Enthalpy and Thermochemistry

Heat at Constant Pressure

Most reactions run in open vessels, where pressure is fixed and volume is free to change. Enthalpy is defined to make that case simple:

$$H = U + PV$$

so that at constant pressure $\Delta H = q_p$, the enthalpy change is the heat exchanged. A reaction with $\Delta H < 0$ is exothermic and warms its surroundings; $\Delta H > 0$ is endothermic and cools them.

Enthalpy is a state function, which gives Hess's law: the enthalpy change of a reaction is the sum of the enthalpy changes of any sequence of steps that connects the same reactants to the same products. Two rules follow, reversing a reaction flips the sign of $\Delta H$, and multiplying a reaction by $n$ multiplies $\Delta H$ by $n$.

The most useful version uses standard enthalpies of formation $\Delta H_f^\circ$, the enthalpy change forming one mole of a compound from its elements in their standard states:

$$\Delta H_{rxn}^\circ = \sum n \Delta H_f^\circ (\text{products}) - \sum n \Delta H_f^\circ (\text{reactants})$$

An element in its standard state has $\Delta H_f^\circ = 0$ by definition, that is a choice of reference point, not a measurement.

Calorimetry measures these quantities. A known mass absorbs the heat and its temperature rise gives $q = mc\Delta T$. A coffee-cup calorimeter runs at constant pressure and therefore measures $\Delta H$ directly; a bomb calorimeter runs at constant volume and measures $\Delta U$ instead.

Finally, reaction enthalpies drift with temperature. Kirchhoff's equation says the drift rate is the difference in heat capacities:

$$\Delta H(T_2) = \Delta H(T_1) + \Delta C_p (T_2 - T_1)$$

Common pitfall: forgetting to scale $\Delta H$ when you scale the equation. Enthalpy is extensive, burning two moles releases twice the heat of one. A Hess cycle that doubles a step must double its enthalpy too, and reversing a step must flip its sign.