Thermochemistry and Hess's Law
Thermochemistry studies the heat absorbed or released during chemical reactions and physical transformations. At its core lies the concept of enthalpy and the principle that energy is conserved, allowing chemists to calculate heat changes for reactions that are difficult or impossible to measure directly. Hess's law is the central tool for these indirect calculations.
Enthalpy: The Heat of Reaction
Enthalpy (H) is a thermodynamic quantity that represents the total heat content of a system at constant pressure. Chemists rarely measure absolute enthalpy; instead, they measure the enthalpy change (ΔH) during a process — the difference between the enthalpy of products and reactants:
ΔH = H(products) − H(reactants)
A negative ΔH indicates an exothermic reaction — the system releases heat to the surroundings. Combustion reactions are classic examples: burning methane releases 890 kJ/mol. A positive ΔH indicates an endothermic reaction — the system absorbs heat. Photosynthesis, which uses sunlight to convert carbon dioxide and water into glucose, is endothermic.
State Functions and Path Independence
Enthalpy is a state function, meaning its value depends only on the current state of the system (temperature, pressure, composition), not on the path taken to reach that state. Whether you climb a mountain by the steep trail or the gentle switchback, the altitude change is the same.
This property is what makes Hess's law possible. If a reaction can proceed by two different routes — directly or through a series of intermediate steps — the total enthalpy change is identical regardless of the route.
Hess's Law
Hess's law states: The total enthalpy change for a reaction is the sum of the enthalpy changes for each step in the process, regardless of the pathway.
This allows chemists to calculate ΔH for a target reaction by combining known reactions algebraically. If you can add, subtract, or reverse known thermochemical equations to arrive at the desired equation, the corresponding ΔH values are combined the same way.
Worked Example: Formation Enthalpy Approach
Calculate ΔH for the reaction:
C₂H₄(g) + H₂(g) → C₂H₆(g)
Using standard enthalpies of formation (ΔH_f°):
- ΔH_f°[C₂H₄(g)] = +52.3 kJ/mol
- ΔH_f°[H₂(g)] = 0 kJ/mol (element in standard state)
- ΔH_f°[C₂H₆(g)] = −84.7 kJ/mol
Apply the general formula:
ΔH°_rxn = Σ ΔH_f°(products) − Σ ΔH_f°(reactants)
ΔH°_rxn = (−84.7) − (52.3 + 0) = −137.0 kJ/mol
The reaction is exothermic, releasing 137.0 kJ per mole of ethane formed. This approach works because the enthalpy of formation defines a common reference point: all elements in their standard states have ΔH_f° = 0.
The Step-by-Step Approach
Alternatively, suppose you know these two reactions:
(1) C₂H₄(g) + 3 O₂(g) → 2 CO₂(g) + 2 H₂O(l) ΔH₁ = −1411 kJ
(2) C₂H₆(g) + 7/2 O₂(g) → 2 CO₂(g) + 3 H₂O(l) ΔH₂ = −1560 kJ
(3) H₂(g) + 1/2 O₂(g) → H₂O(l) ΔH₃ = −286 kJ
To obtain C₂H₄ + H₂ → C₂H₆, use reaction (1) forward, reaction (2) reversed, and reaction (3) forward:
ΔH = ΔH₁ + (−ΔH₂) + ΔH₃ = (−1411) + (+1560) + (−286) = −137 kJ
The same answer confirms the path independence of enthalpy.
Bond Dissociation Energy Approach
A third method estimates ΔH by considering the energy required to break all bonds in the reactants and the energy released when forming all bonds in the products:
ΔH ≈ Σ (bonds broken) − Σ (bonds formed)
Breaking bonds is endothermic (positive), and forming bonds is exothermic (negative). If more energy is released in bond formation than consumed in bond breaking, the reaction is exothermic overall.
This approach gives approximate values because tabulated bond energies are averages over many different molecular environments. For precise work, formation enthalpies or direct calorimetric measurements are preferred.
Calorimetry: Measuring Heat Directly
When direct measurement is possible, chemists use calorimeters to quantify heat changes. A coffee-cup calorimeter (constant pressure) measures ΔH for reactions in solution. A bomb calorimeter (constant volume) measures the heat of combustion. The relationship between heat and temperature change is:
q = m × c × ΔT
where m is mass, c is specific heat capacity, and ΔT is the temperature change. For bomb calorimetry at constant volume, the measured quantity is ΔU (internal energy change), which differs slightly from ΔH by a PΔV term — usually small for reactions involving condensed phases.
Practical Applications
Hess's law is indispensable in chemistry and engineering. It allows calculation of reaction enthalpies for processes that are too slow, too dangerous, or too complex to measure directly. Nutritional scientists use Hess's law with combustion data to determine the caloric content of foods. Materials scientists use it to evaluate the thermodynamic stability of new compounds. Chemical engineers apply it to design industrial processes that optimize energy efficiency by coupling exothermic and endothermic steps.