The First Law of Thermodynamics and Energy Conservation
Thermochemistry is fundamentally an application of the first law of thermodynamics, which states that energy cannot be created or destroyed, only converted from one form to another. The total energy of the universe is constant. In chemical reactions, this principle governs the flow of energy. The internal energy (U) of a system is the sum of all kinetic and potential energies of all particles within the system. The change in internal energy (ΔU) for a process is given by the equation: ΔU = q + w, where q is the heat transferred to the system, and w is the work done on the system. This sign convention is crucial: heat added to the system and work done on the system (e.g., compression) are positive, increasing the system’s internal energy. Heat released by the system and work done by the system (e.g., expansion) are negative, decreasing its internal energy. For reactions at constant volume, no pressure-volume work (PΔV work) is done, so ΔU = q_v, where q_v is the heat transferred at constant volume, typically measured using a bomb calorimeter. However, most chemical reactions occur open to the atmosphere at constant pressure, not constant volume, necessitating a more useful state function: enthalpy.
Enthalpy: The Heat of Reaction at Constant Pressure
Enthalpy (H) is a state function defined for convenience in dealing with constant-pressure processes. It is defined as H = U + PV. The change in enthalpy (ΔH) for a process is given by ΔH = ΔU + Δ(PV). At constant pressure, this simplifies to ΔH = ΔU + PΔV. Substituting the first law (ΔU = q_p + w, where w = -PΔV for pressure-volume work), we get ΔH = (q_p – PΔV) + PΔV = q_p. Therefore, the change in enthalpy is equal to the heat transferred at constant pressure (q_p). This makes enthalpy the central concept in thermochemistry. For a chemical reaction, the enthalpy change is called the heat of reaction. A negative ΔH (q_p 0) indicates an endothermic reaction where heat is absorbed from the surroundings (e.g., photosynthesis). Enthalpy is an extensive property, meaning its value depends on the amount of substance. Consequently, the magnitude of ΔH is directly proportional to the amount of reactant consumed, and its units are typically kilojoules per mole (kJ/mol) of reaction as written.
Calorimetry: Measuring Heat Flow
Calorimetry is the experimental technique used to measure the heat transferred during a chemical or physical process. A calorimeter is an insulated device that prevents heat exchange with the surroundings, allowing for the accurate measurement of heat flow. There are two primary types: constant-pressure and constant-volume calorimeters. A coffee-cup calorimeter is a simple constant-pressure device used for reactions in solution. The heat released or absorbed by the reaction (q_rxn) is equal in magnitude but opposite in sign to the heat gained or lost by the solution and the calorimeter itself: q_rxn = – (q_solution + q_calorimeter). The heat absorbed is calculated using the equation q = m c ΔT, where m is mass, c is the specific heat capacity (the heat required to raise 1 gram of substance by 1°C), and ΔT is the temperature change. A bomb calorimeter operates at constant volume and is used for combustion reactions. It is a robust, sealed container immersed in water. The heat measured is q_v, which is equal to ΔU. To find the enthalpy change (ΔH) at constant pressure, a small correction is applied: ΔH = ΔU + Δ(PV) ≈ ΔU + Δn_gas * RT, where Δn_gas is the change in the number of moles of gas in the balanced chemical equation, R is the gas constant, and T is the temperature in Kelvin.
Standard States and Standard Enthalpy Changes
To compare enthalpy changes meaningfully, chemists use standard conditions. The standard state of a substance is its most stable form at a pressure of 1 bar and a specified temperature, usually 298.15 K (25°C). The standard enthalpy change (ΔH°) is the enthalpy change when all reactants and products are in their standard states. Several specific types of standard enthalpy changes are defined. The standard enthalpy of formation (ΔH_f°) is the enthalpy change for the reaction that forms one mole of a compound from its constituent elements in their standard states. By definition, the standard enthalpy of formation of an element in its standard state is zero. This concept is foundational because it allows for the calculation of the enthalpy change for any reaction using Hess’s Law. The standard enthalpy of combustion (ΔH_c°) is the enthalpy change when one mole of a substance is completely burned in oxygen under standard conditions. The standard enthalpy of reaction (ΔH_rxn°) is the enthalpy change for a reaction under standard conditions with all substances in their standard states.
Hess’s Law: The Law of Constant Heat Summation
Hess’s Law is a powerful consequence of enthalpy being a state function. It states that the total enthalpy change for a reaction is the same regardless of the number of steps or the path taken. This allows for the calculation of ΔH for reactions that are difficult or impossible to measure directly. To apply Hess’s Law, a series of known chemical equations with their known ΔH values are manipulated (reversed, multiplied by a coefficient) and added together to give the target equation. When an equation is reversed, the sign of ΔH is changed. When an equation is multiplied by a coefficient, its ΔH is multiplied by the same coefficient. The algebraic sum of the ΔH values for the manipulated equations gives the ΔH for the target reaction. For example, the enthalpy of formation of carbon monoxide (C + ½O₂ → CO) is difficult to measure because some carbon dioxide always forms. However, it can be calculated using the known enthalpies of combustion of carbon to CO₂ and CO to CO₂. Hess’s Law provides a practical method for constructing energy cycles and determining unknown enthalpy values from tabulated data.
Standard Enthalpies of Formation and Calculating ΔH_rxn
The most efficient and widely used method for calculating the standard enthalpy change of a reaction (ΔH°_rxn) is through standard enthalpies of formation (ΔH_f°). Because enthalpy is a state function, the enthalpy change for any reaction can be found by considering the enthalpy required to break all reactants into their constituent elements and then the enthalpy released when those elements form the products. The formula derived from this concept is: ΔH°_rxn = Σ n ΔH_f°(products) – Σ m ΔH_f°(reactants), where n and m are the stoichiometric coefficients of the products and reactants, respectively, in the balanced chemical equation. This equation signifies that the standard enthalpy of a 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. Extensive tables of ΔH_f° values are available for thousands of compounds. To use this method correctly, one must ensure that the chemical equation is balanced and that the ΔH_f° values are used with their correct signs and for the correct phases (s, l, g), as the phase significantly affects the value. This approach is universally applicable and simplifies thermochemical calculations immensely.
Bond Enthalpies and Estimating Enthalpy Changes
Bond enthalpy (or bond energy) is the average enthalpy change associated with breaking a specific type of chemical bond in one mole of gaseous molecules. Breaking a bond is always an endothermic process (ΔH > 0), while forming a bond is always exothermic (ΔH < 0). In any chemical reaction, bonds are broken in the reactants and new bonds are formed in the products. Therefore, the overall enthalpy change of the reaction can be estimated as: ΔH°_rxn ≈ Σ (bond enthalpies of bonds broken) – Σ (bond enthalpies of bonds formed). This method provides an estimate because tabulated bond enthalpies are average values derived from many different molecules. For example, the C-H bond energy is an average across methane, ethane, and other hydrocarbons. This method is particularly useful for reactions involving gaseous molecules where bond dissociation is the primary energy consideration. It offers a way to approximate ΔH_rxn when experimental or formation data is unavailable and provides a conceptual link between the macroscopic property of enthalpy and the microscopic process of breaking and forming chemical bonds.
The Difference Between ΔH and ΔU
While enthalpy (H) is the preferred function for constant-pressure processes, the relationship between ΔH and the change in internal energy (ΔU) is important. The two are related by the equation ΔH = ΔU + PΔV. For reactions involving only solids and liquids, the Δ(PV) term is very small, so ΔH ≈ ΔU. However, for reactions involving gases, the volume change can be significant. The ideal gas law allows for a simplification: at constant temperature, Δ(PV) = Δ(nRT) = RTΔn_gas. Therefore, ΔH = ΔU + RTΔn_gas, where Δn_gas is the change in the number of moles of gas (moles of gaseous products – moles of gaseous reactants). For the combustion of hydrogen (2H₂(g) + O₂(g) → 2H₂O(l)), Δn_gas = 0 – 3 = -3. The negative value indicates a large decrease in the number of gas moles, meaning the work done by the system (PΔV) is negative (work is done on the system by the atmosphere), causing |ΔH| to be less than |ΔU| for this exothermic reaction. Understanding this distinction is crucial for interpreting calorimetric data and connecting constant-volume and constant-pressure measurements.
State Functions and Path Independence
The concepts of internal energy (U) and enthalpy (H) are state functions. A state function is a property whose value depends only on the current state of the system (e.g., temperature, pressure, volume, composition) and not on the path taken to reach that state. Altitude is a classic analogy: the difference in altitude between the base and summit of a mountain is fixed, regardless of the path taken to climb it. In thermochemistry, this means that ΔU and ΔH for a reaction are determined solely by the initial and final states of the system. This path independence is the foundational principle behind Hess’s Law. In contrast, heat (q) and work (w) are path functions; their values depend on the specific route taken between the initial and final states. A reaction releasing a certain amount of energy as heat (q_p = ΔH) might do different amounts of work depending on how it is carried out, but the sum q + w will always equal ΔU. Recognizing state functions simplifies thermochemical calculations immensely, as it allows for the construction of hypothetical pathways (like those used with standard enthalpies of formation) to determine energy changes.