Enthalpy, symbolized as \(\Delta H\), is a measure of the heat absorbed or released during a chemical reaction or physical process that occurs at a constant pressure. This change in heat content is a fundamental concept in thermochemistry, providing insight into the energy dynamics of a reaction.
A positive \(\Delta H\) indicates an endothermic reaction, meaning the system absorbs heat from its surroundings. Conversely, a negative \(\Delta H\) signifies an exothermic reaction, where heat is released by the system. Calculating \(\Delta H\) is essential for chemists and engineers, as it helps determine the energy requirements and safety considerations for various chemical processes. \(\Delta H\) can be determined through theoretical calculations using tabulated data, manipulating known reaction values, or direct experimental measurement.
Calculating Enthalpy Using Standard Heats of Formation
The standard heat of formation method is a common theoretical approach for determining the enthalpy change of a reaction. This method relies on the principle that enthalpy is a state function, meaning the total change depends only on the initial and final states of the system. This approach requires accessing tabulated data listing the standard heat of formation, denoted as \(\Delta H_f^\circ\), for various compounds.
The standard state is defined as 1 bar (100 kPa) and usually 25 degrees Celsius (298.15 K), with all substances present in their most stable form. The \(\Delta H_f^\circ\) value represents the enthalpy change when one mole of a compound is formed from its constituent elements in these standard states. The standard heat of formation for any element in its most stable form at standard conditions (e.g., \(\text{O}_2\) or solid graphite) is zero by definition.
The overall enthalpy change for a reaction (\(\Delta H_{rxn}^\circ\)) is calculated by subtracting the sum of the standard heats of formation of the reactants from the sum of the products. The general formula is \(\Delta H_{rxn}^\circ = \sum n \Delta H_f^\circ (\text{products}) – \sum m \Delta H_f^\circ (\text{reactants})\). The coefficients \(n\) and \(m\) represent the stoichiometric coefficients from the balanced chemical equation. Since \(\Delta H_f^\circ\) values are typically in kilojoules per mole (\(\text{kJ/mol}\)), multiplying by the stoichiometric coefficient yields the total enthalpy contribution for that species.
Calculating Enthalpy Using Hess’s Law
Hess’s Law of Constant Heat Summation offers a theoretical technique to calculate the enthalpy change for a reaction, especially when direct measurement or formation data is unavailable. Since enthalpy is a state function, the total enthalpy change for a reaction is the same regardless of the pathway taken to convert reactants to products. The method involves treating the target reaction as the sum of several simpler, intermediate reactions whose enthalpy changes are already known. By manipulating these known reactions, the overall reaction can be reconstructed, and the corresponding enthalpy changes are simply summed to find the \(\Delta H\) of the desired reaction.
Two main rules govern the manipulation of the intermediate reactions. First, if a known reaction is reversed to match a component in the target reaction, the sign of its \(\Delta H\) value must also be reversed (e.g., an exothermic reaction becomes endothermic). Second, if an entire reaction, including its stoichiometric coefficients, is multiplied by a certain factor, the associated \(\Delta H\) value must also be multiplied by that exact factor. This is because enthalpy is an extensive property, meaning its value scales directly with the amount of substance involved. By strategically applying these two rules, the intermediate equations can be combined so that all species not present in the final target equation cancel out, leaving the overall desired reaction and its calculated enthalpy change.
Experimental Determination Through Calorimetry
Calorimetry provides the physical method for determining the heat flow of a chemical reaction or process. This technique uses a device called a calorimeter, which is designed to minimize heat exchange with the surroundings, effectively measuring the temperature change that occurs during the reaction. Common laboratory devices range from simple coffee-cup calorimeters, used for reactions in solution, to complex bomb calorimeters for combustion reactions.
The fundamental concept is that the heat released or absorbed by the reaction (\(q_{reaction}\)) is equal in magnitude and opposite in sign to the heat absorbed or released by the calorimeter and its contents (\(q_{solution}\)). This relationship is expressed as \(q_{reaction} = -q_{solution}\).
The heat change of the solution is calculated using the formula \(q = mc\Delta T\). In this equation, \(m\) represents the mass of the substance (often the water or solution in the calorimeter) in grams, and \(c\) is the specific heat capacity, which is the amount of energy required to raise the temperature of one gram of the substance by one degree Celsius. The term \(\Delta T\) is the measured change in temperature, calculated as the final temperature minus the initial temperature.
The measured heat value, \(q\), is typically reported in joules or kilojoules. Since measurements are usually conducted at constant atmospheric pressure, \(q_{reaction}\) is numerically equal to the enthalpy change (\(\Delta H\)) for the specific amount of reactants used. To find the standard \(\Delta H\) in units of kilojoules per mole, the calculated \(q_{reaction}\) value must be divided by the number of moles of the limiting reactant that participated in the experiment.