The standard enthalpy of formation, symbolized as \(\Delta H_f^\circ\), is a fundamental concept in thermochemistry that quantifies the energy change involved in creating a chemical compound. This value represents the heat absorbed or released when exactly one mole of a substance is produced from its constituent elements in their most stable forms. Knowing the standard enthalpy of formation for various compounds is crucial for predicting the overall energy balance of any chemical reaction. Calculations using this enthalpy allow chemists and engineers to determine if a process will release heat (exothermic) or absorb heat (endothermic).
Establishing the Standard Thermodynamic Baseline
The superscript “\(\circ\)” in the symbol \(\Delta H_f^\circ\) signifies that the value is measured under specific reference conditions known as the standard state. This state is defined by a pressure of 1 bar and a specified temperature, most often 298.15 K (\(25^\circ \text{C}\)). The physical state of the substance—solid, liquid, or gas—must correspond to its most stable form under these conditions.
The foundation for all calculations involving this thermodynamic property is the establishment of a zero point for the energy scale. By convention, the standard enthalpy of formation for any element in its most stable physical state under standard conditions is defined as exactly zero kilojoules per mole (\(0 \text{ kJ/mol}\)). For instance, the standard state for oxygen is diatomic gas, \(\text{O}_2(\text{g})\), and for carbon it is graphite, \(\text{C}(\text{graphite})\). This zero-point reference means that any energy change associated with forming these elements from themselves is zero. This convention allows all compound formation enthalpies to be measured relative to the stability of the pure elements.
Calculating Formation Enthalpy via Hess’s Law
One method for determining an unknown \(\Delta H_f^\circ\) is by applying Hess’s Law of Constant Heat Summation. This law states that the total enthalpy change for a chemical process is the same, regardless of the number of steps taken to complete the reaction. This principle is utilized when the direct formation reaction of a compound from its elements is difficult or impossible to measure experimentally.
The process begins by writing the target formation reaction, ensuring that exactly one mole of the desired product is formed from its elements in their standard states. For example, to find the \(\Delta H_f^\circ\) for carbon monoxide, \(\text{CO}(\text{g})\), the target reaction is \(\text{C}(\text{graphite}) + \frac{1}{2}\text{O}_2(\text{g}) \rightarrow \text{CO}(\text{g})\). Next, a series of known reactions, whose enthalpy changes (\(\Delta H\)) have been measured, are identified that can be arithmetically combined to yield the target reaction.
These known reactions must be manipulated to align with the target equation. If a reaction is reversed, the sign of its \(\Delta H\) value must also be reversed. Similarly, if the coefficients of a reaction are multiplied by a factor, the \(\Delta H\) value must be multiplied by the same factor.
For instance, to calculate the \(\Delta H_f^\circ\) for carbon monoxide, one might use the known combustion of carbon to carbon dioxide (\(\Delta H_1\)) and the combustion of carbon monoxide to carbon dioxide (\(\Delta H_2\)). The first reaction is \(\text{C}(\text{graphite}) + \text{O}_2(\text{g}) \rightarrow \text{CO}_2(\text{g})\). The second reaction is \(\text{CO}(\text{g}) + \frac{1}{2}\text{O}_2(\text{g}) \rightarrow \text{CO}_2(\text{g})\). By reversing the second reaction (changing \(\Delta H_2\) to \(-\Delta H_2\)) and summing the two modified equations, the unwanted \(\text{CO}_2(\text{g})\) cancels out. The sum of the manipulated \(\Delta H\) values then directly yields the standard enthalpy of formation for the target compound, \(\Delta H_f^\circ(\text{CO})\).
Calculating Formation Enthalpy from Experimental Reaction Enthalpies
The standard enthalpy of formation for a substance can also be calculated indirectly if it is a participant in a measurable reaction, such as a combustion or neutralization reaction. This method uses the relationship between the enthalpy of a reaction and the standard enthalpies of formation of all the species involved.
The fundamental equation for the standard enthalpy of reaction, \(\Delta H_{rxn}^\circ\), is expressed as the sum of the formation enthalpies of the products minus the sum of the formation enthalpies of the reactants. Mathematically, this relationship is written as:
\(\Delta H_{rxn}^\circ = \sum n \Delta H_f^\circ\text{(products)} – \sum m \Delta H_f^\circ\text{(reactants)}\)
where \(n\) and \(m\) are the stoichiometric coefficients from the balanced chemical equation. This equation is particularly useful when the \(\Delta H_{rxn}^\circ\) is determined through calorimetry, and the \(\Delta H_f^\circ\) values for all other components are available from reference tables.
To isolate the unknown formation enthalpy of a single compound, the equation is simply rearranged algebraically. Consider a combustion reaction where a fuel, like propane (\(\text{C}_3\text{H}_8\)), is burned, and its overall reaction enthalpy is measured. The reaction \(\text{C}_3\text{H}_8(\text{g}) + 5\text{O}_2(\text{g}) \rightarrow 3\text{CO}_2(\text{g}) + 4\text{H}_2\text{O}(\text{l})\) involves four species. Since \(\text{O}_2(\text{g})\) is an element in its standard state, its \(\Delta H_f^\circ\) is zero. The formation enthalpies for the products, \(\text{CO}_2(\text{g})\) and \(\text{H}_2\text{O}(\text{l})\), are known from tables. The measured \(\Delta H_{rxn}^\circ\) for the combustion is substituted into the equation, along with the known tabulated values. The equation is then solved for the one remaining unknown, \(\Delta H_f^\circ(\text{C}_3\text{H}_8)\), which provides the standard enthalpy of formation for the propane.