Thermochemistry studies the heat energy transfers accompanying chemical reactions and physical transformations. This field measures the heat content of a system, known as enthalpy (\(H\)). The change in enthalpy (\(\Delta H\)) measures the heat absorbed or released during a process carried out at constant pressure. Reactions that release heat are exothermic (negative \(\Delta H\)), while those that absorb heat are endothermic (positive \(\Delta H\)). While determining \(\Delta H\) is often straightforward, direct measurement is sometimes impractical or impossible. Hess’s Law, formally known as the Law of Constant Heat Summation, provides a powerful, indirect method for calculating this value by treating the overall reaction as a series of simpler, known steps.
The Law of Constant Heat Summation
The fundamental principle underlying Hess’s Law is that enthalpy is a “state function.” This means the change in enthalpy for a chemical reaction depends only on the chemical identities and physical states of the starting materials and the final products. The total energy change is independent of the specific path or the number of intermediate steps taken to get from the initial state to the final state.
To visualize this concept, consider the change in elevation when climbing a mountain. The total altitude gained from the base to the summit is a fixed value, regardless of the trail you choose. Whether you take a steep, direct path or a winding, multi-stage route, the vertical distance covered remains the same.
In chemical terms, the reactants represent the base and the products represent the summit. Therefore, if a reaction can be broken down into a series of steps, the sum of the enthalpy changes for those individual steps will exactly equal the enthalpy change for the single-step overall reaction. This additive property is a direct consequence of the conservation of energy.
This principle allows chemists to calculate the \(\Delta H\) for a target reaction by algebraically combining the \(\Delta H\) values of other reactions whose energy changes have been previously measured. The law provides a mathematical framework for constructing a theoretical pathway when a direct experimental path is unavailable.
Rules for Manipulating Chemical Equations
Applying Hess’s Law involves manipulating and combining known thermochemical equations to match the desired overall reaction. Specific rules govern how these manipulations affect the associated enthalpy values.
Reversing Equations
If a reaction is written in the reverse direction, the sign of its enthalpy change must also be reversed. For example, if the formation of a compound is an exothermic process (\(\Delta H\) is negative), the reverse reaction—the decomposition of that compound—must be an endothermic process (\(\Delta H\) is positive). This sign change reflects that the energy absorbed in one direction must be released in the other to maintain the total energy balance.
Scaling Coefficients
Enthalpy is an extensive property, meaning it depends on the quantity of matter. If all coefficients in an equation are multiplied by a factor, the \(\Delta H\) value must also be multiplied by that same factor. This proportional relationship ensures that the enthalpy change correctly reflects the total energy transfer for the new stoichiometric amounts.
Once the individual reactions are manipulated to contain the correct chemical species on the correct sides of the equation, they are added together algebraically. Any species that appear identically on both the reactant side of one equation and the product side of another are considered intermediates and are cancelled out.
The goal of this algebraic combination is to ensure that only the reactants and products of the target reaction remain. The final step is to sum the enthalpy changes of all the manipulated equations to determine the \(\Delta H\) for the net reaction.
Utility in Thermochemistry
The primary utility of Hess’s Law lies in its ability to calculate the heat of reaction for processes that cannot be measured directly in a laboratory. Some reactions proceed too slowly to measure accurately, while others occur too quickly or violently, making calorimetry—the direct measurement of heat—impractical or even dangerous.
For example, the formation of carbon monoxide from solid carbon and oxygen is difficult to measure directly because the reaction almost always produces some carbon dioxide as a side product. By using Hess’s Law, the \(\Delta H\) for carbon monoxide formation can be calculated indirectly using the easily measured enthalpy changes for the combustion of carbon to carbon dioxide and the combustion of carbon monoxide to carbon dioxide.
This law is also fundamental in creating tables of standard enthalpies of formation (\(\Delta H_f\)). The standard enthalpy of formation is the heat change when one mole of a compound is formed from its elements in their most stable states. Since many compounds are not formed directly from their elements, their \(\Delta H_f\) values are computed using Hess’s Law. The compiled \(\Delta H_f\) data then serve as essential building blocks for predicting the energy change of virtually any other chemical reaction.