

• Bond lengths and angles change between reactants and products, altering the vibrational and rotational energy stored within molecules.
• The attractive and repulsive interactions between molecules change, particularly relevant when phase change accompanies reaction or when solution-phase reactions involve significant changes in molecular interactions.
• If the reaction produces a net change in volume against a constant external pressure, that mechanical PV work is included in the enthalpy change — the term that distinguishes ΔH from ΔU.

All of these events combine to change the internal energy of the system — both kinetic and potential contributions — which at constant pressure manifests as the measurable heat effect quantified by ΔH_rxn.

What the calorimeter cannot separate

Here is the critical limitation of the calorimeter: it measures the combined result of both categories above. It cannot separate the electron rearrangement contribution from the structural and configurational contribution. Both arrive together as a single heat measurement. The calorimeter was never designed to make this distinction — it predates any awareness that two distinct phenomena were even involved.

This matters because, as Gibbs showed and as Chapter 14 establishes, the maximum work obtainable from a reaction is not ΔH_rxn but ΔGrxn. The relationship between these quantities is:

ΔH_rxn = ΔG_rxn + TΔS_rxn

The calorimeter gives you ΔH_rxn — the sum. What ΔG_rxn and TΔS_rxn each physically represent at the atomic level, and how they relate to the two categories of phenomena described above, is a question that deserves careful treatment. The physical meaning of TΔS_rxn in particular — what it represents, what causes it, and why it cannot be extracted from a calorimeter measurement alone — is the subject of Chapter 15. As you will see there, the electrochemical cell played a pivotal historical role in separating what the calorimeter could not.

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