Enthalpy and Hess's law

Isobaric processes and the essence of enthalpy

Most real chemical processes, including the vital activity of biological organisms, proceed at constant, most often atmospheric, pressure. Such processes are called isobaric ($p = const$).

Under these conditions, the volume of the system may change, causing expansion or compression work to be performed. Therefore, the heat of the process ($Q$) at constant pressure is equal to the change not simply in internal energy ($U$), but specifically in enthalpy ($\Delta H$). If a chemical reaction proceeds freely without performing useful work (for example, without conversion into electrical energy), the released heat will be maximal and numerically equal to the enthalpy change.

Measurements and thermochemical equations

Thermochemistry studies the thermal effects of reactions. In practice, they are measured in calorimeters. For example, in a bomb calorimeter, an exact weighed sample of a substance is burned in oxygen under pressure, and the released energy heats the surrounding water. The standard heat of combustion is calculated from the temperature change of the water.

In thermochemical equations, in addition to the mass balance, energy changes and the phase state must be recorded.

• The state of aggregation (g — gas, l — liquid, s(c) — solid crystalline) is critically important, as the energy level depends on it.
• Allotropic modifications are taken into account. Thus, the combustion of $1\text{ mol}$ of diamond releases more heat ($-395.4\text{ kJ}$) than the combustion of graphite ($-393.5\text{ kJ}$).
• A negative enthalpy value ($\Delta_r H^\circ < 0$) means that the reaction is exothermic and proceeds with the release of heat.

Heats of formation and combustion

Standardized values at $25^\circ C$ ($298.15\text{ K}$) and atmospheric pressure $101.3\text{ kPa}$ are used for calculations:

1. Standard heat of formation ($\Delta_f H^\circ$) — the thermal effect of the synthesis of $1\text{ mol}$ of a compound from simple substances.
2. Standard heat of combustion ($\Delta_c H^\circ$) — the thermal effect of the complete oxidation of $1\text{ mol}$ of a substance by oxygen to higher oxides. An exception is nitrogen, which is released as a simple gas ($N_2$).

Often processes overlap. The combustion of a simple substance is simultaneously the reaction of the formation of its oxide. For example, the heat of combustion of gaseous hydrogen numerically coincides with the heat of formation of liquid water ($-285.8\text{ kJ/mol}$).

Application of Hess's law

Hess's law is indispensable for calculating the thermal effects of reactions that do not proceed directly. A classic example is the synthesis of hydrogen peroxide ($H_2O_2$) from simple substances. This process always proceeds with the formation of a mixture of products, so the heat is calculated via a multi-step pathway: through the direct combustion of hydrogen into water and the subsequent subtraction of the heat of peroxide decomposition.

There are two main corollaries for rapid calculations:

• By heats of formation: the sum of the values of reactants is subtracted from the sum of the values of products.
• By heats of combustion: the sum of the values of products is subtracted from the sum of the values of reactants.

In all formulas, stoichiometric coefficients ($\nu$) from the reaction equation must be taken into account.

Class and exam questions

What else to study on this topic

• Structure and operating principle of a bomb calorimeter
• Mathematical proof of calculation formulas via thermochemical cycles
• Effect of allotropic modifications on enthalpy using graphite and diamond as an example
• Ratio of maximum released heat to useful work performed

Other topics in "Chapter 6. Patterns of Chemical Reactions"

Prepared by WhiteCoat Pro faculty in accordance with the medical school curriculum. For educational purposes only.