Hess's Law
Enthalpy is a state function
Understanding Hess's Law
Hess's Law, formulated by Swiss-Russian chemist Germain Hess in 1840, states that the total enthalpy change of a chemical reaction is independent of the pathway taken from reactants to products. This fundamental principle in thermochemistry is based on the first law of thermodynamics and the fact that enthalpy is a state function. Whether a reaction occurs in one step or multiple steps, the net enthalpy change remains constant, making it possible to calculate reaction enthalpies that cannot be measured directly in the laboratory.
The mathematical foundation of Hess's Law allows chemists to determine enthalpies of formation for unstable intermediates, combustion reactions, and other processes that are difficult to measure experimentally. By manipulating known thermochemical equations—reversing reactions, multiplying by coefficients, and adding equations algebraically—we can construct thermochemical cycles that reveal the energy changes in complex reaction mechanisms. This approach has been instrumental in developing standard enthalpy tables and understanding energy relationships in chemical processes.
The practical applications of Hess's Law extend across industrial chemistry, biochemistry, and environmental science. Engineers use it to predict heat requirements in manufacturing processes, biochemists apply it to understand metabolic pathways, and environmental scientists employ it to calculate energy balances in atmospheric reactions. The law's power lies in its ability to break down complex reactions into manageable steps, making thermochemical calculations accessible and predictable.
The Formula
ΔHtotal = ΔH₁ + ΔH₂ + ΔH₃ + ...
The total enthalpy change is independent of pathway; sum intermediate steps to find overall ΔH.
Manipulation Rules:
- If a reaction is reversed, the sign of ΔH changes
- If a reaction is multiplied by a factor, multiply ΔH by the same factor
- Species appearing on both sides cancel when equations are added
Step-by-Step Example
Problem: Calculate ΔH for the formation of carbon monoxide: C(s) + ½O₂(g) → CO(g)
Given thermochemical equations:
(1) C(s) + O₂(g) → CO₂(g); ΔH₁ = -393.5 kJ
(2) CO(g) + ½O₂(g) → CO₂(g); ΔH₂ = -283.0 kJ
Step 1: Identify Target Equation
We need C(s) on the reactant side and CO(g) on the product side. Analyze which given equations contain these species.
Step 2: Manipulate Equations
Equation (1) already has C(s) as a reactant, so keep it as is.
Equation (2) has CO(g) as a reactant, but we need it as a product. Reverse equation (2):
CO₂(g) → CO(g) + ½O₂(g); ΔH = +283.0 kJ (sign changed)
Step 3: Add Equations
C(s) + O₂(g) → CO₂(g); ΔH = -393.5 kJ
CO₂(g) → CO(g) + ½O₂(g); ΔH = +283.0 kJ
Net: C(s) + ½O₂(g) → CO(g)
(CO₂ cancels; O₂ - ½O₂ = ½O₂)
Step 4: Calculate Total ΔH
ΔHtotal = -393.5 + 283.0 = -110.5 kJ
Answer: ΔH = -110.5 kJ
The negative value indicates this is an exothermic reaction.
Key Applications
1. Standard Enthalpies of Formation
Hess's Law enables calculation of standard enthalpies of formation (ΔH°f) for compounds that cannot be synthesized directly from elements. By combining combustion data and known formation enthalpies, chemists construct cycles to determine these values accurately.
2. Born-Haber Cycles
In ionic compound formation, Hess's Law underpins Born-Haber cycles, which calculate lattice energies by combining sublimation, ionization, electron affinity, and formation enthalpies. This application is crucial for understanding ionic bonding energetics.
3. Biochemical Pathways
Metabolic processes involve multiple enzyme-catalyzed steps. Hess's Law allows biochemists to calculate the overall energy change of complex pathways like glycolysis or the citric acid cycle by summing individual reaction enthalpies, regardless of intermediate steps.
4. Industrial Process Design
Chemical engineers apply Hess's Law to optimize reaction conditions in industrial processes. By analyzing alternative reaction pathways, they can select the most energy-efficient routes for large-scale production, reducing costs and environmental impact.
Thermochemical Data Comparison
| Reaction Type | Example | ΔH (kJ/mol) |
|---|---|---|
| Combustion of C | C(s) + O₂(g) → CO₂(g) | -393.5 |
| Combustion of CO | CO(g) + ½O₂(g) → CO₂(g) | -283.0 |
| Formation of CO | C(s) + ½O₂(g) → CO(g) | -110.5 |
| Formation of H₂O(l) | H₂(g) + ½O₂(g) → H₂O(l) | -285.8 |
| Formation of NH₃(g) | ½N₂(g) + 3/2H₂(g) → NH₃(g) | -46.1 |
Common Mistakes to Avoid
Mistake 1: Forgetting to Change Sign When Reversing
When you reverse a reaction, you must change the sign of ΔH. If ΔH = -283.0 kJ forward, then ΔH = +283.0 kJ reversed.
Mistake 2: Not Balancing Coefficients Properly
If you multiply a reaction by a coefficient to match stoichiometry, you must multiply the entire ΔH value by the same factor. Doubling a reaction doubles its enthalpy change.
Mistake 3: Incorrect Unit Conversion
Ensure all ΔH values are in the same units (kJ or kJ/mol) before adding. Mixing units leads to incorrect results.
Mistake 4: Forgetting to Cancel Species
When adding equations, species appearing on both sides must cancel. Verify that your final equation contains only the target reactants and products.
Important Tips:
- Draw an enthalpy diagram to visualize the pathway.
- Double-check that your final equation matches the target reaction exactly.
- Keep track of physical states (s, l, g, aq) as they affect enthalpy values.
- Work systematically: identify target, manipulate equations, then add.
Tips
- Reverse a reaction: change sign of ΔH.
- Multiply reaction by factor: multiply ΔH by same factor.
- Cancel species appearing on both sides when summing.