Hess's law

Hess's law of constant heat summation is a fundamental principle in physical chemistry and thermodynamics. It describes how energy moves during chemical reactions. Specifically, the law focuses on enthalpy, which is the total heat content within a system. The law states that the total enthalpy change during a complete chemical reaction is independent of the sequence of steps taken. This means the total energy change remains the same regardless of the specific path the reaction follows. This principle is essential because it allows scientists to calculate energy changes that are difficult to measure directly.

To understand the mechanism, one must view enthalpy as a state function. A state function is a property that depends only on the initial and final states of a system. It does not matter how the system moved from the start to the end. In a chemical reaction, the enthalpy change is denoted as ΔH. If a reaction occurs at constant pressure, this change equals the heat absorbed or released. If the net enthalpy change is negative, the reaction is exothermic, meaning it releases heat. If the value is positive, the reaction is endothermic, meaning it absorbs heat.

Scientists use algebraic operations to apply Hess's law to complex reactions. They do this by combining several basic chemical equations to reach a net equation. If the enthalpy changes for each individual step are known, they can be summed together. The sum of these individual steps will equal the enthalpy change for the overall reaction. This process relies on the standard enthalpies of formation. These are the energy changes involved when elements form specific compounds in their standard states. By adding or subtracting these values, chemists can predict the energy needed for complex synthesis.

Germain Hess was the chemist who discovered this principle. He was a Swiss-born Russian chemist and physician. He published his findings in 1840. His work provided a way to uphold the first law of thermodynamics. This law states that energy cannot be created or destroyed. If the total enthalpy changed based on the path taken, it would violate this law. Hess proved that the energy change is tied only to the reactants and the products.

One practical example involves the reaction of carbon and oxygen. One can measure the direct step of graphite and oxygen reacting to form carbon dioxide (CO2). This reaction has a ΔH of −393.5 kJ/mol. Alternatively, the reaction can happen in two smaller steps. First, graphite reacts with oxygen to form carbon monoxide (CO). This step has a ΔH of −110.5 kJ/mol. Second, the carbon monoxide reacts with more oxygen to form carbon dioxide. This second step has a ΔH of −283.0 kJ/mol. When you add these two steps together, the total is −393.5 kJ/mol. This matches the direct measurement exactly.

Another example uses boron and hydrogen to find specific values. Scientists can use known reactions involving boron trioxide (B2O3) and water (H2O) to find the enthalpy of formation for diborane (B2H6). By multiplying equations by appropriate factors and reversing their directions, they can cancel out common terms. For instance, they might use the reaction of boron and hydrogen to reach a specific product. This mathematical approach allows them to find the ΔfH for reactions that are otherwise inaccessible. This demonstrates how enthalpy changes are additive across different chemical routes.

Beyond simple heat, Hess's law can be expanded to other thermodynamic properties. Concepts like entropy and Gibbs free energy are also state functions. This means they follow similar rules regarding the path taken. An example of this extension is the Bordwell thermodynamic cycle. This cycle uses measured equilibria and redox potentials to find Gibbs free energy values. By combining these values with enthalpy data from Hess's law, scientists can calculate entropy. This is helpful when entropy has not been measured directly in a laboratory setting.

Today, Hess's law remains a vital tool for many scientific applications. It is used to determine the heats of formation for unstable intermediates. Examples include gases like carbon monoxide (CO) or nitric oxide (NO). It also helps scientists understand heat changes during phase transitions. These are changes in the state of matter, such as melting or boiling. Additionally, it is used to calculate lattice energies in ionic substances. This is often done through a Born–Haber cycle. These applications connect the law to broader studies in thermochemistry and molecular structure.