The change in enthalpy (\(\Delta H\)) of a chemical reaction is a measurement of the heat absorbed or released during the process under constant pressure. This measurement, often expressed in kilojoules per mole (\(\text{kJ/mol}\)), predicts whether the process will release heat (exothermic) or absorb heat (endothermic). Understanding this energy exchange is relevant across many fields, from optimizing industrial chemical production to predicting the energy yield of fuels.
Calculating Using Standard Enthalpies of Formation
The enthalpy of a reaction (\(\Delta H_{\text{rxn}}\)) can be calculated using tabulated values known as the standard enthalpy of formation (\(\Delta H_f^\circ\)). This value is the heat change that occurs when one mole of a compound is created from its elements in their most stable states under standard conditions, typically \(25^\circ\text{C}\) and \(1\) atmosphere of pressure.
The standard enthalpy of reaction is the sum of the standard enthalpies of formation of the products minus the sum of the standard enthalpies of formation of the reactants. This is represented by the equation \(\Delta H_{\text{rxn}}^\circ = \sum n \Delta H_{f, \text{products}}^\circ – \sum m \Delta H_{f, \text{reactants}}^\circ\), where \(n\) and \(m\) are the stoichiometric coefficients. Elements in their standard state, such as \(\text{O}_2\text{(g)}\) or \(\text{C(graphite)}\), have a standard enthalpy of formation of zero because no energy is required to form them from themselves.
To find the enthalpy of combustion for propane (\(\text{C}_3\text{H}_8\)), one looks up the \(\Delta H_f^\circ\) values for the products (\(\text{CO}_2\text{(g)}\) and \(\text{H}_2\text{O(g)}\)) and the reactant (\(\text{C}_3\text{H}_8\text{(g)}\)). The value for \(\text{O}_2\text{(g)}\) is zero. The final step involves multiplying each compound’s \(\Delta H_f^\circ\) by its coefficient in the balanced equation and then applying the subtraction formula.
Applying Hess’s Law
Hess’s Law provides a method to calculate the enthalpy change of a reaction that cannot be measured directly. Enthalpy is a state function, meaning the total change in enthalpy is independent of the path taken from the initial reactants to the final products. Therefore, if a reaction occurs in multiple steps, the total enthalpy change for the overall process is the sum of the enthalpy changes for the individual steps.
This approach is particularly useful when a reaction is too slow, too fast, or too complex to measure in a single laboratory step. To apply Hess’s Law, one must algebraically manipulate a series of known reactions to match the target reaction. If a known reaction must be reversed to align with the target equation, the sign of its \(\Delta H\) value must also be reversed. For instance, an exothermic reaction becomes endothermic when reversed.
If the stoichiometric coefficients of a known reaction are multiplied by a factor, the corresponding \(\Delta H\) value must also be multiplied by that same factor. After all intermediate equations are manipulated and summed, any species appearing on both the reactant and product sides is canceled out. The sum of the adjusted \(\Delta H\) values for the intermediate steps then yields the final enthalpy for the target reaction.
Estimating Enthalpy Using Bond Energies
When precise tabulated data is unavailable, the enthalpy of a reaction can be estimated using average bond energies. These energies represent the amount of energy required to break a specific bond type in one mole of gaseous molecules. Energy is absorbed to break the bonds in the reactant molecules, and energy is released when new bonds form to create the product molecules.
The enthalpy of reaction (\(\Delta H_{\text{rxn}}\)) is calculated by subtracting the total energy released by forming product bonds from the total energy required to break reactant bonds. This is summarized by the formula: \(\Delta H_{\text{rxn}} = \sum (\text{Energy of bonds broken}) – \sum (\text{Energy of bonds formed})\). Breaking bonds requires energy, so these values are positive inputs. Conversely, the formation of new bonds releases energy, so this term is subtracted.
This calculation provides a reasonable estimate, but it is not perfectly accurate because it relies on average bond energies. The energy of a bond can slightly vary depending on the specific molecule and its surrounding atoms. Therefore, the calculated \(\Delta H\) may deviate from the true value, often by about \(5-10\%\), because the calculation does not account for the exact molecular environment in the reaction.
Determining Enthalpy Through Calorimetry
Calorimetry is the experimental method used to directly measure the heat flow associated with a chemical reaction in a laboratory setting. The apparatus used for this measurement is called a calorimeter. Calorimeters can range from a simple insulated container, like a coffee-cup calorimeter, to a complex, sealed device known as a bomb calorimeter.
The fundamental principle involves allowing the reaction to occur within the calorimeter and measuring the resulting temperature change (\(\Delta T\)) in a surrounding substance, usually water. The heat absorbed or released by the reaction (\(q\)) is calculated using the formula \(q = mc\Delta T\), where \(m\) is the mass of the surrounding substance and \(c\) is its specific heat capacity, which is the heat energy required to raise the temperature of one gram of a substance by one degree Celsius.
Once the heat (\(q\)) is determined, the enthalpy change (\(\Delta H\)) for the reaction is found by dividing the heat transferred by the number of moles of the reactant consumed. If the temperature of the surroundings increases, heat was released by the reaction, indicating an exothermic process with a negative \(\Delta H\). Conversely, a decrease in temperature means the reaction absorbed heat, indicating a positive \(\Delta H\) for the endothermic process.