Enthalpy (\(H\)) describes the heat content of a system. When chemical processes occur, the change in heat content is known as the enthalpy change (\(\Delta H\)). The standard enthalpy of formation, symbolized as \(\Delta H_f^\circ\), is a specific type of enthalpy change used to measure and compare the energy stored in chemical compounds. This value represents the heat absorbed or released when exactly one mole of a substance is created from its basic, constituent elements under standardized conditions. The elements must begin in their most stable physical state to ensure the resulting \(\Delta H_f^\circ\) is consistent. Standard enthalpy of formation is typically reported in units of kilojoules per mole (kJ/mol).
Defining Standard Conditions and Reference States
To ensure consistent measurements, the standard state defines uniform conditions. This state specifies a pressure of exactly one bar (approximately one atmosphere) and a concentration of 1 M for dissolved substances. Although temperature is not strictly defined, thermodynamic tables commonly use 298 K (25°C) to tabulate standard enthalpy values. The degree symbol (°) appended to the enthalpy symbol (\(\Delta H\)) indicates measurement under these standard conditions.
The basis for all formation enthalpy calculations is a fundamental reference point: the most stable form of an element in its standard state is assigned a standard enthalpy of formation of zero. For example, the reference state for oxygen is gaseous molecular oxygen (O2(g)), and for carbon, it is solid graphite (C(s)). This means the \(\Delta H_f^\circ\) for these forms is set to 0 kJ/mol. This convention allows the calculation of the relative energy content of compounds and is applied to all elements, such as hydrogen (H2(g)) and nitrogen (N2(g)).
Calculation Method 1: Using Reaction Summation (Hess’s Law)
Hess’s Law is a powerful technique for calculating the standard enthalpy of formation, especially for compounds that cannot be synthesized directly. This law states that because enthalpy is a state function, the total enthalpy change for a reaction is the same regardless of the path taken. This principle allows a complex formation reaction to be treated as the sum of several simpler reactions with known enthalpy changes. By algebraically combining these known reactions, the enthalpy of the target formation reaction can be derived.
The method involves manipulating known chemical equations and their corresponding enthalpy values until they sum to the desired formation equation. If a known reaction is reversed, the sign of its enthalpy change (\(\Delta H\)) must also be reversed. If the coefficients of a reaction are multiplied by a factor, its \(\Delta H\) value must be multiplied by the same factor.
For example, to find the \(\Delta H_f^\circ\) for methane (CH4), one uses the known combustion enthalpies of carbon, hydrogen, and methane. The known equations are adjusted so that intermediate substances cancel out, leaving the target formation reaction: C(s) + 2H2(g) → CH4(g). The sum of the adjusted \(\Delta H\) values of the intermediate steps yields the \(\Delta H_f^\circ\) for methane. This technique is useful when the direct synthesis of a compound is difficult to measure accurately.
Calculation Method 2: Isolating Unknown Values from Known Reaction Enthalpies
The most common algebraic approach relies on the relationship between the overall standard enthalpy of reaction (\(\Delta H_{rxn}^\circ\)) and the formation enthalpies of its components. \(\Delta H_{rxn}^\circ\) is calculated using the formation enthalpies of all products and reactants. This relationship is mathematically expressed as the sum of the formation enthalpies of the products minus the sum of the formation enthalpies of the reactants. Each value must be multiplied by its respective stoichiometric coefficient from the balanced equation.
The general formula is \(\Delta H_{rxn}^\circ = \sum n \Delta H_f^\circ (\text{products}) – \sum m \Delta H_f^\circ (\text{reactants})\), where \(n\) and \(m\) are the molar coefficients. This formula can be rearranged to solve for a single unknown \(\Delta H_f^\circ\) value if the overall \(\Delta H_{rxn}^\circ\) and the formation enthalpies for every other substance are known. This method uses a single algebraic equation, distinguishing it from the reaction summation technique.
For example, if the standard enthalpy of combustion for propane (C3H8) is measured, and the \(\Delta H_f^\circ\) values for carbon dioxide (CO2) and water (H2O) are known, the formation enthalpy of propane can be found. Since the formation enthalpy of oxygen (O2) is zero by definition, the only unknown remaining is the \(\Delta H_f^\circ\) of propane. By plugging in the known values and the measured \(\Delta H_{rxn}^\circ\), the equation is algebraically solved for the unknown compound.