Enthalpy, symbolized as \(\Delta H\), is a thermodynamic property representing the heat absorbed or released during a chemical reaction when the pressure remains constant. \(\Delta H\) quantifies this energy change. Understanding the enthalpy of a reaction is fundamental for predicting its energetic outcome.
A reaction’s \(\Delta H\) value indicates whether the process is endothermic or exothermic. A negative \(\Delta H\) means the system releases heat into the surroundings, classifying the reaction as exothermic. Conversely, a positive \(\Delta H\) signifies that the reaction absorbs heat from the surroundings, making it an endothermic process. Since enthalpy is a state function, its value depends only on the initial and final states of the system, which allows for calculation using various methods.
Calculating Enthalpy Using Standard Formation Data
A theoretical method for determining the enthalpy change of a reaction involves using the standard enthalpy of formation, denoted as \(\Delta H_f^\circ\). This value is the heat change when one mole of a compound is created from its constituent elements in their most stable forms under standard conditions (1 atmosphere and typically 25°C). Elements in their most stable form, such as \(\text{O}_2(g)\), have a \(\Delta H_f^\circ\) value of zero.
The general formula for calculating the standard enthalpy of a reaction (\(\Delta H_{rxn}^\circ\)) is to sum the standard enthalpies of formation of the products and subtract the sum of the standard enthalpies of formation of the reactants. The relationship 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 stoichiometric coefficients from the balanced chemical equation.
For example, to find the \(\Delta H_{rxn}^\circ\) for the combustion of methane, \(\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l)\), we use the tabulated \(\Delta H_f^\circ\) values for each compound. The formation enthalpy for each substance is multiplied by its coefficient in the balanced equation before the subtraction is performed. This method is precise because it uses experimentally measured and tabulated values.
Calculating Enthalpy Using Bond Energies
An alternative approach estimates the enthalpy change by considering the energy required to break and form chemical bonds. This method uses average bond energies, which are the energy needed to break one mole of a specific type of bond in the gaseous state. Breaking bonds always requires an input of energy, making the process endothermic (\(\Delta H\) positive). Conversely, forming new bonds releases energy (exothermic, \(\Delta H\) negative).
The equation for this approximation is: \(\Delta H_{rxn} = \sum \text{(Energy used to break bonds)} – \sum \text{(Energy released when forming bonds)}\). Drawing the Lewis structures is an initial step to correctly count the total number of each type of bond present.
For example, in the reaction \(\text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2\text{HCl}(g)\), one \(\text{H-H}\) bond and one \(\text{Cl-Cl}\) bond are broken, while two \(\text{H-Cl}\) bonds are formed. This method is inherently less precise than using standard formation data because the bond energies used are averages and do not account for the specific molecular environment.
The average bond energy method is most accurate for reactions that occur entirely in the gaseous phase. However, it is a valuable tool for reactions where the standard enthalpy of formation data is unavailable or for quickly estimating the reaction enthalpy.
Using Hess’s Law Principles
Hess’s Law of Constant Heat Summation provides a powerful way to calculate the enthalpy change for a reaction that is difficult or impossible to measure directly. The law states that the total enthalpy change for a chemical reaction is constant, regardless of the number of steps or the path taken from the initial reactants to the final products. This is a direct consequence of enthalpy being a state function.
To apply Hess’s Law, one must treat a target chemical equation as the sum of several known reactions with established \(\Delta H\) values. The known reactions must be algebraically manipulated so that when they are added together, they yield the target equation. Two primary rules govern this manipulation:
- If a reaction is reversed, the sign of its \(\Delta H\) value must also be reversed. A reaction that was exothermic becomes endothermic, and vice versa.
- If the stoichiometric coefficients of a reaction are multiplied by a factor, the \(\Delta H\) value for that reaction must also be multiplied by the exact same factor. This is because enthalpy is an extensive property.
After manipulating the component reactions, all the equations are summed, and intermediate species that appear on both the reactant and product sides are canceled out. The \(\Delta H\) values of the manipulated equations are then added together to find the \(\Delta H\) for the overall target reaction. This technique allows chemists to determine the enthalpy of complex reactions by using a series of simpler, measurable steps.
Determining Enthalpy Through Calorimetry
Calorimetry is an experimental technique used to measure the heat transfer during a reaction, unlike theoretical methods that rely on tabulated data. Calorimetry involves using a device called a calorimeter, which is designed to be thermally isolated from the surroundings.
The underlying principle is that the heat released or absorbed by the chemical reaction causes a measurable change in the temperature of the surrounding material, often water. This heat flow, represented by \(q\), is calculated using the equation \(q = mc\Delta T\). In this formula, \(m\) is the mass of the substance that absorbs the heat, \(c\) is the specific heat capacity of that substance, and \(\Delta T\) is the observed change in temperature.
The heat measured, \(q\), is equal in magnitude but opposite in sign to the heat change of the reaction, assuming no heat is lost to the calorimeter or the environment. Since the reaction occurs at constant atmospheric pressure in an open calorimeter, the measured heat flow (\(q\)) is numerically equal to the enthalpy change (\(\Delta H\)) for the reaction. If the temperature of the water increases (\(\Delta T\) is positive), the reaction released heat, so \(\Delta H\) is negative (exothermic).
To find the standard molar enthalpy change, the calculated heat \(q\) is divided by the number of moles of the limiting reactant that participated in the experiment. This provides the enthalpy in units such as kilojoules per mole (\(\text{kJ/mol}\)). Calorimetry is a practical method that offers a direct, real-world measurement of the energy associated with a chemical process.